The diseases in glands of human bodies have been increased with high rate in the last decade. Thyroid is one of these glands that its disease has spread worldwide. The main function of thyroid gland is to balance the metabolism and cells' activity. Since it does its own task abnormally, thyroid disorders will occur and the negligence of them may cause irreparable events. Because of inaccessibility of Endocrinologist experts for most people, modeling and developing an expert system for diagnosis thyroid's disease that can be accessible in everywhere is vital. This paper presents a fuzzy rule-based expert system for diagnosis thyroid's disease. This proposed system includes three steps: pre-processing (feature selection), neuro-fuzzy classification and system evaluating. In the proposed system, the process of diagnosis encounters with vagueness and uncertainty in final decision. So, we handled the imprecise knowledge by using fuzzy logic. In neuro-fuzzy classification step, we generated initial fuzzy rules by k-means algorithm and then scaled conjugate gradient algorithm (SCG) was used to determine the optimum values of parameters. In the last step, we used the generated fuzzy rules to model and evaluate the system. This system can help non-experts who are suspicious of their thyroid function or it can be used as a diagnosis assistance system to help experts for assuring their diagnosis.

This paper presents a multi agent system which can help type 2 diabetic patients. Because of diabetes nature, medical care and lifestyle can both prevent the complications of this illness, so self-managing is very crucial for these patients. Therefore, each effective factor of controlling diabetes and increasing patients' knowledge including: suitable diet and monitoring blood glucose level, is assigned to be an agent which works independently whilst coordinates and cooperates with other agents. The proposed architecture of this multi agent system organizes all the various agents of this system in a way that not only each of them can accomplish their responsibility, but also they can have effective interaction with other agents. This designed system has the ability to develop a model that can be easily used by patients suffering from type 2 diabetes.

Osteomyelitis is an infection of the bone that leads to tissue destruction and often to debility. Early diagnosis of infection is critical, as prompt antibiotic treatment reduces the rate of amputation. Vascular insufficiency and lack of sensation predispose diabetic patients to foot infection that can lead to bone infection. Magnetic Resonance Imaging (MRI) has been shown to be capable of revealing primary marrow abnormalities with improved specificity comparing to other imaging options [1]. There will be an inevitable degree of variability in image interpretation as long as it relies on human visual perception. Therefore, tools that automate pattern recognition and image analysis can support clinical decision-making and may reduce this variability. The proposed system can be used as a basis for the computer-assisted radiology of diabetic foot infection. This paper presents a system for detecting the toe bones in axial diabetic foot MRI and categorizing them. The first aim of the system is to detect the toe bones using segmentation and filtering criteria. Detecting criteria are selected based on the experience of previous diagnoses and medical research in the area. Afterwards, the bag of feature approach is used to categorize the detected toe bones as infected, not infected or noise. For this purpose, we construct the visual vocabulary by clustering features that are extracted from a set of training images and use them to train multiclass linear support vector machine classifier for each of the three categories.

Stock price prediction is an important task for most investors and professional analysts. However, it is a tough problem because of the uncertainties involved in prices. This paper presents a four-layer fuzzy multiagent system (FMAS) architecture to develop a hybrid artificial intelligence model based on the coordination of intelligent agents performing data preprocessing and function approximation tasks for next-day stock price prediction. The first layer is dedicated to metadata creation. The second layer is aimed at data preprocessing using stepwise regression analysis and self-organizing map neural network clustering for modularizing prediction problems. The third layer is aimed at model building for each cluster using genetic fuzzy systems and evaluating built models to choose the best evolved fuzzy system for each cluster. Finally, the fourth layer provides model analysis and knowledge presentation. The capability of FMAS is evaluated by applying it on stock price data gathered from IT and airline sectors and comparing the outcomes with the results of other methods. The results show that FMAS outperforms all previous methods, so it can be considered as a suitable tool for stock price prediction problems. © 2012 Wiley Periodicals, Inc. © 2012 Wiley Periodicals, Inc.

Organizations have to be competitive in their market throughout the globalization process. Thus, they need to achieve customer demands in strategic ways focusing on customer satisfaction. At this point, decision makers encounter with uncertainties based on reducing the deviation in the production/service processes. The uncertainty problem of supplier selection for a Turkish Machinery Industry Corporation will be discussed in this paper. The uncertainty due to the subjective assessment used in supplier selection will be modeled by fuzzy logic. The structure identification of supplier selection system will be modeled with fuzzy functions. Comparisons of fuzzy functions and membership functions based on uncertainty problem of supplier selection system will be discussed.

