In a recent article, we mathematically extended conventional discrete-time finite Markov chains, characterized by an $N \times N$ transition probability matrix, to discrete-time finite fuzzy Markov chains capable of modeling fuzzy states and fuzzy events, which frequently arise in fields such as biomedicine. This advancement is built upon the theory of stochastic fuzzy discrete event systems (SFDESs) and the supervised learning algorithm for FDESs, previously published by the authors. The fuzzy Markov chain is represented by a single-event SFDES comprising $N^{2}$ FDES, each with its own occurrence probability and an associated $N \times N$ event transition matrix, which is automatically learned using the aforementioned learning algorithm. Additionally, each FDES is associated with a set of fuzzy sets that fuzzify the random variable values and are required to satisfy specific constraints. Manually designing these fuzzy sets can be challenging, especially for modelers with little or no prior knowledge of fuzzy set theory. To overcome this challenge, we develop stochastic gradient descent-based algorithms that simultaneously learn constrained Gaussian fuzzy sets and the event transition matrices. To reduce the complexity of parameter learning, the Gaussian fuzzy sets are designed such that their means are computed directly from the terminal points of the subintervals that divide the ranges of the random variables, rather than being learned. Furthermore, dependencies between the Gaussian fuzzy sets for each random variable are introduced, reducing the number of standard deviations to be learned to $N$ for all Gaussian fuzzy sets in an FDES, while the remaining standard deviations are computed based on these dependencies. In addition, we establish that these new algorithms are fully applicable to continuous-time finite fuzzy Markov chains, extending their utility to a broader range of applications. An illustrative example is provided to demonstrate the effectiveness of the learning algorithms. These new algorithms make fuzzy Markov chains more accessible to modelers, regardless of their familiarity with fuzzy sets, while enhancing the overall practicality of the approach.

Fuzzy Discrete Event Systems (FDES) extend traditional Discrete Event Systems (DES) by incorporating fuzzy logic to handle uncertainties and vagueness in system states and events. While supervisory control of FDES has been studied before, existing approaches often assume crisp distinctions between safe and unsafe states and do not consider target states. In this paper, we substantially extend the existing results in the literature by developing three new frameworks of supervisory control. First, we introduce a threshold-based safe-state supervisory control framework where fuzzy states are classified as partially safe or unsafe based on a user-defined threshold. Second, we propose a target-seeking supervisory control framework. The framework allows supervisors to select control actions that ensure the supervised system can always reach some target fuzzy states. Third, we propose a threshold-based target-seeking supervisory control framework, where target fuzzy states are subject to user-specified thresholds. For all these frameworks, we derive necessary and sufficient conditions for existence of the supervisors and develop algorithms for calculating them online. The proposed methods enhance the flexibility and applicability of FDES supervisory control, allowing complete or partial fulfillment of control targets while ensuring threshold-based safety and target seeking. This is particularly important in real-world scenarios such as medical treatment planning, where the goal is to maximize treatment effectiveness while minimizing adverse side effects.

The industrial flotation process involves multimodal data and cross-procedural knowledge, presenting significant challenges for knowledge system management and traditional knowledge graph (KG) construction methods. This study develops a large language model (LLM)-driven framework to construct a domain-specific multimodal KG. The Flotation Knowledge Tree ontology is designed as the structural backbone of the KG to organize multi-level operations and interactions while integrating heterogeneous flotation data. To enhance the LLM's domain adaptability, adaptive prompt optimization is proposed to iteratively refine the extraction template with flotation-specific examples and performance feedback, enabling more accurate triple extraction. Additionally, a fuzzy information entropy-driven Retrieval-Augmented Generation (RAG) method is proposed, leveraging fuzzy logic to assign weights to key terms and numerical contexts to preserve causal relationships and semantic integrity under data uncertainty. Furthermore, we established a two-stage LLM-driven pipeline to generate initial triples using a LoRA fine-tuned lightweight LLM with the optimized prompt and fuzzy RAG context, followed by refinement with a large-scale LLM for precision and ontology alignment. Validated triples are mapped onto the Flotation Knowledge Tree to form a structured, high-quality KG with minimal manual intervention. This framework fuses ontology structuring, fuzzy semantic retrieval, and LLM reasoning to enable automated, domain-tailored knowledge assembly for industrial flotation processes. The constructed KG is evaluated using the Flotation Knowledge Tree-based method, achieving a score of 0.92, with a structural score of 0.97 and a semantic score of 0.88, demonstrating robustness and coherence.

Multi-task video classification is a challenging task in video understanding, which is particularly evident in industrial applications. Existing multi-task learning methods enhance task performance by sharing representations of different tasks, which lacks systematic guidance with prior knowledge. In industrial process, abundant prior knowledge is underutilized for video understanding, because the prior knowledge is usually unstructured text which is hard to be embedded for video understanding. To address this limitation, we introduce a novel fuzzy rule graph representation that systematically encodes expert knowledge derived from manual video observations, providing a highly generalized and structured knowledge representation. Correspondingly, a novel multi-channel fuzzy rule graph embedding (MC-FRGE) method is proposed to model relationships among fuzzy rules. Then, a self-supervised two-stream attention autoencoder is constructed for visual feature extraction. Combining the MC-FRGE and the two-stream attention autoencoder, a novel knowledge guided multi-task video classification (KG-MTVC) framework is developed. Finally, experimental results on both the general video understanding dataset HMDB51 and a specialized zinc flotation process video dataset demonstrate the effectiveness of the proposed method. Our implementation is available at https://github.com/Galazxhy/KG-MTVC.git

We introduce a new class of fuzzy discrete event systems (FDESs) called stochastic FDESs (SFDESs), which is significantly different from the probabilistic FDESs (PFDESs) in the literature. It offers an effective modeling framework for applications that are unsuitable for the PFDES framework. An SFDES is comprised of multiple fuzzy automata that occur randomly one at time with different occurrence probabilities. It uses either the max-product fuzzy inference or the max–min fuzzy inference. This article focuses on single-event SFDES—each of the fuzzy automata of such an SFDES has one event. Assuming nothing is known about an SFDES, we develop an innovative technique capable of determining number of fuzzy automata and their event transition matrices as well as estimating their occurrence probabilities. The technique, called prerequired-pre-event-state-based technique, creates and uses merely$N$particular pre-event state vectors of dimension$N$to identify event transition matrices of$M$fuzzy automata, involving a total of$MN^{2}$unknown parameters. One necessary and sufficient condition and three sufficient conditions are established for the identification of SFDES with different settings. The technique does not have any adjustable parameter or hyperparameter to set. A numerical example is provided to concretely illustrate the technique.

We recently introduced a novel category of fuzzy discrete event systems (FDESs) termed stochastic FDESs (SFDESs), wherein multiple fuzzy automata occur randomly with different probabilities. We also developed two techniques for identifying event transition matrices in single-event SFDES employing the max-product fuzzy inference. One of them, named the equation-systems-based technique, focuses on the single-event SFDES identification, where the fuzzy automaton of each FDES has only one event. Expanding on our research, this article delves into multievent SFDES identification, allowing each FDES to encompass a sequence of events. This is a new research direction that has not been mentioned in the literature before. Upon activation of an FDES, all its events occur sequentially. Our mathematical proof first establishes the associativity of the max-product inference operation, leading to the introduction of a pivotal and novel concept called an equivalent overall event transition matrix for a consecutive event sequence. This concept establishes a theoretical framework for utilizing the equation-systems-based technique in a novel three-step method for identifying multievent SFDESs. The technique is employed in the first two steps to: 1) determine the number of fuzzy automata in an SFDES and 2) calculate their occurrence frequencies. In the third step, multievent transition matrices of the SFDES are learned by using the stochastic-gradient-descent-based algorithms that we previously developed for multievent FDESs, provided the numbers of consecutive events for each fuzzy automaton within the SFDES are known. Theoretical analysis reveals, for the first time, the interconnections between the event transition matrices learned by the algorithms, the equivalent overall event transition matrices derived from these matrices, and the target event transition matrices. To illustrate our findings, we present an informative example.

