Graph neural networks (GNNs) excel in various graph-based tasks due to their exceptional ability to process non-Euclidean data. However, recent research indicates that their predictive performance is highly vulnerable to perturbations from intentionally manipulated data. Current node injection attack methods disrupt GNN training by injecting numerous nodes, often in excessive amounts, making them easily detectable. To address this issue, this study introduces a structure-aware node injection attack (SNIA), which enables effective and subtle attacks under extreme budget constraints. The scheme leverages the network topology to construct an attack candidate set and applies homogeneity constraints to regulate the generation of perturbed features. By eliminating the dependency on surrogate models for generating perturbed data, SNIA effectively diminishes the global classification performance of GNNs based on the network's inherent structure. We conducted attack experiments with the SNIA scheme on real-world network datasets against both general and defensive GNNs. The experimental findings reveal that it significantly surpasses the existing state-of-the-art methods in attack efficiency, while also showcasing outstanding generalization and resilience.

Accurately identifying influential nodes in complex networks is crucial for understanding their structure and dynamics. Traditional methods for measuring node centrality often struggle to capture the inherent uncertainties in node relationships and to model specific higher-order interaction patterns, limiting their reliable evaluations in hypergraph contexts. To address this challenge, we propose a novel approach called Fuzzy Multi-Hierarchical Centrality (FMHC), which integrates fuzzy theory with multi-hierarchical topological analysis for centrality assessment in hypergraphs. By synthesizing inter-node fuzzy distances, node-to-edge fuzzy membership degrees, and mutual information associations among nodes and edges, FMHC constructs a multi-hierarchical evaluation architecture to generate comprehensive and discriminative importance scores for each node. Extensive experiments on nine real-world datasets demonstrate that FMHC consistently outperforms eight classical and state-of-the-art benchmarks across three key evaluation criteria: the capacity to identify nodes with high spreading influence, alignment with the Susceptible-Infected-Recovered (SIR) epidemic model, and monotonicity in ranking discrimination. These findings validate the effectiveness, robustness, and superiority of FMHC in hypergraph environments.

Emotion recognition in conversation is essential for achieving intelligent human-robot interaction (HRI). Accurate emotional understanding allows robots to engage in more natural and context-aware interactions with users. A novel graph reinforcement representation architecture (RGATN) is proposed for emotion recognition in HRI. The RGATN aims to analyze multi-modal conversational information to infer users' emotional states during interaction. Specifically, the architecture integrates a residual graph network (Res-GN) and a cross-modal graph channel attention network (CM-GCA). The Res-GN is proposed to efficiently represents information by reducing redundancy in fully connected graphs and incorporating all potential connectivity relationships. To address the inconsistencies in the quality of different modalities in HRI scenarios, the CM-GCA mechanism is presented. This mechanism preserves information from each modality while reconstructing and enhancing the overall graph representation by leveraging the adaptive cross-modal channel attention. The proposed method improves emotion recognition accuracy and robustness in HRI. We evaluated the method on three benchmark datasets, including IEMOCAP, MELD and M$^{3}$ED, achieving weighted F1-score of 72.07%, 67.99% and 53.16%, respectively. Additionally, preliminary application experiments conducted on a self-built database demonstrated a recognition accuracy of 78.75%. The results highlight the ability to effectively adapt to inconsistent modal quality, further confirming its effectiveness in real-world HRI scenarios.

A multibranch adaptive graph convolutional network is proposed for human action recognition by combining graph convolutional networks (GCNs), adaptive learning, and multibranch feature extraction. Through the adaptive graph convolution module, this method can adaptively change parameters during the training process, thereby enhancing the flexibility of the model. Furthermore, the integration of shallow-level features (skeleton joints), with deep-level features including skeleton information, motion information, and motion difference information allows our model to capture both spatial and temporal dynamics of human actions, leading to a more comprehensive representation of human action features. The introduction of the spatio-temporal attention mechanism enables our model to focus on key frames and skeleton joints. The attitude correction module makes the input data to the network more reasonable and reduces the interference of noise. The inclusion of the adaptive mechanism makes the network no longer limited to the inherent physical connections, and the flexibility of the network is enhanced. The addition of second-order features makes the features of the skeletal data fully exploited. This attention mechanism enhances the discriminative ability of the model and improves its ability to recognize subtle variations and important cues in human actions. Through experiments on benchmark datasets, NTU-RGB-D and Kinetics-400, our method achieves significant improvements in action recognition performance compared with existing approaches. On the Kinetics-400 dataset, we achieved 36.5% and 59.6% recognition rates under the Top-1 and Top-5 evaluation metrics, respectively, which is an improvement of about 1% compared with the state-of-the-art method. On the NTU-RGB-D dataset, we achieved 95.8% and 89.4% recognition rates under the X-view and X-subject modes, respectively, with excellent results. These results validate the effectiveness of the multi-branch adaptive graph convolutional network for human action recognition tasks.