Location Set Covering Problem (LSCP) is a traditional problem in the location literature. LSCP is used in locating fire stations, computer networks, and many other service facilities. This paper proposes a covering problem with variable radii. In this problem, the cost to establish a facility is a monotonically increasing function of distance to the farthest covered node by the facility. The problem is to cover all the demand nodes with the least total cost, where the number, location, coverage radii and the assignment of demands to facilities should be determined. Here, the travel times between nodes are considered to be fuzzy variables. A combination of fuzzy simulation and Simulated Annealing (SA) is proposed in order to solve this problem and a numerical example is given for validation of the proposed model.

Fuzzy functions are used to identify the structure of system models and reasoning with them. Fuzzy functions can be determined by any function identification method such as Least Square Estimates (LSE), Maximum Likelihood Estimates (MLE) or Support Vector Machine Estimates (SVM). However, estimating fuzzy functions using LSE method is structurally a new and unique approach for determining fuzzy functions. By using this approach, there is no need to know or to develop an in-depth understanding of essential concepts for developing and using the membership functions and selecting the t-norms, co-norms and implication operators. Furthermore, there is no need to apply fuzzification and defuzzification methods. The goal of this paper is to improve the Type-2 fuzzy image processing expert system based on Type-2 fuzzy function to diagnose the Astrocytoma tumors (most important category of brain tumors) in T1-weighted MR Images with contrast. This expert system has four steps, Pre-processing, Segmentation, Feature extraction and Approximate reasoning. The focus of this paper is to improve the last step, Approximate reasoning step, by using fuzzy function strategy instead of fuzzy rule-base approach. The results show that Type-2 fuzzy function approach requires less computation steps with less computational complexity and could provide better results.

The fuzzy C-regression Method (FCRM) based on fuzzy C-means (FCM) clustering algorithm was proposed by Hathaway and Bezdek to solve the switching regression problems, and it was applied to fuzzy models by many to build more powerful fuzzy inference systems. The FCRM methods require initialization parameters which are in need for proper identification, since uncertain information can create imperfect expressions, which may hamper the predictive power of these models. This paper investigates the behavior of the FCRM models under uncertain parameters. The upper and lower bounds of the membership values can be identified based on the limits of level of fuzziness parameter around the certain information points such as local functions and ensemble point values. This is a further step to identify the footprint-of-uncertainty of membership values when FCRM is used. It is shown that the uncertainty of membership values induced by the level of fuzziness parameter can be identified based on first order approximations of the membership value calculation function.

Although traditional fuzzy models have proven to have high capacity of approximating the real-world systems, they have some challenges, such as computational complexity, optimization problems, subjectivity, etc. In order to solve some of these problems, this paper proposes a new fuzzy system modeling approach based on improved fuzzy functions to model systems with continuous output variable. The new modeling approach introduces three features: i) an improved fuzzy clustering (IFC) algorithm, ii) a new structure identification algorithm, and iii) a nonparametric inference engine. The IFC algorithm yields simultaneous estimates of parameters of c-regression models, together with fuzzy c-partitioning of the data, to calculate improved membership values with a new membership function. The structure identification of the new approach utilizes IFC, instead of standard fuzzy c-means clustering algorithm, to fuzzy partition the data, and it uses improved membership values as additional input variables along with the original scalar input variables for two different choices of regression methods: least squares estimation or support vector regression, to determine ldquofuzzy functionsrdquo for each cluster. With novel IFC, one could learn the system behavior more accurately compared to other FSM models. The nonparametric inference engine is a new approach, which uses the alike -nearest neighbor method for reasoning. Empirical comparisons indicate that the proposed approach yields comparable or better accuracy than fuzzy or neuro-fuzzy models based on fuzzy rules bases, as well as other soft computing methods.