In a distributed system, the plant and its controlling entity, the supervisor, are situated in separate locations, communicating remotely. This setup introduces delays and the potential for information loss during communication. This study delves into the supervisory control of networked fuzzy discrete event systems, an area relatively unexplored in existing literature. The plant is conceptualized as a fuzzy discrete event system with inherent constraints. Events within this system are both observed and managed from a distance by the supervisor, encountering two types of delays and losses. One type occurs during observation, where the plant transmits information to the supervisor, whereas the other arises during control, stemming from communication between the supervisor and the plant. The article first addresses the challenge of estimating states in the presence of observation delays and losses. An online methodology is devised to compute these state estimates. Leveraging these estimates, a supervisor is then designed to selectively enable or disable events, ensuring that the plant never transitions into undesirable or unsafe fuzzy states. A necessary and sufficient condition is established to guarantee the existence of such a supervisor. In addition, online techniques are developed to implement the computation of the supervisor's control actions.

We recently proposed a new class of fuzzy discrete event systems called the stochastic fuzzy discrete event systems (SFDES), which has the potential to be useful in a variety of applications, including those in healthcare. An SFDES is comprised of multiple fuzzy automata with different occurrence probabilities. Assuming the number of states is known, goals of SFDES identification are: 1) determining number of fuzzy automata and their event transition matrices, and 2) estimating the occurrence probabilities of the fuzzy automata. In this article, we develop an innovative technique, named the equation-systems-based technique, which uses whatever pre- and post-event state vector pairs available to establish and solve equation systems to achieve the identification goals. The ability of using arbitrary state vector pairs is a crucial and practical advantage over another SFDES identification technique that we previously published. That technique, called the prerequired-pre-event-state-based technique, requires the system of interest to be subject to some special pre-event states during the identification process, which may not be feasible for many real-world systems. The new equation-systems-based technique has no adjustable parameter to set or hyperparameter to experiment with. Theoretical analysis is conducted on the Technique, resulting in necessary or sufficient conditions as well as formulas for computing the minimal (or near minimal) number of state vector pairs needed for various SFDES settings. Computer simulation results are provided to demonstrate the effectiveness of the Technique.

The binary nature of the states and transitions in discrete-time finite Markov chains makes this modeling methodology unsuitable for many practical systems, such as those found in biomedicine. To address this fundamental limitation, we have extended in this article Markov chains to fuzzy Markov chains capable of handling fuzzy states and fuzzy events. This innovative and significant advancement is founded on the theory of stochastic fuzzy discrete event systems (SFDES) and the supervised learning algorithm for fuzzy discrete event systems (FDES), recently published by the authors. We mathematically generalize a traditional Markov chain with$N$states to a fuzzy Markov chain with$N$fuzzy states, which is represented by an SFDES consisting of$N^{2}$FDES. Each FDES has its own$N \times N$event transition matrix that is automatically learned by the aforementioned learning algorithm. Crucially, the fuzzy Markov chain fully preserves the stochastic characteristics defined by the transition probability matrix of the binary Markov chain, ensuring identical stochastic behaviors. A defuzzifier is used to yield crisp model output. The structurally more complex fuzzy Markov chain encompasses its binary counterpart as a special case and degenerates into it when fuzzy states degenerate into binary states. A simulation example is provided to illustrate the systematic design procedure and demonstrate the higher prediction accuracy of the fuzzy Markov chain over its binary counterpart. Due to their advantages, fuzzy Markov chains have the potential to address real-world stochastic problems beyond the reach of conventional Markov chains, especially in biomedicine.

This article introduces a novel sliding mode control (SMC) law to achieve trajectory tracking for a class of descriptor systems with unknown uncertainties. It approximates the uncertainties by a cerebellar model articulation control (CMAC) neural network. We formulate the problem of training the CMAC as a scheme of estimating a reachable set for a discrete-time nonlinear system. A new online learning algorithm based on output feedback control of reachable set estimation is developed and the approximation error is bounded in an ellipsoidal reachable set. In order to dispel the effect of the approximation error of the CMAC, we develop a compensation controller by using the reachable set bounds. Controller gains and parameters of the learning algorithm are obtained via linear matrix inequalities (LMIs). Our computer simulation results show that the proposed CMAC-based SMC technique can achieve convergent tracking errors. The technique is applied to a salient permanent magnet synchronous motor (PMSM) in our lab and demonstrates excellent performance.

In this article, supervised learning of fuzzy discrete-event systems (FDES) is investigated. A learning algorithm that performs supervised learning for multievent transition matrices of a sequence of fuzzy discrete events is derived. FDES can be used to describe a large class of practical systems that consist of fuzzy discrete states, fuzzy discrete events, and transitions among fuzzy discrete states via fuzzy discrete events. Because fuzzy discrete states, fuzzy discrete events, and fuzzy transitions are well defined in FDES, the FDES model is highly explainable, which is important in many applications, especially in biomedical applications. Based on this explainable model, the proposed learning algorithm can be used to learn events and event sequences in the model. Hence, it allows system developers to build an explainable model for a complex system based on the data available. Simulations using MATLAB are conducted to verify the effectiveness of the proposed algorithm.

Supervisory control of fuzzy discrete event systems (FDES) under partial observation is investigated in this article. Without loss of generality, we consider FDES with constraints where a FDES is modeled by a fuzzy automaton. Sequences of events that can be generated by the system are regarded as constraints and are modeled by a crisp automaton. A supervisor is designed to control the FDES so that the supervised system is prevented from entering a prespecified set of illegal/unsafe fuzzy states. A necessary and sufficient condition for the existence of a supervisor is obtained. When the condition is satisfied, an online supervisor can be designed. Fuzzy state estimation problem is first solved, as the supervisor is fuzzy-state-estimate-based. A method is developed to estimate fuzzy state iteratively after observation of each new event. We show that the supervisor so developed ensures the safety of the system and is least restrictive among all possible safe supervisors. Potential of the theoretical results for real-world applications is illustrated through an example of HIV/AIDS treatment decision-making.

Compared to other system modeling techniques, the fuzzy discrete event systems (FDESs) methodology has the unique capability of modeling a class of event-driven systems as fuzzy automata with ambiguous state and event-invoked state transition. In two recent papers, we developed algorithms for online-supervised learning of the fuzzy automaton's event transition matrix using fuzzy states before and after the occurrence of fuzzy events. The post-event state was assumed to be readily available while the pre-event state was either directly available or estimatable through learning. This article is focused on algorithm development for learning the transition matrix in a different setting-when the pre-event state is available but the post-event state is not. We suppose the post-event state is described by a fuzzy set that is linked to a (physical) variable whose value is available. Stochastic-gradient-descent-based algorithms are developed that can learn the transition matrix plus the parameters of the fuzzy sets when the fuzzy sets are of the Gaussian type. Computer simulation results are presented to confirm the theoretical development.

Many biomedical systems and some engineering systems can be modeled as fuzzy discrete event systems. In this article, fuzzy discrete event systems with constraints (FDESwC) are introduced and detectabilities of FDESwC are investigated. While detectabilities of conventional crisp discrete event systems (DES) have been investigated before, detectabilities of FDESwC are much more complex because the state space of FDESwC is infinite, unlike that of crisp DES. To overcome this difficulty, trajectories of FDESwC bounded by$N$observations are considered and$N$-detectabilities are introduced.$N$-detectabilities of crisp DES are first defined and proved to be equivalent to detectabilities if$N$is sufficiently large. Fuzzy$N$-detectabilities of FDESwC are then defined. An algorithm is derived to check fuzzy$N$-detectabilities. While fuzzy detectabilities require to determine which state the system is in, this requirement can be relaxed in some applications. To do so, fuzzy$D$-detectabilities are introduced and investigated, where the requirement is to distinguish certain pairs of states.

The fuzzy discrete event system theory is unique in that it is capable of modeling a class of event-driven systems as fuzzy automata with states and event-invoked state transitions being ambiguous. At present, the theory lacks a self-learning component, an important topic that has hardly been touched in the literature. In this article, we use stochastic gradient descent to develop online learning algorithms for the fuzzy automata. We uncover an inherent obstacle in the initial derived algorithms that fundamentally restricts their learning capability owing to dependences of the model parameters to be learned. We develop a novel mechanism to not only overcome the obstacle but also make the learning adaptive. Our final algorithms can learn an event transition matrix based on automaton's states before and after the occurrence of a fuzzy event, and learn the transition matrix and multidimensional Gaussian fuzzy sets yielding initial automaton states from relevant input variables and target states. Computer simulation results are presented to show learning performance of the final algorithms.