A multiscale sequence information fusion (MSSIF) method is presented for dynamic facial expression recognition (DFER) in video sequences. It exploits multiscale information by integrating features from individual frames, subsequences, and entire sequences through a transformer-based architecture. This hierarchical feature fusion process includes deep feature extraction at the frame level to capture intricate visual details, intrasubsequence fusion using self-attention mechanisms for analyzing adjacent frames, and intersubsequence fusion to synthesize long-term emotional dynamics across time scales. The efficacy of MSSIF is demonstrated through extensive evaluation on three video datasets: eNTERFACE'05, BAUM-1s, and AFEW, where it achieves overall recognition accuracies of 60.1%, 60.7%, and 58.8%, respectively. These results substantiate MSSIF's superior performance in accurately recognizing facial expressions by managing short and long-term dependencies within video sequences, making it a potent tool for real-world applications requiring nuanced dynamic facial expression detection.

An original attention-based indoor scene recognition model combining local and global features is proposed. Multi-strategy data augmentation using several different functions and intensities can improve the classification performance. Then, local features are extracted using a convolutional layer and a single self-attention, thus solving the problem of large intra-class variance. The multi-attention mechanism is used to fuse the local feature information extracted from different foci to obtain a more complete global feature representation. The multi-head attention mechanism allows the network to extract features in parallel in different directions of attention, which helps the network to better capture global information, improves the network's ability to understand and represent the input data, and solves the problem of high inter-class similarity. Finally, the extracted features are fed into the classifier to complete the classification of indoor scene images. Experiments are conducted on four data sets (IndoorCVPR09, SUN397, 15-Scenes and self-built small sample scientific indoor scene dataset), yield excellent results. The results show that the developed algorithm effectively solves the two problems of high intra-class diversity and high inter-class similarity. As a result, the model has achieved competitive results. Preliminary application experiments are developed in our HRI system, indicating that the proposed indoor scene recognition model can be applied to the complete environmental perception in HRI.

A coupled multimodal emotional feature analysis (CMEFA) method based on broad-deep fusion networks, which divide multimodal emotion recognition into two layers, is proposed. First, facial emotional features and gesture emotional features are extracted using the broad and deep learning fusion network (BDFN). Considering that the bi-modal emotion is not completely independent of each other, canonical correlation analysis (CCA) is used to analyze and extract the correlation between the emotion features, and a coupling network is established for emotion recognition of the extracted bi-modal features. Both simulation and application experiments are completed. According to the simulation experiments completed on the bimodal face and body gesture database (FABO), the recognition rate of the proposed method has increased by 1.15% compared to that of the support vector machine recursive feature elimination (SVMRFE) (without considering the unbalanced contribution of features). Moreover, by using the proposed method, the multimodal recognition rate is 21.22%, 2.65%, 1.61%, 1.54%, and 0.20% higher than those of the fuzzy deep neural network with sparse autoencoder (FDNNSA), ResNet-101 + GFK, C3D + MCB + DBN, the hierarchical classification fusion strategy (HCFS), and cross-channel convolutional neural network (CCCNN), respectively. In addition, preliminary application experiments are carried out on our developed emotional social robot system, where emotional robot recognizes the emotions of eight volunteers based on their facial expressions and body gestures.