This paper introduce a type-2 fuzzy function system for uncertainty modeling using evolutionary algorithms (ET2FF). The type-1 fuzzy inference systems (FISs) with fuzzy functions, which do not entail if ... then rule bases, have demonstrated better performance compared to traditional FIS. Nonetheless, the performance of these approaches is usually affected by their uncertain parameters. The proposed method implements a three-phase learning strategy to capture the uncertainties in fuzzy function systems induced by learning parameters, as well as fuzzy function structures. The improved fuzzy clustering initially finds hidden structures, and the genetic learning algorithm optimizes interval type-2 fuzzy sets to capture their optimum uncertainty interval. The proposed ET2FF architecture is evaluated using an extensive suite of real-life applications such as manufacturing process and financial market modeling. The results show that the proposed ET2FF method is comparable--if not superior--to earlier FIS in terms of generalization performance and robustness.

In this paper, a type-2 Fuzzy Rule Based Expert System is developed for analysing the stock markets. Interval type-2 fuzzy logic system permits us to model rule uncertainties and every membership value of an element is interval itself. The proposed type-2 fuzzy model applies the technical and fundamental indexes as the input variables. The fuzzy rule based model is tested on the stock market of an automotive manufactory in Asia. The proposed model can forecast the stock price variation. This can help the investors the select the best portfolio.

This paper presents a new Evolutionary Fuzzy System Modeling strategy alternative to Fuzzy Rule Bases, and does not entail if…then rule base structure. The new approach, which is based on Improved Fuzzy Functions with Genetic algorithms, is proposed to reduce complexity of earlier fuzzy system models and improve modeling accuracy. Structure identification of the new approach is based on a supervised Improved Fuzzy Clustering (IFC) method with a dual optimization algorithm, which yields improved membership values. The merit of the proposed FSM is that uncertain information on natural grouping of data samples, i.e., membership values, is utilized as additional predictors while structuring fuzzy functions. Presented model is applied to desulphurization process of a steel company in Canada. It is shown that proposed approach is superior in comparison to earlier fuzzy, neuro-fuzzy, and non-fuzzy system models in terms of robustness and error reduction.

Fuzzy system modeling (FSM) is one of the most prominent tools that can be used to identify the behavior of highly nonlinear systems with uncertainty. Conventional FSM techniques utilize type 1 fuzzy sets in order to capture the uncertainty in the system. However, since type 1 fuzzy sets express the belongingness of a crisp value$x^{\prime}$of a base variable$x$in a fuzzy set$A$by a crisp membership value$\mu_{A} (x^{\prime})$, they cannot fully capture the uncertainties due to imprecision in identifying membership functions. Higher types of fuzzy sets can be a remedy to address this issue. Since, the computational complexity of operations on fuzzy sets are increasing with the increasing type of the fuzzy set, the use of type 2 fuzzy sets and linguistic logical connectives drew a considerable amount of attention in the realm of fuzzy system modeling in the last two decades. In this paper, we propose a black-box methodology that can identify robust type 2 Takagi–Sugeno, Mizumoto and Linguistic fuzzy system models with high predictive power. One of the essential problems of type 2 fuzzy system models is computational complexity. In order to remedy this problem, discrete interval valued type 2 fuzzy system models are proposed with type reduction. In the proposed fuzzy system modeling methods, fuzzy C-means (FCM) clustering algorithm is used in order to identify the system structure. The proposed discrete interval valued type 2 fuzzy system models are generated by a learning parameter of FCM, known as the level of membership, and its variation over a specific set of values which generate the uncertainty associated with the system structure.

This paper addresses the bullwhip effect in a multi-stage supply chain, where all demands, lead times, and ordering qualities are fuzzy. To simulate the bullwhip effect, a modified Hong Fuzzy Time Series, by adding a GA module for gaining of window basis, is presented. Next, a back propagation neural network is used for defuzzification. The model can forecast the trends of fuzzy data. To minimize the total cost and reduce the bullwhip effect, an agent-based system is developed. The system can propose the reasonable ordering policies. The results show that the proposed system is superior than the previous analytical methods in terms of discovering the best available ordering policies.

One of the sources of uncertainty, which perhaps is identified as parameter uncertainty, is the level of fuzziness in fuzzy system modeling. Given the optimum number of clusters and the cluster centers, one can explore type-2 membership values that capture the uncertainty of memberships. We explore variations of type-2 membership values with the entropy measure for an artificially created 12 data sets. Crisp to fuzzy data sets are constructed so that each data set has a different standard deviation within each cluster. In turn, each cluster has the same standard deviation for a given artificial data set. Members of a given artificial data set are generated randomly. Results are assessed by means of a particular entropy measure. It is shown that the content of the information uncertainty increases in certain ranges and decreases in other ranges of the level of fuzziness.