To make the fuzzy discrete event system theory more useful in a wide range of applications, it is crucial to equip it with learning capability, an issue that has hardly been touched upon in the literature. In this paper, we develop stochastic-gradient-decent-based algorithms for online learning of the event transition matrices and parameters of the fuzzy sets fuzzifying input variables of a fuzzy discrete event system modeled as a fuzzy automaton. We uncover an intrinsic obstacle in the algorithms that significantly impedes the learning owing to dependences of the fuzzy set parameters on the matrix. As a remedy, we modify the algorithms using the exponential penalty function. Preliminary computer simulation results are presented to illustrate learning performance of our final algorithms.

This study focuses on estimation and compensation on the unknown measurement noises of large-scale systems subject to nonlinear dynamics and interconnections. Interval type-2 T-S fuzzy model is used to describe each nonlinear subsystem. For the sake of attenuating adverse impacts from the unknown measurement noises, a combined method of reachable set bounding and estimation-compensation control is proposed. First, we introduce an augmented fuzzy observer that fulfills a simultaneous estimation for the system states and unknown measurement noises, which guarantees that the estimation error is bounded within the ellipsoidal boundary. Then, a fuzzy compensation controller is used to attenuate the impacts from the unknown measurement noises. Finally, simulation results show the effectiveness of our method against the unknown measurement noises.

The fundamental difference between an interval type-2 (IT2) fuzzy controller and a type-1 fuzzy controller is the footprint of uncertainty (FOU) of an IT2 fuzzy set. In this paper, we study how FOUs affect the analytical structure (i.e., the input-output mathematical relationship) of a broad class of IT2 Mamdani and takagi-sugeno (TS) controllers. The controllers employ arbitrary fuzzy rules, the Karnik-Mendel (KM) or Enhanced KM type-reducer, the minimum AND operator, and the centroid defuzzifier. The controllers utilize commonly used IT2 fuzzy sets for their input variables and any kind of type-2 fuzzy sets for their output variable. We prove that, with increase of FOUs of the input fuzzy sets, the Mamdani controllers approach constant controllers, and the TS controllers approach piecewise linear controllers. The resemblance to the constant or pricewise linear controllers increases as the FOUs increase. When all the FOUs are at their maximum (to reflect the highest level of uncertainties), the Mamdani and TS controllers become the constant controllers and piecewise linear controllers, respectively. We investigate how change in the resemblance takes place progressively as FOUs increase. We also show that an increase in the resemblance narrows control gain variations for part of the IT2 controllers, which can worsen control performance. These findings implicit controller design-too large FOUs are generally undesirable for the input fuzzy sets because they can make an IT2 controller behave like a constant or piecewise linear controller. Real-time control experiment results are provided to illustrate the theoretical analysis.

As part of the zinc hydrometallurgy plant, the iron removal process is a complex system with four cascaded reactors. Tighter process-index control is difficult to achieve due to the complicated, long, and time-varying removal process. The control performance is also affected by the quality of the ore source and external disturbances. Little research is documented in the literature to address these difficulties and manual control is widely used. An innovative hybrid control strategy is developed to control the iron removal process' indices within narrow ranges with minimum cost of additive regents, including oxygen and zinc oxide. This strategy is composed of an optimal setting model, a model-based optimal controller, an integrated prediction model, a fuzzy-logic-based feedforward compensator, and a model feedback adjustor. The optimal setting model automatically optimizes the set-points of the process indices under different production conditions. To achieve the process requirements with minimal cost, the model-based optimal controller is designed. The integrated prediction model is established to provide a more accurate on-line prediction of the process indices by integrating the mechanism prediction model and an error compensation model based on the least-square support vector machine. Based on the predicted process indices, the compensator is developed for the optimal controller. The adjustor provides a parameter adjustment mechanism. Four-week-long industrial experiments in the largest zinc hydrometallurgy plant in China show that the control strategy can not only improve the process-indexes control performance, but also save 6.55% oxygen and 4.61% zinc oxide consumptions, which translates to 222 858 m3oxygen and 1236 t zinc oxide per year (a saving of about $570 000). The hybrid control strategy can be extended to cover other similar processes in the zinc hydrometallurgy and other industries.

Fuzzy discrete event systems are useful models for solving complex practical problems in biomedical and other fields. The theory of detectabilities in conventional crisp discrete event systems investigates state determination or estimation based on event observation. The theory is also important to fuzzy discrete event systems (e.g., disease diagnosis and treatment effectiveness evaluation). In this paper, we investigate fuzzy detectabilities for fuzzy discrete event systems. We first introduce fuzzy discrete event systems with constraints, which provide a new and more realistic model for complex systems. We also extend detectabilities of crisp discrete event systems to N-detectabilities and prove the relation between detectabilities and N-detectabilities. We then define fuzzy N-detectabilities and develop an algorithm to check fuzzy N-detectabilities of a fuzzy discrete event system. The computational complexity of the algorithm is analyzed.

A conventional controller's explicit input-output mathematical relationship, also known as its analytical structure, is always available for analysis and design of a control system. In contrast, virtually all type-2 (T2) fuzzy controllers are treated as black-box controllers in the literature in that their analytical structures are unknown, which inhibits precise and comprehensive understanding and analysis. In this regard, a long-standing fundamental issue remains unresolved: how a T2 fuzzy set's footprint of uncertainty, a key element differentiating a T2 controller from a type-1 (T1) controller, affects a controller's analytical structure. In this paper, we describe an innovative technique for deriving analytical structures of a class of typical interval T2 (IT2) TS fuzzy controllers. This technique makes it possible to analyze the analytical structures of the controllers to reveal the role of footprints of uncertainty in shaping the structures. Specifically, we have mathematically proven that under certain conditions, the larger the footprints, the more the IT2 controllers resemble linear or piecewise linear controllers. When the footprints are at their maximum, the IT2 controllers actually become linear or piecewise linear controllers. That is to say the smaller the footprints, the more nonlinear the controllers. The most nonlinear IT2 controllers are attained at zero footprints, at which point they become T1 controllers. This finding implies that sometimes if strong nonlinearity is most important and desired, one should consider using a smaller footprint or even just a T1 fuzzy controller. This paper exemplifies the importance and value of the analytical structure approach for comprehensive analysis of T2 fuzzy controllers.

This paper presents a novel approach to automatically creating an interval type-2 fuzzy neural network (IT2-FNN) from a type-1 fuzzy TSK system (T1-TSK). The IT2-FNN is constructed in such a way that it takes advantage of the well-behaving T1-TSK. Our approach makes designing the IT2-FNN more efficient and the resulting system is expected to perform better than the T1-TSK due to the footprint of uncertainty of the IT2 fuzzy sets, especially when the system is subject to heavy external or internal uncertainties. There are two automated procedures in the IT2-FNN formation: (1) antecedent structure construction, and (2) learning of the parameters in both the antecedent and consequent. The structure construction is based on antecedent structure of the T1-TSK and consists of three steps - IT2 fuzzy set creation, similarity categorization, and mergence. The IT2 fuzzy sets are directly initialized from the fuzzy sets of the T1-TSK. Then, the IT2 fuzzy sets are classified into different groups based on their similarities. Finally, the IT2 fuzzy sets in each group are merged to create a representative IT2 fuzzy set for each group. The parameter learning procedure uses a hybrid learning algorithm to attain the optimal values for all the parameters. The learning algorithm adopts a new adaptive steepest descent algorithm and a linear least-squares method to adjust the antecedent parameters and consequent parameters, respectively. One benchmark modelling problem is utilized to compare our approach with the T1-TSK systems in the literature under various scenarios. The comparison results show our IT2-FNN performs better than the T1-TSK systems, especially when there are strong uncertainties. In summary, the IT2-FNN can not only achieve better performance but its structure is simpler than that of the similar type-2 fuzzy neural networks in the literature.