Convolutional feature-based broad learning with long short-term memory (CBLSTM) is proposed to recognize multidimensional facial emotions in human–robot interaction. The CBLSTM model consists of convolution and pooling layers, broad learning (BL), and long- and short-term memory network. It aims to obtain the depth, width, and time scale information of facial emotion through three parts of the model, so as to realize multidimensional facial emotion recognition. CBLSTM adopts the structure of BL after processing was done at the convolution and pooling layer to replace the original random mapping method and extract features with more representation ability, which significantly reduces the computational time of the facial emotion recognition network. Moreover, we adopted incremental learning, which can quickly reconstruct the model without a complete retraining process. Experiments on three databases are developed, including CK+, MMI, and SFEW2.0 databases. The experimental results show that the proposed CBLSTM model using multidimensional information produces higher recognition accuracy than that without time scale information. It is 1.30% higher on the CK+ database and 1.06% higher on the MMI database. The computation time is 9.065 s, which is significantly shorter than the time reported for the convolutional neural network (CNN). In addition, the proposed method obtains improvement compared to the state-of-the-art methods. It improves the recognition rate by 3.97%, 1.77%, and 0.17% compared to that of CNN-SIPS, HOG-TOP, and CMACNN in the CK+ database, 5.17%, 5.14%, and 3.56% compared to TLMOS, ALAW, and DAUGN in the MMI database, and 7.08% and 2.98% compared to CNNVA and QCNN in the SFEW2.0 database.

The advent of the fourth industrial revolution along with developments in other emerging technologies, such as Internet of Things, big data, artificial intelligence as well as cloud and quantum computing, smart healthcare systems (SHS) are becoming ubiquitous in our daily lives. Meanwhile, patients, doctors, and other medical personnel rely on the safe and efficient storage, transmission, and analysis of medical images and electronic health records for successful diagnosis, treatment, and management of different ailments. Moreover since, for various reasons, medical images are always the target of different illicit criminal activities, studies to utilise advanced information technologies to safeguard the confidentiality, integrity, and availability of such data have become a major priority in all SHS platforms. Our study evaluates recent efforts to deploy emerging technologies to design, secure, and enhance the efficiency of SHS that are based on medical images. It is hoped that this work will stimulate further interest aimed at the pursuit of more advanced algorithms and frameworks covering all aspects of security and privacy in emerging and future smart healthcare applications.

The two-stage fuzzy fusion based-convolution neural network is proposed for dynamic emotion recognition by using both facial expression and speech modalities, which not only can extract discriminative emotion features which contain spatio-temporal information, but also can effectively fuse facial expression and speech modalities. Moreover, the proposal is able to handle situations where the contributions of each modality data to emotion recognition are very imbalanced. The local binary patterns coming from three orthogonal planes and spectrogram are considered first to extract low-level dynamic emotion, so that the spatio-temporal information of these modalities can be obtained. To reveal more discriminative features, two deep convolution neural networks are constructed to extract high-level emotion semantic features. Moreover, the two stage fuzzy fusion strategy is developed by integrating canonical correlation analysis and fuzzy broad learning system, so as to take into account the correlation and difference between different modal features, as well as handle the ambiguity of emotional state information. The experimental results obtained on benchmark databases show that the accuracies of the proposed method are higher than those of existing methods (such as the hybrid deep model, and the rule-based and machine learning method) on SAVEE, eNTERFACE’05, and AFEW databases.

The weight-adapted convolution neural network (WACNN) is proposed to extract discriminative expression representations for recognizing facial expression. It aims to make good use of the convolution neural network's (CNN's) potential performance in avoiding local optima and speeding up convergence by the hybrid genetic algorithm (HGA) with optimal initial population, in such a way that it realizes deep and global emotion understanding in human-robot interaction. Moreover, the idea of novelty search is introduced to solve the deception problem in the HGA, which can expend the search space to help genetic algorithm jump out of local optimum and optimize large-scale parameters. In the proposal, the facial expression image preprocessing is conducted first, then the low-level expression features are extracted by using a principal component analysis. Finally, the high-level expression semantic features are extracted and recognized by WACNN which is optimized by HGA. In order to evaluate the effectiveness of WACNN, experiments on JAFFE, CK+, and static facial expressions in the wild 2.0 databases are carried out by using k -fold cross validation, and experimental results show the recognition accuracies of the proposal are superior to that of the state-of-the-art, such as local directional ternary pattern and weighted mixture deep neural network (DNN), which aim to extract discriminative and are the DNN-based methods. Moreover, recognition accuracies of the proposal are also higher than the deep CNN without HGA, which indicates that the proposal has better global optimization ability. Meanwhile, preliminary application experiments are also carried out by using the proposed algorithm on the emotional social robot system, where nine volunteers and two-wheeled robots experience the scenario of emotion understanding. Application results indicate that the wheeled robots can recognize basic expressions, such as happy, surprise, and so on.