A schema for the investigation of the philosophical grounding of fuzzy theory is proposed. In particular, the ontological grounding is investigated. It is shown that certain equivalences that exist in classical theory break down in fuzzy theory. In turn, this leads to the generation of new formulas and the laws of conservation fuzzy theory.

Feature selection is one of the most important issues in fields such as system modelling and pattern recognition. In this study, a new feature selection algorithm that combines feature wrapper and feature filter approaches is proposed in order to identify the significant input variables in systems with continuous domains. The proposed method utilizes functional dependency concept and k-nearest neighbourhood method to implement the feature filter and feature wrapper, respectively. It is common to have outliers and noise in real-life data. In order to make the proposed feature selection algorithm noise and outlier resistant, approximate functional dependencies are used by utilizing membership values that inherently cope with uncertainty in the data.

Belief (Bel), plausibility (Pl), and probability (P) measures can be formulated on interval-valued type 2 fuzzy sets with their representation in terms of α-level (crisp) sets. Recently, it was shown that interval-valued type 2 fuzzy sets naturally arise with modified and restricted multivalued maps of Dempster. An analogy to Dempster's upper and lower probabilities, upper and lower beliefs, and Pl and P measures can be determined over interval-valued type 2 fuzzy sets. It is shown that the application of appropriate t-norms over α-values of α-level crisp sets in combination with the axiom of Bel measure entails appropriate weights for the overlapping α-level (crisp) set conjunctions where Bel measure is applicable. © 2004 Wiley Periodicals, Inc.

Dempster, Pawlak, and Turksen schema can be re-structured to generate interval-valued Type 2 fuzzy sets, with suitable modifications to Dempster's multi-valued maps and Pawlak's rough sets. In this restructuring, we investigate Turksen's interpretation of Zadeh's CWW that generate interval-valued Type 2 fuzzy sets. First, it can be shown that there is a natural transformation between Dempster's and Pawlak's construction schemas. Secondly, Dempster's and Pawlak's upper set formulation schema is modified. Thirdly, multi-valued maps are restricted to a special well known subset of information granules. This modification and restriction forms the "Dempster-Pawlak-Zadeh" unification (Turksen, 2001). With this unification, we generate FDCF and FCCF expressions for concept combinations in Zadeh's CWW with the application of linguistic operators such as "AND", "OR", etc. Finally, it is proposed that the combinations of concepts formulated in this manner be a formulation for the CWW.

In this paper a k-nearest neighborhood based fuzzy reasoning is introduced. The proposed approach is necessary in order to estimate the firing degree of each rule for a fuzzy if-then rule base where the antecedent is an n-dimensional vector. The proposed methodology is applied to well known Box and Jenkins gas-furnace data and compared with two other algorithms. The first algorithm is the slightly modified version of the well-known Sugeno-Yasukawa (1993) methodology proposed by Turksen, Bazoon et al. (1997), and the second algorithm is the adaptive network-based fuzzy inference schema proposed by Jang (1996). The test data prediction RMSE's obtained from the gas-furnace data is 1.03 for Turksen-Bazoon approach, 0.52 for ANFIS and 0.43 for the proposed algorithm.

CWW, computing with words, is enriched by upper and lower membership functions. Upper and lower membership functions are the bounds identified by interval valued Type-2 fuzziness. Interval-valued Type-2 representation and reasoning exists in membership acquisition and in combination of linguistic concepts. Upper and lower membership functions capture both imprecision and uncertainty associated with meaning in CWW. A much more rich meaning of words can be represented and reasoned with when we use Full Type-2 membership functions. In Full Type-2 representation and reasoning, degrees of uncertainty are captured as well as their bounds. But this entails a more complex representation and reasoning.

A new fuzzy system modeling approach that uses an inference mechanism working in the input-output space is proposed. The new inference mechanism eliminates the need to identify the membership functions on each separate system variable axis and avoids the problems due to the projection step of some popular fuzzy system modeling approaches. In the new method, inputs and outputs are first clustered together by means of the fuzzy c-means (FCM) algorithm, with several levels of fuzziness, m, and numbers of clusters, c. Instead of a cluster validity index, the system output error is used as our performance index while selecting the best (m,c) pairs. Then, a modified version of the classical simulated annealing algorithm is used to identify the relative weights of the system input variables.