BACKGROUND: Finding highly relevant articles from biomedical databases is challenging not only because it is often difficult to accurately express a user's underlying intention through keywords but also because a keyword-based query normally returns a long list of hits with many citations being unwanted by the user. This paper proposes a novel biomedical literature search system, called BiomedSearch, which supports complex queries and relevance feedback. METHODS: The system employed association mining techniques to build a k-profile representing a user's relevance feedback. More specifically, we developed a weighted interest measure and an association mining algorithm to find the strength of association between a query and each concept in the article(s) selected by the user as feedback. The top concepts were utilized to form a k-profile used for the next-round search. BiomedSearch relies on Unified Medical Language System (UMLS) knowledge sources to map text files to standard biomedical concepts. It was designed to support queries with any levels of complexity. RESULTS: A prototype of BiomedSearch software was made and it was preliminarily evaluated using the Genomics data from TREC (Text Retrieval Conference) 2006 Genomics Track. Initial experiment results indicated that BiomedSearch increased the mean average precision (MAP) for a set of queries. CONCLUSIONS: With UMLS and association mining techniques, BiomedSearch can effectively utilize users' relevance feedback to improve the performance of biomedical literature search.

Finding highly relevant articles from biomedical databases is challenging because it is often very difficult to accurately express a user's underlying intention through keywords, and a keyword-based query normally returns a long list of hits. This paper proposes a novel biomedical literature search system, called BiomedSearch, which supports complex queries and relevance feedback. In this system, we developed a weighted interest measure and an association mining algorithm to find the strength of association between the query and each concept in the article(s) selected by the user as feedback. The top ?? concepts were utilized to form a k-profile used for the next-round search. BiomedSearch relies on Unified Medical Language System (UMLS) knowledge sources to map text files to standard biomedical concepts. It was designed to support queries with any levels of complexity. The prototype system was preliminarily evaluated using three topics and related Genomics data from TREC (Text Retrieval Conference) 2006 Genomics Track. Initial results indicated that BiomedSearch could effectively utilize users' relevance feedback to improve search performance.

The polynomial fuzzy models are capable of modeling complex dynamic systems. They have attracted increasing attention in the recent years as the models of choice for the development of more advanced fuzzy controllers. Little effort has been made to study the models themselves though. Like many other types of models, a polynomial fuzzy model aims at describing the physical system's dynamics based on the measured input-output data of the system. Importantly, a polynomial fuzzy model that appears to mimic the measured data reasonably well does not guarantee its validity. One way to assess model's quality is to check whether its stability is consistent with that of the physical system, which is the theme of our investigation. In this paper, we first propose a type of discrete-time polynomial fuzzy dynamic models, which comprises the general Takagi-Sugeno (T-S) fuzzy model as a special case. Then, based on the Lyapunov's linearization method, a necessary and sufficient condition is established for analytically determining the local asymptotic stability of the proposed models. A numerical example is given to illustrate the effectiveness and utility of our method.

Type-2 fuzzy controllers have been mostly viewed and treated as black boxes in that their input-output mathematical mappings (i.e., analytical structures) are unknown. In contrast, this is never the case for any conventional controller. In this paper, we show an innovative analytical structure derivation technique for the interval Type-2 TS fuzzy controllers whose configurations are as follows: two input variables, two linear input fuzzy sets for each input variable, linear TS fuzzy rules, Zadeh AND operator, the Karnik-Mendel center-of-sets type reducer, and the centroid defuzzifier. Revealing the analytical structure of any Type-2 fuzzy controller, this one included, is important as it can lead to better understanding of the controller and more productive analysis and design of the Type-2 fuzzy control system.

Advanced driver assistance systems, such as unintentional lane departure warning systems, have recently drawn much attention and R & D efforts. Such a system may assist the driver by monitoring the driver or vehicle behaviors to predict/detect driving situations (e.g., lane departure) and alert the driver to take corrective action. In this paper, we show how the support vector machine (SVM) methodology can potentially provide enhanced unintentional lane departure prediction, which is a new method relative to literature. Our binary SVM employed the Radial Basis Function kernel to classify time series of select vehicle variables. The SVM was trained and tested using the driver experiment data generated by VIRTTEX, a hydraulically powered 6-degrees-of-freedom moving base driving simulator at Ford Motor Company. The data that we used represented 16 drowsy subjects (three-hour driving time per subject) and six control subjects (20 minutes driving per subject), all of which drove a simulated 2000 Volvo S80. The vehicle variables were all sampled at 50 Hz. There were a total of 3,508 unintentional lane departure occurrences for the drowsy drivers and only 23 for four of the six control drivers (two had none). The SVM was trained by over 60,000 time series examples (the actual number depended on the prediction horizon) created from 50% of the lane departures. The training data were removed from the testing data. During the testing, the SVM made a lane departure prediction at every sampling time for every one of the 22 drivers (over 6.8 million predictions in total). The overall sensitivity and specificity of the SVM with a 0.2-second prediction horizon for the 22 drivers were 99.77465% and 99.99997%, respectively. The SVM predicted, on average 0.200181 seconds in advance, lane departure correctly for all the control drivers, but missed 4 of the 1,758 and gave false positives for another 2 for the drowsy drivers. For the prediction horizon of 0.4s, there was 1 false positive case for the control subjects, and the false negative and false positive cases rose substantially to 10 and 137 for the drowsy drivers, respectively.

In many real-world applications, it is important to mine causal relationships where an event or event pattern causes certain outcomes with low probability. Discovering this kind of causal relationships can help us prevent or correct negative outcomes caused by their antecedents. In this paper, we propose an innovative data mining framework and apply it to mine potential causal associations in electronic patient data sets where the drug-related events of interest occur infrequently. Specifically, we created a novel interestingness measure, exclusive causal-leverage, based on a computational, fuzzy recognition-primed decision (RPD) model that we previously developed. On the basis of this new measure, a data mining algorithm was developed to mine the causal relationship between drugs and their associated adverse drug reactions (ADRs). The algorithm was tested on real patient data retrieved from the Veterans Affairs Medical Center in Detroit, Michigan. The retrieved data included 16,206 patients (15,605 male, 601 female). The exclusive causal-leverage was employed to rank the potential causal associations between each of the three selected drugs (i.e., enalapril, pravastatin, and rosuvastatin) and 3,954 recorded symptoms, each of which corresponded to a potential ADR. The top 10 drug-symptom pairs for each drug were evaluated by the physicians on our project team. The numbers of symptoms considered as likely real ADRs for enalapril, pravastatin, and rosuvastatin were 8, 7, and 6, respectively. These preliminary results indicate the usefulness of our method in finding potential ADR signal pairs for further analysis (e.g., epidemiology study) and investigation (e.g., case review) by drug safety professionals.

Most fuzzy controllers, type-1 (T1) or type-2 (T2), have been used and treated as black boxes in that their explicit mathematical input-output mappings (i.e., analytical structures) are unknown. Revealing and analyzing the analytical structure is important as it will lay a solid foundation for better understanding, more insightful analysis, and more effective design of fuzzy control systems. We previously developed a general technique to derive the analytical structures of the type-1 fuzzy controllers that employed Zadeh AND operator. We now extend our study to a class of typical interval type-2 fuzzy controller that adopt Zadeh AND operator and the popular Karnik-Mendel iterative center-of-sets type reducer. A novel analytical structure deriving technique is developed. And the resulting input-output mathematical relationship for the controller is received.