As a cutting-edge branch of unmanned aerial vehicle (UAV) technology, the cooperation of a group of UAVs has attracted increasing attention from both civil and military sectors, due to its remarkable merits in functionality and flexibility for accomplishing complex extensive tasks, e.g., search and rescue, fire-fighting, reconnaissance, and surveillance. Cooperative path planning (CPP) is a key problem for a UAV group in executing tasks collectively. In this paper, an attempt is made to perform a comprehensive review of the research on CPP for UAV groups. First, a generalized optimization framework of CPP problems is proposed from the viewpoint of three key elements, i.e., task, UAV group, and environment, as a basis for a comprehensive classification of different types of CPP problems. By following the proposed framework, a taxonomy for the classification of existing CPP problems is proposed to describe different kinds of CPPs in a unified way. Then, a review and a statistical analysis are presented based on the taxonomy, emphasizing the coordinative elements in the existing CPP research. In addition, a collection of challenging CPP problems are provided to highlight future research directions.

A fuzzy deep neural network with sparse autoencoder (FDNNSA) is proposed for intention understanding based on human emotions and identification information (i.e., age, gender, and region), in which the fuzzy C-means (FCM) is used to cluster the input data, and deep neural network with sparse autoencoder (DNNSA) is designed for emotional intention understanding in human-robot interaction. It aims to make robots capable of recognizing human emotions and understanding related emotional intention, the FCM is suitable for gathering similar information so that the calculations of dimensionality of DNNSA will be reduced, and the sparse autoencoder of DNNSA can make the neuron of DNNSA sparse to reduce the complexity of the network in such a way human-robot interaction is running smoothly. To validate the proposal, simulation experiments based on benchmark databases such as facial expression database of CK+, and speech emotion corpus of CASIA were completed. The experimental results show that the proposal outperforms the baseline algorithms of Softmax regression (SR), DNNSA, FCM-based SR (FSR), Softplus, Gath Geva-based DNNSA (GDNNSA), and ensemble DNNSA (EDNNSA). Preliminary application experiments are performed in the development of emotional social robot system, where volunteers experience the scenario of “drinking at the bar”. The obtained results indicate that the proposed FDNNSA can promote robot understanding of emotional intention of human.

Two-layer fuzzy support vector regression-Takagi-Sugeno (TLFSVR-TS) model is proposed for emotion understanding in human-robot interaction (HRI), where the real-time dynamic emotion is recognized according to facial expression, and emotional intention understanding is obtained mainly based on human emotions and identification information. It aims to make robots capable of recognizing and understanding human emotions, in such a way that make HRI run smoothly. TLFSVR-TS considers about the priori knowledge inferred from human personal preference to reduce the uncertainty of various people, and multiple support vector regression (SVR) corresponding to different genders/provinces/ages of human to guarantee the local learning ability. Preliminary application experiments are performed in the developing emotional social robot system, where 30 volunteers experience the scenario of “drinking in the bar.” Results show that the proposal receives higher understanding accuracy than that of TLFSVR, kernel fuzzy c-means clustering is fused with SVR, and SVR.

A method to suppress exogenous disturbances in a nonlinear system is presented based on equivalent-input-disturbance (EID) approach. The nonlinear term is considered to be useful and should not be rejected in this paper. The method has two exceptional merits: it is a output-feedback control method, and the only restriction of the nonlinear term is used to ensure the stability of the NEID-based control system. Finally, the design procedure is illustrated by a numerical example.

The tensor product model transformation (TPMT) is an emerging numerical framework of the Takagi-Sugeno (T-S) fuzzy (or polytopic) system modeling for a linear matrix inequality based system control design. A nested TPMT (NTPMT) is proposed in this paper, which merges the dimensions of the tensors and performs the TPMT iteratively. The resultant fuzzy model is in a multilevel nested tensor product (TP) structure. The vertex tensor obtained by NTPMT has fewer dimension results than the original TPMT so the number of vertices or fuzzy rules, which have been the main bottleneck for further application of the TPMT in higher dimensional systems, is expected to decrease significantly. It is also proven that the NTPMT contains the hierarchical fuzzy logic, meaning that the NTPMT is capable of conducting hierarchical fuzzy modeling and reduction. Furthermore, because the inclusion of multiple TPMTs is prone to augment the conservativeness of the resultant fuzzy model, a suboptimal convex hull rectification algorithm for the TPMT is developed based on a newly defined tightness measure, and then extended to render the NTPMT as less conservative as possible. Finally, numerical simulations on two real physical systems (two- and four-parameter dimension) are verified to demonstrate the performance of the methods.