The expressions of "excluded middle" and "crisp contradiction" are reexamined starting with their original linguistic expressions which are first restated in propositional and then predicate forms. It is shown that, in order to generalize the truth tables and hence the normal forms, the membership assignments in predicate expressions must be separated from their truth qualification. In two-valued logic, there is no need to separate them from each other due to reductionist Aristotalean dichotomy. Whereas, in infinite (fuzzy) valued set and logic, the separation of membership assignments from their truth qualification forms the bases of a new reconstruction of the truth tables. The results obtained from these extended truth tables are reducible to their Boolean equivalents under the axioms of Boolean theory. Whereas, in fuzzy set and logic theory, we obtain a richer and more complex interpretations of the "fuzzy middle" and "fuzzy contradiction."

This paper presents a fuzzy-logic control structure, containing the fuzzy-logic model of the dynamic system and fuzzy control rules that ensure the stability and robust performance. The robust fuzzy rules are designed based on a generalized formulation of sliding mode control for a class of nonlinear multi-input multi-output systems. The proposed fuzzy-logic control scheme was applied to the trajectory control of a four-degree-of-freedom robot, and compared with the high-gain PID controllers. A superior tracking performance was achieved.

A systemic approach of fuzzy-logic modeling from the system input-output data is applied to modeling dynamics behavior of a four degree-of-freedom robot manipulator. The output of the fuzzy model is compared with the experimental data and with that of an analytical simulation. The simplicity of the fuzzy model and its improved accuracy is significant.

The proposed fuzzy data mining and expert system approach has two main modules: knowledge representation and approximate reasoning. The knowledge representation module is based on a modified fuzzy c-means (FCM) algorithm which is an extension of classical FCM algorithm in several respects. Hence, knowledge representation is developed with an unsupervised learning with respect to a given input-output data set. The approximate reasoning module contains four reasoning parameters that are subject to supervised learning for a given input-output data set and error minimization criteria.

This paper proposes a systematic methodology of fuzzy logic modeling for complex system modeling. It has a unified parameterized reasoning formulation, an improved fuzzy clustering algorithm, and an efficient strategy of selecting significant system inputs and their membership functions. The reasoning mechanism introduces 4 parameters whose variation provides a continuous range of inference operation. As a result, we are no longer restricted to standard extremes in any step of reasoning. The fuzzy model itself can then adjust the reasoning process by optimizing the inference parameters based on input-output data. The fuzzy rules are generated through fuzzy c-means (FCM) clustering. Major bottlenecks are addressed and analytical solutions are suggested. We also address the classification process to extend the derived fuzzy partition to the entire output space. In order to select suitable input variables among a finite number of candidates (unlike traditional approaches) we suggest a new strategy through which dominant input parameters are assigned in one step and no iteration process is required. Furthermore, a clustering technique called fuzzy fine clustering is introduced to assign the input membership functions. In order to evaluate the proposed methodology, two examples-a nonlinear function and a gas furnace dynamic procedure-are investigated in detail. The significant improvement of the model is concluded compared to other fuzzy modeling approaches.

Turksen's (1995, 1986) fuzzy normal forms and Kandel et al.'s (1995) and Schwede and Kandel's (1977) fuzzy maps are unified to establish universal truth tables and normal forms. After an introduction to the topic, we start out with a discussion on linguistic assertions. Next, we develop a new universal truth table construction in order to generate normal forms for both the 16 main concepts of two variables, as well as the subconcepts that can be generated from them. It is shown how fuzzy propositional and fuzzy predicate expressions can be generated with the universal truth table construction. Furthermore, it is shown that the laws of conservation hold in a general way on the "fuzzified laws of exclude middle and contradiction" generated by the class of t norms and their dual t conorms.