Early detection of unknown adverse drug reactions (ADRs) in postmarketing surveillance saves lives and prevents harmful consequences. We propose a novel data mining approach to signaling potential ADRs from electronic health databases. More specifically, we introduce potential causal association rules (PCARs) to represent the potential causal relationship between a drug and ICD-9 (CDC. (2010). International Classification of Diseases, Ninth Revision (ICD-9). [Online]. Available: http://www.cdc.gov/nchs/icd/icd9.html) coded signs or symptoms representing potential ADRs. Due to the infrequent nature of ADRs, the existing frequency-based data mining methods cannot effectively discover PCARs. We introduce a new interestingness measure, potential causal leverage, to quantify the degree of association of a PCAR. This measure is based on the computational, experience-based fuzzy recognition-primed decision (RPD) model that we developed previously (Y. Ji, R. M. Massanari, J. Ager, J. Yen, R. E. Miller, and H. Ying, "A fuzzy logic-based computational recognition-primed decision model," Inf. Sci., vol. 177, pp. 4338-4353, 2007) on the basis of the well-known, psychology-originated qualitative RPD model (G. A. Klein, "A recognition-primed decision making model of rapid decision making," in Decision Making in Action: Models and Methods, 1993, pp. 138-147). The potential causal leverage assesses the strength of the association of a drug-symptom pair given a collection of patient cases. To test our data mining approach, we retrieved electronic medical data for 16,206 patients treated by one or more than eight drugs of our interest at the Veterans Affairs Medical Center in Detroit between 2007 and 2009. We selected enalapril as the target drug for this ADR signal generation study. We used our algorithm to preliminarily evaluate the associations between enalapril and all the ICD-9 codes associated with it. The experimental results indicate that our approach has a potential to better signal potential ADRs than risk ratio and leverage, two traditional frequency-based measures. Among the top 50 signal pairs (i.e., enalapril versus symptoms) ranked by the potential causal-leverage measure, the physicians on the project determined that eight of them probably represent true causal associations.

The current approach to postmarketing surveillance primarily relies on spontaneous reporting. It is a passive surveillance system and limited by gross underreporting (<;;10% reporting rate), latency, and inconsistent reporting. We propose a new interestingness measure, causal-leverage, to signal potential adverse drug reactions (ADRs) from electronic health databases which are readily available in most modern hospitals. This measure is based on an experience-based fuzzy recognition-primed decision (RPD) model that we developed previously which assesses the strength of association of a drug-ADR pair within each individual patient case. Using the causal-leverage measure, we develop a data mining algorithm to evaluate the associations between a given drug enalapril and all potential ADRs in a real-world electronic health database. The experimental results have shown that our approach can effectively shortlist some known ADRs. For example, the known ADR hyperkalemia caused by enalapril was ranked as top 1% among all the 3954 potential ADRs in our database.

Research results on type-2 (T2) fuzzy control have started to emerge in the literature over the past several years. None of these results, however, are concerned with the explicit input-output mathematical structure of a T2 fuzzy controller. As the literature on type-1 (T1) fuzzy control has demonstrated, revealing such structure information is important as it will deepen our precise understanding of how and why T2 fuzzy controllers function in the context of control theory and lay a foundation for more rigorous system analysis and design. In this paper, we derive the mathematical structure of two Mamdani interval T2 fuzzy-proportional-integral (PI) controllers that use the following identical elements: two interval T2 triangular input fuzzy sets for each of the two input variables, four singleton T1 output fuzzy sets, a Zadeh and operator, and the center-of-sets type reducer. One controller employs the popular centroid defuzzifier, while the other employs a new defuzzifier that we propose, which is called the average defuzzifier. The advantages of using the latter defuzzifier are given, which include the fact that the derivation method originally developed by us in previous papers for the T1 fuzzy controllers can be directly adopted for the T2 controller, and the results are general with respect to the design parameters. This is not the case for the other T2 controller, for which we have developed a novel derivation approach partially depending on numerical computations. Our derivation results prove explicitly both controllers to be nonlinear PI controllers with variable gains (i.e., the expressions are different). We analyze the gain-variation characteristics and extend these findings to the corresponding T2 fuzzy-proportional-derivative (PD) controllers. Our new results are consistent with the relevant structure results on the T1 fuzzy-PI and PD controllers in the literature and contain them as special cases. We discuss how the new structure information can be utilized to design and tune the T2 controllers, even when the mathematical model of the system to be controlled is unknown. Neither derivation method is restrictive only to the T2 controllers in this paper-they are directly applicable to other T2 controllers with more complex configurations.

Discovering unknown adverse drug reactions (ADRs) in postmarketing surveillance as early as possible is of great importance. The current approach to postmarketing surveillance primarily relies on spontaneous reporting. It is a passive surveillance system and limited by gross underreporting (<10% reporting rate), latency, and inconsistent reporting. We propose a novel team-based intelligent agent software system approach for proactively monitoring and detecting potential ADRs of interest using electronic patient records. We designed such a system and named it ADRMonitor. The intelligent agents, operating on computers located in different places, are capable of continuously and autonomously collaborating with each other and assisting the human users (e.g., the food and drug administration (FDA), drug safety professionals, and physicians). The agents should enhance current systems and accelerate early ADR identification. To evaluate the performance of the ADRMonitor with respect to the current spontaneous reporting approach, we conducted simulation experiments on identification of ADR signal pairs (i.e., potential links between drugs and apparent adverse reactions) under various conditions. The experiments involved over 275,000 simulated patients created on the basis of more than 1000 real patients treated by the drug cisapride that was on the market for seven years until its withdrawal by the FDA in 2000 due to serious ADRs. Healthcare professionals utilizing the spontaneous reporting approach and the ADRMonitor were separately simulated by decision-making models derived from a general cognitive decision model called fuzzy recognition-primed decision (RPD) model that we recently developed. The quantitative simulation results show that 1) the number of true ADR signal pairs detected by the ADRMonitor is 6.6 times higher than that by the spontaneous reporting strategy; 2) the ADR detection rate of the ADRMonitor agents with even moderate decision-making skills is five times higher than that of spontaneous reporting; and 3) as the number of patient cases increases, ADRs could be detected significantly earlier by the ADRMonitor.

In a 2002 paper, we combined fuzzy logic with discrete-event systems (DESs) and established an automaton model of fuzzy DESs (FDESs). The model can effectively represent deterministic uncertainties and vagueness, as well as human subjective observation and judgment inherent to many real-world problems, particularly those in biomedicine. We also investigated optimal control of FDESs and applied the results to optimize HIV/AIDS treatments for individual patients. Since then, other researchers have investigated supervisory control problems in FDESs, and several results have been obtained. These results are mostly derived by extending the traditional supervisory control of (crisp) DESs, which are string based. In this paper, we develop state-feedback control of FDESs that is different from the supervisory control extensions. We use state space to describe the system behaviors and use state feedback in control. Both disablement and enforcement are allowed. Furthermore, we study controllability based on the state space and prove that a controller exists if and only if the controlled system behavior is (state-based) controllable. We discuss various properties of the state-based controllability. Aside from novelty, the proposed new framework has the advantages of being able to address a wide range of practical problems that cannot be effectively dealt with by existing approaches. We use the diabetes treatment as an example to illustrate some key aspects of our theoretical results.

Type-2 (T2) fuzzy systems have gained increasing attention in the recent years. There have been a number of T2 fuzzy control studies in the literature but only one of them is involved in adaptive control. The objective of this paper is to develop a new and theoretically rigorous interval T2 adaptive fuzzy controller for controlling uncertain systems. Our adaptive controller contains a T2 fuzzy system component that is mathematically proven to be capable of approximating any continuous function to any degree of accuracy (in contrast, the sole work in the literature just assumes the universal approximation ability without showing any proof). Based on the Lyapunov method, we design the adaptive laws with mathematical proofs for stability and convergence of the closed-loop system. The controller updates its parameters online to control an uncertain system and track a reference trajectory. Our simulation study involves a nonlinear inverted pendulum. The simulation results demonstrate that the interval T2 adaptive fuzzy controller can achieve the system stability as designed and maintain good tracking performance. We also use the simulation to study the system performance under noise and disturbance.