A three-layer weighted fuzzy support vector regression (TLWFSVR) model is proposed for understanding human intention, and it is based on the emotion-identification information in human-robot interaction. The TLWFSVR model consists of three layers, including adjusted weighted kernel fuzzy c-means for data clustering, fuzzy support vector regressions (FSVR) for information understanding, and weighted fusion for intention understanding. It aims to guarantee the quick convergence and satisfactory performance of the local FSVR via adjusting the weights of each feature in each cluster, in such a way that importance of different emotion-identification information is represented. Moreover, smooth human-oriented interaction can be obtained by endowing robot with human intention understanding capability. Experimental results show that the proposed TLWFSVR model obtains higher intention understanding accuracy and less computational time than that of two-layer fuzzy support vector regression, support vector regression, and back propagation neural network (BPNN), respectively. Additionally, the preliminary application experiments are performed in the developing human-robot interaction system, called emotional social robot system, where 12 volunteers and 2 mobile robots experience a scenario of “drinking at a bar.” Application results indicate that the bartender robot is able to understand customers' order intentions.

A two-layer fuzzy kernel regression (TLFKR) model is proposed for understanding human emotional intention in human-robot interaction, where TLFKR model consists of two layers, including fuzzy c-means (FCM) with kernel ridge regression (Kernel 1) for information analysis layer, fuzzy support vector regressions (FSVR) (Kernel 2) for intention understanding layer. TLFKR model represents the weight impact for each emotional information and aims to improve smooth human-robot interaction by endowing robot with human emotional intention understanding capability. Experimental Results show that the proposal obtains an intention understanding accuracy of 65.67%/68.33%/80.67% with the clusters number c=2/3/6 (according to different genders/ages/nationalities), which are 7.34%/7.18%/8.67% and 18.67%/21.33%/33.67% higher than that of TLFSVR and SVR, respectively. Additionally, preliminary application experiments are performed in the developing emotional social robot system, where two mobile robots and volunteers experience a scenario of “drinking at a bar”, and social robots are able to express basic emotions and understand human order intention.

Many web-based online learning systems focus more on textual and/or image based content delivery without including experiment systems, or if included they are usually operated under pre-defined conditions, such as fixed scenarios and pre-determined delivery orders. These limitations hinder personalized learning and collaboration between students and discourage student engagement. To circumvent these limitations, an Intelligent Web-based Experiment Management System (IWEMS) using multi-agent concept is presented. In the system, three kinds of software agents are used: (i) Student-Agent, responsible for assessing the knowledge levels of students. A fuzzy set based algorithm is used and the results are plotted through a dynamic polar chart; (ii) Teacher-Agent, responsible for tracking experiment progress of each student and recommending personalized the next-to-do experiment to him or her; and (iii) Co-Agent, responsible for group formation based on similar knowledge levels to facilitate collaborative learning between students. A prototype of this system is developed using a Java Agent Development Framework(JADE), where a client/server architecture and a MySQL database are used. It demonstrates the validity of the design and effectiveness of this system's functionality, achieves the personalization recommendation of next-to-do experiment and collaborative learning environment.

A method to analyze the similarity between two quantum images of the same size is proposed based on a representation for the quantum images. The similarity value is estimated according to the probability distribution of the results from quantum measurements. The proposed method is fast because a single operation can transform the entire information encoded in two images simultaneously. Two simulation-based experiments, which provide a reasonable estimation to the quantum images' similarity, are implemented using Matlab on a classical computer by means of linear algebra with complex vectors as quantum states and unitary matrices as unitary transformations. It also opens the door towards image searching from a database on quantum computers.

There are millions of people that regularly play Go in many countries around the world. Played by two players, Black and White, the stones of their colors are placed consecutively on an empty intersection of a square grid. In order to support beginners of Go to enjoy and concentrate on the game, this paper proposes a fuzzy markup language (FML)-based emotional expression system and applies it to computer Go. First, the knowledge base and rule base of the proposed system are defined by using FML. Based on the inferred board situation of the Go regional alarm level system, the fuzzy inference mechanism for emotional pleasure and the fuzzy inference mechanism for emotional arousal are responsible for inferring the pleasure degree and arousal degree, respectively. Emotional expression mapping mechanism maps the inferred pleasure degree and arousal degree into the emotional expression of the eye robot. The protocol transmission mechanism finally sends the pre-defined protocol to the eye robot via universal serial bus (USB) interface to make the eye robot express its emotional motions. From the experimental results, it shows that the eye robot could support Go's beginners to keep their tension, have them fun, and understand about Go when playing game of Go.