A heuristically derived stabilization strategy for an unstable and unintuitive plant by fuzzy control is described. It is shown that the often used classical fuzzy controller, which is both static and time invariant, is incapable of stabilizing such types of plants. However, a simple modification to the classical fuzzy controller architecture that separates the measurement and control phases, together with a hierarchical control strategy, enable the unstable and unintuitive plant to be stabilized. The fuzzy control strategy, as well as the new fuzzy controller architecture, are based on the consideration of "what a human subject would do when dealing with a physical plant which is both unstable and unintuitive". The stabilization strategy is then generalized to other mathematically similar systems. While the rules for the stabilization of the plant are heuristically defined, the membership functions associated with the rules are tuned by a simulated annealing procedure.

Issues of rule search in fuzzy expert systems are investigated. Computation of overall similarity measure (OSM) is studied between a system observation and the left hand side of a rule for a class of T-similarity measure (SM) models. It is shown that for an n-antecedent system, if the connective AND in both the left hand side of a rule and a system observation is taken to be a t-norm operator which is the same t-norm operator used in the T-similarity measure model, then the OSM can be obtained by: 1) computing the SM between the linguistic term of an antecedent variable in the rule and the observation of the corresponding antecedent variable separately for each of the antecedent variables in the rule, and 2) combining all of these SMs using the t-norm operator. Thus, one avoids the computation of the OSM via the n-dimensional matrix operations. Based on an analysis of the relationship between the OSM and SMs for an n-antecedent system, a search scheme, called two-level tree search, is proposed as opposed to an exhaustive search to save search cost associated with the computation of the OSM. Computational complexity is analyzed for both the exhaustive and the two-level tree search schemes.>

We propose a new approach that integrates syllogistic reasoning and knowledge-base consistency level maintenance based on the framework of multi-objective decision-making. Syllogistic reasoning is formulated as a maximization process of the degree to which a priori inference rules (i.e., the prior knowledge) are compatible with given data (i.e., the empirical knowledge) while simultaneously using the rules to make inference from the data. Our method estimates the default values of missing membership values in the observed data, and, at the same time, the evaluation of the consistency degree of the prior knowledge is computed with the empirical knowledge. The unique feature of our method is the feedback capability of the empirical knowledge through the evaluation process in determining the most preferable default value. In contrast to the traditional inference methods that concentrates on the estimation part of the problem, leaving the evaluation part for some other "learning mechanism", our method treats the dynamic interaction process between prior and empirical knowledge based on the multi-objective consistency maximization.>

To provide confidence in a rule generation and reduction scheme, it is necessary to show an equivalence between at least two alternative approaches that provide the same reduced rule sets. For this purpose we present two rule reduction schemes in fuzzy knowledge based systems. These two schemes are based on: (1) a pseudo-Boolean analysis, and (2) the ID3 algorithm. Here, we show an equivalence between these two rule reduction schemes. As a consequence of this equivalence, we propose to substitute an online and automated expert system shell that uses the ID3 algorithm in place of the manual pseudo-Boolean simplification method for the purposes of rule reduction in fuzzy knowledge bases. For both approaches, we assign pseudo-Boolean variables to the intervals, identified as semantic intervals, on the base-axis of a membership representation. The pseudo-Boolean simplification of disjunctions of conjunctions formulae (DCF) is efficiently learnable from examples in the sense of Valiant (1984, 1985). Positive and negative examples are provided to illustrate that the equivalence holds for all nonnull nodes in decision trees under the condition of extending all the examples to possible attribute combinations. This approach supports an interactive learning environment for the design of fuzzy expert systems where a rule reduction algorithm constitutes an important component of the design process. Another important component is a rule generation algorithm. Two illustrative experiments are provided to demonstrate the rule generation and reduction.>

An approximate analogical reasoning schema (AARS) which exhibits the advantages of fuzzy set theory and analogical reasoning in expert systems development is described. The AARS avoids going through the conceptually complicated compositional rule of inference. It uses a similarity measure of fuzzy sets as well as a threshold to determine whether a rule should be fired and a modification function inferred from a similarity measure to deduce a consequent. Some numerical examples to illustrate the operation of the schema are presented. Finally, the proposed schema is compared with conventional expert systems and existing fuzzy expert systems.>

A new approach, i.e. the view through the fuzzy normal forms is presented that differs from previous approaches. The authors' concern is based on the fact that the implication as well as other connectives are linguistic entities that are inescapably associated with fuzziness. They are interested in the manner in which they introduce, or rather, add fuzziness into the statement in which they are included. New insight is brought into the structure of the `generalized modus ponens by their representation'.