In 2001, we originated a theory of fuzzy discrete-event systems (FDESs) that generalized the conventional/crisp discrete-event systems (DESs). Vagueness and imprecision concerning states and event transitions of DESs were represented by membership grades and computed via fuzzy logic. Our application of the FDES theory to computerized human immunodeficiency virus/acquired immune deficiency syndrome treatment regimen selection, although preliminarily successful, suggests that a more comprehensive FDES theory is needed to address two general issues critically important not only to biomedical applications, but also to real-world problems in other industries. First, domain experts should have means other than point estimates and type-1 fuzzy sets mandated in the current framework to describe uncertainties, subjectivity, and imprecision in their (complex) knowledge and experience. Second, when a group of experts with distinct opinions is involved, they should not be forced to reach consensus for the sake of system development. This is because collective consensus may not be achievable, which is often the case in medicine, where individual expertspsila opinions should be equally respected since the underlying ground truth is unknown most of the time. The theory of extended FDES presented in this paper addresses both the problems and contains the FDES theory as a special case. Experts are now allowed to use interval numbers and type-1 and type-2 fuzzy sets to intuitively and quantitatively express their diverse knowledge and experience, which will then be processed by the new theory to form fuzzy state vectors and fuzzy event transition matrices. Accordingly, we have established mathematical operations that cover the computations of fuzzy states, fuzzy event transitions, and parallel composition. Numerical examples are provided.

As a very effective method for universal purpose pattern recognition, support vector machine (SVM) was proposed for dichotomic classification problem, which exhibits a remarkable resistance to overfitting, a feature explained by the fact that it directly implements the principle of structural risk minimization. However, in real world, most of classification problems consist of multiple categories. In an attempt to extend the binary SVM classifier for multiclass classification, decision-tree-based multiclass SVM was proposed recently, in which the structure of decision tree plays an important role in minimizing the classification error. The present study aims at developing a systematic way for the design of decision tree for multiclass SVM. Kernel-induced distance function between datasets was discussed and then kernelized hierarchical clustering was developed and used in determining the structure of decision tree. Further, simulation results on satellite image interpretation show the superiority of the proposed classification strategy over the conventional multiclass SVM algorithms.

Discovering unknown adverse drug reactions (ADRs) in postmarketing surveillance as early as possible is highly desirable. Nevertheless, current postmarketing surveillance methods largely rely on spontaneous reports that suffer from serious underreporting, latency, and inconsistent reporting. Thus these methods are not ideal for rapidly identifying rare ADRs. The multiagent systems paradigm is an emerging and effective approach to tackling distributed problems, especially when data sources and knowledge are geographically located in different places and coordination and collaboration are necessary for decision making. In this article, we propose an active, multiagent framework for early detection of ADRs by utilizing electronic patient data distributed across many different sources and locations. In this framework, intelligent agents assist a team of experts based on the well-known human decision-making model called Recognition-Primed Decision (RPD). We generalize the RPD model to a fuzzy RPD model and utilize fuzzy logic technology to not only represent, interpret, and compute imprecise and subjective cues that are commonly encountered in the ADR problem but also to retrieve prior experiences by evaluating the extent of matching between the current situation and a past experience. We describe our preliminary multiagent system design and illustrate its potential benefits for assisting expert teams in early detection of previously unknown ADRs. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 827–845, 2007.

The U.S. Department of Health and Human Services Human Immunodeficiency Virus (HIV)/Acquired Immune Deficiency Syndrome (AIDS) treatment guidelines are modified several times per year to reflect the rapid evolution of the field (e.g., emergence of new antiretroviral drugs). As such, a treatment-decision support system that is capable of self-learning is highly desirable. Based on the fuzzy discrete event system (FDES) theory that we recently created, we have developed a self-learning HIV/AIDS regimen selection system for the initial round of combination antiretroviral therapy, one of the most complex therapies in medicine. The system consisted of a treatment objectives classifier, fuzzy finite state machine models for treatment regimens, and a genetic-algorithm-based optimizer. Supervised learning was achieved through automatically adjusting the parameters of the models by the optimizer. We focused on the four historically popular regimens with 32 associated treatment objectives involving the four most important clinical variables (potency, adherence, adverse effects, and future drug options). The learning targets for the objectives were produced by two expert AIDS physicians on the project, and their averaged overall agreement rate was 70.6%. The system's learning ability and new regimen suitability prediction capability were tested under various conditions of clinical importance. The prediction accuracy was found between 84.4% and 100%. Finally, we retrospectively evaluated the system using 23 patients treated by 11 experienced nonexpert faculty physicians and 12 patients treated by the two experts at our AIDS Clinical Center in 2001. The overall exact agreement between the 13 physicians' selections and the system's choices was 82.9% with the agreement for the two experts being both 100%. For the seven mismatched cases, the system actually chose more appropriate regimens in four cases and equivalent regimens in another two cases. It made a mistake in one case. These (preliminary) results show that 1) the System outperformed the nonexpert physicians and 2) it performed as well as the expert physicians did. This learning and prediction approach, as well as our original FDESs theory, is general purpose and can be applied to other medical or nonmedical problems.

Grid technologies facilitate innovative applications among dynamic virtual organizations, while the ability to deploy, manage, and properly remain functioning via traditional approaches has been exceeded by the complexity of the next generation of grid systems. An important method for addressing this challenge may require nature-inspired computing paradigms. This technique will entail construction of a bottom-up multiagent system; however, the appropriate implementation mechanism is under consideration in order for the autonomous and distributed agents to emerge as a controlled grid service or application. A credit card management service in economic interactions is considered in this article for a decentralized control approach. This consideration is based on a preliminarily developed ecological network-based grid middleware that has features desired for the next generation grid systems. The control scheme, design, and implementation of the credit card management service are presented in detail. The simulation results show that (1) agents are accountable for their activities such as behavior invocation, service provision, and resource utilization and (2) generated services or applications adapt well to dynamically changing environments such as agent amounts as well as partial failure of agents. The approach presented herein is beneficial for building autonomous and adaptive grid applications and services. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 1269–1288, 2006.

Treatment decision-making is complex and involves many factors. A systematic decision-making and optimization technology capable of handling variations and uncertainties of patient characteristics and physician's subjectivity is currently unavailable. We recently developed a novel general-purpose fuzzy discrete event systems theory for optimal decision-making. We now apply it to develop an innovative system for medical treatment, specifically for the first round of highly active antiretroviral therapy of human immunodeficiency virus/acquired immunodeficiency syndrome (HIV/AIDS) patients involving three historically widely used regimens. The objective is to develop such a system whose regimen choice for any given patient will exactly match expert AIDS physician's selection to produce the (anticipated) optimal treatment outcome. Our regimen selection system consists of a treatment objectives classifier, fuzzy finite state machine models for treatment regimens, and a genetic-algorithm-based optimizer. The optimizer enables the system to either emulate an individual doctor's decision-making or generate a regimen that simultaneously satisfies diverse treatment preferences of multiple physicians to the maximum extent. We used the optimizer to automatically learn the values of 26 parameters of the models. The learning was based on the consensus of AIDS specialists A and B on this project, whose exact agreement was only 35%. The performance of the resulting models was first assessed. We then carried out a retrospective study of the entire system using all the qualifying patients treated in our institution's AIDS Clinical Center in 2001. A total of 35 patients were treated by 13 specialists using the regimens (four and eight patients were treated by specialists A and B, respectively). We compared the actually prescribed regimens with those selected by the system using the same available information. The overall exact agreement was 82.9% (29 out of 35), with the exact agreement with specialists A and B both at 100%. The exact agreement for the remaining 11 physicians not involved in the system training was 73.9% (17 out of 23), an impressive result given the fact that expert opinion can be quite divergent for treatment decisions of such complexity. Our specialists also carefully examined the six mismatched cases and deemed that the system actually chose a more appropriate regimen for four of them. In the other two cases, either would be reasonable choices. Our approach has the capabilities of generalizing, learning, and representing knowledge even in the face of weak consensus, and being readily upgradeable to new medical knowledge. These are practically important features to medical applications in general, and HIV/AIDS treatment in particular, as national HIV/AIDS treatment guidelines are modified several times per year.

For conventional fuzzy systems, Mamdani type or TS type, it is; well known that the number of fuzzy rules and adjustable parameters exponentially increases with the number of input variables. This problem is often referred as curse of dimensionality. Hierarchical fuzzy systems have been proposed to resolve this problem. At present, however, it is unclear whether or not hierarchical fuzzy systems can truly resolve this issue. In this paper, we investigate the zero-order TS fuzzy systems and their corresponding hierarchical fuzzy systems. We rigorously prove that to approximate any continuous functions with the same degree of accuracy, the number of parameters used by the hierarchical fuzzy systems are exactly the same as those employed by the TS systems. This result implies that the hierarchical fuzzy systems do not offer a real solution, at least for the zero-order TS fuzzy systems

The United Nations estimates that 38 million people worldwide are infected with HIV/AIDS, and that more than 22 million have died. Like most diseases, treatment decision-making for this disease is currently more an art than science. This is partially because every patient is unique, with his/her own history, set of genetic traits, predisposition to side effects, and prognosis. We reported previously how we had developed a theoretical framework of novel fuzzy discrete event systems, which are knowledge-based (Lin and Ying, 2002). We showed how to apply it to develop a part of HIV/AIDS regimen selection system for treating antiretroviral-naive patients (Lin et al., 2004). In the present paper, we describe our recent development - we have furthered the system design by adding a Genetic-Algorithm-Based Regimen Selection Optimizer and a Treatment Objectives Classifier to the system. The full system is capable of prescribing a regimen for any given patient. The Optimizer enables the system to either emulate an individual doctor's decision-making or generate a regimen that simultaneously satisfies diverse treatment preferences of multiple physicians to the maximum extent. We show the promising preliminary results of retrospective evaluation of the system using 48 treatment-naive patients who started antiretroviral treatment in our AIDS Clinic in 2001. Our fuzzy DES approach possesses a number of unique features and advantages that are especially important to medical applications: (1) higher flexibility and scalability, and (2) easier knowledge upgrade for accommodating fast treatment strategy evolution with minimal system modification. These are particularly important to HIV/AIDS treatment as the U.S. Public Health Service updates its treatment guidelines at least once a year

As the only effective treatment strategy against HIV/AIDS, highly active antiretroviral therapy (HAART) is an extremely promising development in the treatment of HIV/AIDS. The success of HAART highly depends on patient's adherence to this complex treatment. Recent studies found that poor adherence was a major cause of treatment failure and emerging drug resistance, and thus it is important to understand the factors that contribute to good and poor adherence. However, the discovery of factors salient to adherence is constrained by the well known fact that medical data gathering is expensive and thus usually only a limited amount of information is available. Our study of HIV/AIDS treatment adherence is no exception - we only have data on 33 patients. For this reason, we apply the support vector machine (SVM) to model the relationship of nine patient factors to the level of medication adherence. To establish the baseline performance, we first randomly generated test data sets of comparable sample size and data dimension to the patient pool. A SVM was evaluated using the test data. The SVM was then applied to the real patient data. Finally, a three-layer neural network with back propagation learning was applied to the patient data as well as the test data. The results show that the SVM performed reasonably well and significantly outperformed the neural networks. Our work demonstrates that SVM techniques can be effective in quantitatively modeling complex relationships important in clinical medicine even when the data set size is very small by industrial standards. To our knowledge, this is the first application of a SVM to HIV/AIDS.

It is well-known that the multiple sliding surface control was developed to eliminate the problem of “explosion of complexity” inherent in the celebrated backstepping method. In this paper, we extend the multiple sliding surface control method further for systems in nonlinear block controllable form. As an application of the proposed control scheme, the robust attitude control law was synthesized for highly maneuverable missiles. Contrary to the classical SISO methods, all nonlinearities of missile attitude dynamics as well as coupling effects between roll, yaw and pitch channels due to roll rate are fully accommodated in the designed nonlinear control law.

Mamdani fuzzy models have always been used as black-box models. Their structures in relation to the conventional model structures are unknown. Moreover, there exist no theoretical methods for rigorously judging model stability and validity. I attempt to provide solutions to these issues for a general class of fuzzy models. They use arbitrary continuous input fuzzy sets, arbitrary fuzzy rules, arbitrary inference methods, Zadeh or product fuzzy logic AND operator, singleton output fuzzy sets, and the centroid defuzzifier. I first show that the fuzzy models belong to the NARX (nonlinear autoregressive with the extra input) model structure, which is one of the most important and widely used structures in classical modeling. I then divide the NARX model structure into three nonlinear types and investigate how the settings of the fuzzy model components, especially input fuzzy sets, dictate the relations between the fuzzy models and these types. I have found that the fuzzy models become type-2 models if and only if the input fuzzy sets are linear or piecewise linear (e.g., trapezoidal or triangular), becoming type 3 if and only if at least one input fuzzy set is nonlinear. I have also developed an algorithm to transfer type-2 fuzzy models into type-1 models as far as their input–output relationships are concerned, which have some important properties not shared by the type-2 models. Furthermore, a necessary and sufficient condition has been derived for a part of the general fuzzy models to be linear ARX models. I have established a necessary and sufficient condition for judging local stability of type-1 and type-2 fuzzy models. It can be used for model validation and control system design. Three numeric examples are provided. Our new findings provide a theoretical foundation for Mamdani fuzzy modeling and make it more consistent with the conventional modeling theory. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 103–125, 2005.

Treatment decision-making for most diseases is currently partial art and partial science. To a large extent, this is due to the fact that every patient is unique, and many symptoms and diagnoses are inherently imprecise and difficult to measure. A systematic decision-making and optimization technology capable of handling all the clinical difficulties is still unavailable despite significant efforts documented in the literature, including the use of artificial intelligence and statistical methods. One promising approach is the novel fuzzy discrete event systems whose theoretical framework was recently developed by us. We apply it to treatment planning for HIV/AIDS patients who have never received antiretroviral therapy. We show how to design such a system. We have also statistically evaluated the preliminary results produced by the system in comparison with two AIDS specialists on our team. The results indicate strong agreement between the physicians and the fuzzy discrete event system. This is the first application of fuzzy discrete event systems in the literature.

Understanding the analytical structure of fuzzy controllers clears away the difficulties in analyzing the fundamental attributes of fuzzy controllers. This study focuses on some common fuzzy controllers and gives conditions for their structures to be equivalent to certain conventional controllers, especially nonlinear PI/PD controllers with variable gains. All the fuzzy controllers use Mamdani type of fuzzy rules, product fuzzy AND operator, singleton output fuzzy sets, and the centroid defuzzifier.

In this article, we propose a new approach to the virus DNA–based evolutionary algorithm (VDNA-EA) to implement self-learning of a class of Takagi-Sugeno (T-S) fuzzy controllers. The fuzzy controllers use T-S fuzzy rules with linear consequent, the generalized input fuzzy sets, Zadeh fuzzy logic and operators, and the generalized defuzzifier. The fuzzy controllers are proved to be nonlinear proportional-integral (PI) controllers with variable gains. The fuzzy rules are discovered automatically and the design parameters in the input fuzzy sets and the linear rule consequent are optimized simultaneously by the VDNA-EA. The VDNA-EA uses the VDNA encoding method that stemmed from the structure of the VDNA to encode the design parameters of the fuzzy controllers. We use the frameshift decoding method of the VDNA to decode the DNA chromosome into the design parameters of the fuzzy controllers. In addition, the gene transfer operation and bacterial mutation operation inspired by a microbial evolution phenomenon are introduced into the VDNA-EA. Moreover, frameshift mutation operations based on the DNA genetic operations are used in the VDNA-EA to add and delete adaptively fuzzy rules. Our encoding method can significantly shorten the code length of the DNA chromosomes and improve the encoding efficiency. The length of the chromosome is variable and it is easy to insert and delete parts of the chromosome. It is suitable for complex knowledge representation and is easy for the genetic operations at gene level to be introduced into the VDNA-EA. We show how to implement the new method to self-learn a T-S fuzzy controller in the control of a nonlinear system. The fuzzy controller can be constructed automatically by the VDNA-EA. Computer simulation results indicate that the new method is effective and the designed fuzzy controller is satisfactory. © 2003 Wiley Periodicals, Inc.

In order to make it possible to effectively represent deterministic uncertainties and vagueness as well as the human subjective observation and judgement inherent to many real-world problems, especially those in biomedicine, we introduce, in this paper, fuzzy states and fuzzy events and generalize (crisp) discrete event systems (DES) to fuzzy DES. The largely graph-based current framework of the crisp DES is unsuitable for the expansion, and we have thus reformulated it using state vectors and event transition matrices which can be extended to fuzzy vectors and matrices by allowing their elements to take values between 0 and 1. To measure information related to fuzzy DES, we generalize the crisp DES observability. The new observability allows one to determine whether or not the system output observed is sufficient for decision making. Finally, we extend the optimal control of DES to fuzzy DES. The new fuzzy DES theory is consistent with the existing theory, both at the conceptual and the computation levels, in that the former contains the latter as a special case when the memberships must be either 0 or 1. Numerical examples are provided to illustrate the theoretical development.

Laser thermal therapies have shown great promise for minimally invasive treatment of benign and malignant tissue lesions. The paper presents a time-varying fuzzy control laser system to control tissue temperature in fresh pig liver samples for coagulation at 65/spl deg/C and tissue welding at 85/spl deg/C. The technical difficulties of our study lie in two facts: (1) laser tissue heating is a highly nonlinear time-varying dynamic process, and (2) the output power of the 810 nm diode laser that we used is not adjustable during operation. We have overcome the difficulties by regulating the laser via a variable on-off signal sequence, which is computed, at each sampling time, by our nonlinear time-varying fuzzy controller. The structure of the fuzzy controller is analytically analyzed and the result is related to the PD controller. Our experiments using the fuzzy control system show that the average of the absolute values of the maximum temperature derivations for three coagulation experiments and three welding experiments is 0.45/spl deg/C and 2.90/spl deg/C, respectively.

Recent studies have shown that both Mamdani-type and Takagi-Sugeno-type fuzzy systems are universal approximators in that they can uniformly approximate continuous functions defined on compact domains with arbitrarily high approximation accuracy. In this paper, we investigate necessary conditions for general multiple-input single-output (MISO) Mamdani fuzzy systems as universal approximators with as minimal system configuration as possible. The general MISO fuzzy systems employ almost arbitrary continuous input fuzzy sets, arbitrary singleton output fuzzy sets, arbitrary fuzzy rules, product fuzzy logic AND, and the generalized defuzzifier containing the popular centroid defuzzifier as a special case. Our necessary conditions are developed under the practically sensible assumption that only a finite set of extrema of the multivariate continuous function to be approximated is available. We have first revealed a decomposition property of the general fuzzy systems: A r-input fuzzy system can always be decomposed to the sum of r simpler fuzzy systems where the first system has only one input variable, the second one two input variables, and the last one r input variables. Utilizing this property, we have derived some necessary conditions for the fuzzy systems to be universal approximators with minimal system configuration. The conditions expose the strength as well as limitation of the fuzzy approximation: (1) only a small number of fuzzy rules may be needed to uniformly approximate multivariate continuous functions that have a complicated formulation but a relatively small number of extrema; and (2) the number of fuzzy rules must be large in order to approximate highly oscillatory continuous functions. A numerical example is given to demonstrate our new results.

The Takagi-Sugeno (TS) fuzzy modeling technique, a black-box discrete-time approach for system identification, has widely been used to model behaviors of complex dynamic systems. The analytical structure of TS fuzzy models, however, is unknown, causing at two major problems. First, the fuzzy models cannot be utilized to design controllers of the physical systems modeled. Second, there is no systematic technique for designing a controller that is capable of controlling any given TS fuzzy model to achieve the desired tracking or setpoint control performance. In this paper, we provide solutions to these problems. We have proved that a general class of TS fuzzy models is a nonlinear time-varying ARX (Auto-Regressive with eXtra input) model. We have established a simple condition for analytically determining the local stability of the general TS fuzzy dynamic model. The condition can also be used to analytically check the quality of a TS fuzzy model and invalidate the model if the condition warrants. We have developed a feedback linearization technique for systematically designing an output tracking controller so that the output of a controlled TS fuzzy system of the general class achieves perfect tracking of any bounded time-varying trajectory. We have investigated the stability of the tracking controller and established a condition, in relation to the stability of non-minimum phase systems, for analytically deciding whether a stable tracking controller can be designed using our method for any given TS fuzzy system. Three numerical examples are provided to illustrate the effectiveness and utility of our results and techniques.

Both Takagi-Sugeno (TS) and Mamdani fuzzy systems are known to be universal approximators. We investigate whether one type of fuzzy approximators is more economical than the other. The TS fuzzy systems are the typical two-input single-output TS fuzzy systems. We first establish necessary conditions on minimal system configuration of the TS fuzzy systems as function approximators. We show that the number of the input fuzzy sets and fuzzy rules needed by the TS fuzzy systems depend on the number and locations of the extrema of the function to be approximated. The resulting conditions reveal the strength of the TS fuzzy approximators. The drawback, though, is that a large number of fuzzy rules must be employed to approximate periodic or highly oscillatory functions. We then compare these necessary conditions with the ones that we established for the general Mamdani fuzzy systems in our previous papers. Results of the comparison unveil that the minimal system configurations of the TS and Mamdani fuzzy systems are comparable. Finally, we prove that the minimal configuration of the TS fuzzy systems can be reduced and becomes smaller than that of the Mamdani fuzzy systems if nontrapezoidal or nontriangular input fuzzy sets are used. We believe that all the results in present paper hold for the TS fuzzy systems with more than two input variables but the proof seems to be mathematically difficult. Our new findings are valuable in designing more compact fuzzy systems, especially fuzzy controllers and models which are two most popular and successful applications of the fuzzy approximators.

We investigated the analytical structure of the Takagi-Sugeno (TS) type of fuzzy controllers, which was unavailable in the literature. The TS fuzzy controllers we studied employ a new and simplified TS control rule scheme in which all the rule consequent use a common function and are proportional to one another, greatly reducing the number of parameters needed in the rules. Other components of the fuzzy controllers are general: arbitrary input fuzzy sets, any type of fuzzy logic, and the generalized defuzzifier, which contains the popular centroid defuzzifier as a special case. We proved that all these TS fuzzy controllers were nonlinear variable gain controllers and characteristics of the gain variation were parametrized and governed by the rule proportionality. We conducted an in-depth analysis on a class of nonlinear variable gain proportional-derivative (PD) controllers. We present the results to show: (1) how to analyze the characteristics of the variable gains in the context of control; (2) why the nonlinear variable gain PD controllers can outperform their linear counterpart; and (3) how to generate various gain variation characteristics through the manipulation of the rule proportionality.

Takagi-Sugeno (TS) fuzzy systems have been employed as fuzzy controllers and fuzzy models in successfully solving difficult control and modeling problems in practice. Virtually all the TS fuzzy systems use linear rule consequent. At present, there exist no results (qualitative or quantitative) to answer the fundamentally important question that is especially critical to TS fuzzy systems as fuzzy controllers and models, "Are TS fuzzy systems with linear rule consequent universal approximators?" If the answer is yes, then how can they be constructed to achieve prespecified approximation accuracy and what are the sufficient renditions on systems configuration? In this paper, we provide answers to these questions for a general class of single-input single-output (SISO) fuzzy systems that use any type of continuous input fuzzy sets, TS fuzzy rules with linear consequent and a generalized defuzzifier containing the widely used centroid defuzzifier as a special case. We first constructively prove that this general class of SISO TS fuzzy systems can uniformly approximate any polynomial arbitrarily well and then prove, by utilizing the Weierstrass approximation theorem, that the general TS fuzzy systems can uniformly approximate any continuous function with arbitrarily high precision. Furthermore, we have derived a formula as part of sufficient conditions for the fuzzy approximation that can compute the minimal upper bound on the number of input fuzzy sets and rules needed for any given continuous function and prespecified approximation error bound, An illustrative numerical example is provided.

We have constructively proved a general class of multi-input single-output Takagi-Sugeno (TS) fuzzy systems to be universal approximators. The systems use any types of continuous fuzzy sets, fuzzy logic AND, fuzzy rules with linear rule consequent and the generalized defuzzifier. We first prove that the TS fuzzy systems can uniformly approximate any multivariate polynomial arbitrarily well, and then prove they can also uniformly approximate any multivariate continuous function arbitrarily well. We have derived a formula for computing the minimal upper bounds on the number of fuzzy sets and fuzzy rules necessary to achieve the prespecified approximation accuracy for any given bivariate function. A numerical example is furnished. Our results provide a solid-theoretical basis for fuzzy system applications, particularly as fuzzy controllers and models.