A multimodal gesture recognition method is proposed based on Choquet integral by fusing information from camera and 3D accelerometer data. By calculating the optimal fuzzy measures for the camera recognition module and the accelerometer recognition module, the proposal obtains enough recognition rate 92.7% in average for 8 types of gestures by improving the recognition rate approximate 20% compared to that of each module. The proposed method aims to realize the casual communication from humans to robots by integrating nonverbal gesture messages and verbal messages.

Emotional states based three-dimensional (3-D) Fuzzy Atmosfield (FA) is proposed to express the feeling between humans and robots in communication, and is built with 3-D coordinates, i.e. "friendly-hostile", "lively-calm", and "casual formal" axes. The FA aims to be an effective tool to proceed with the communication paying attention to the atmosphere generated by individual emotional state which is calculated from bimodal communication cues namely emotional-speech and emotional gesture by using weighted fusion and fuzzy inference. A novel emotion recognition approach is presented which consists of two steps, i.e., classification of six basic emotions for initial emotional states in the Affinity-Pleasure-Arousal emotion space, and emotional transition from prior state by using fuzzy logic. Home party enjoying demonstration confirms FA's availability empirically by questionnaires from unrelated persons of authors' group, where smooth communication between four humans and five eye robots is realized in Mascot Robot System.

A bi-modal emotion recognition approach is proposed for recognition of four emotions that integrate information from gestures and speech. The outputs from two unimodal emotion recognition systems based on affective speech and expressive gesture are fused on a decision level fusion by using weight criterion fusion and best probability plus majority vote fusion methods, and the performance of classifier which performs better than each uni-modal and is helpful in recognizing suitable emotions for communication situations. To validate the proposal, fifty Japanese words (or phrases) and 8 types of gestures that are recorded from five participants are used, and the emotion recognition rate increases up to 85.39%. The proposal is able to extent to using more than other modalities and useful in automatic emotion recognition system for human-robot communication.

Friendly user interface is desired for robots and computer systems which support human in all areas of daily life, e.g., information service, educational system, support service for elderly, etc.. Presence expressions by eye robot is proposed, where the eye robot expressions help human to more deeply understand robot, and then effectively provide their service in its situation e.g., a personal learning program and an entertainment program. The proposed presence expression is applied a personal education system that involves the eye robot, learning contents on a laptop PC with a web camera, a wii remote (Nintendo Co.,Ltd.) for measuring attention span of a subject based on 3D accelerometer information. To estimate effects of presence expression by the eye robot, subjective questioner is performed in the personal education system. Three type of leaning programs are conducted by the system for 10 subjects with subjective questionnaires evaluated with the 3-poin scale. The results show that the proposed expressions by the eye robot help the subject to feel like one is watching and to have an uncanny impression. As a result, the system has enabled the subjects to take the program with feeling of tension. This research plans to apply computer go system, another personal educational and entertainment system, where the system realizes casual communication in the games.

A fuzzy logic based multi-modal gesture recognition method is proposed, where both camera images and hand motion data (given by a 3D acceleration sensor put on human wrists) are used to notify the emotion of humans to robots in real time. To demonstrate the validity, it is applied to a part of the home party scenario enjoyed by five eye robots and four human participants, where 8 types of human emotional-gestures are successfully recognized by robots. The proposed method aims to realize the casual communication between robots and humans in the mascot robot system that has been developed by authors' group.

The paper deals with an approach to applications of e-approximate representation of type-2 fuzzy sets using triangulated irregular network (TIN). Geometric algorithms are designed for operations of type-2 fuzzy sets without using manner of upper or lower surfaces. Operations involving meet under minimum, join under minimum, negation, inference process of type-2 fuzzy sets are presented as applications of geometric representation to operations of type-2 fuzzy sets.

Clustering is often viewed as a synonym of techniques used to reveal the structure in data. The inherent geometrical diversity of data is a strong motivating factor to search for geometrically flexible clusters design supported by the clustering algorithms. In this study, we introduce a concept of geometrically variable fuzzy clustering (making use of Fuzzy C-Means, FCM), in which the fuzzification coefficients are associated with individual clusters thus endowing them with significant geometric flexibility. We introduce a hybrid optimization environment in which both global and local optimization mechanisms are engaged. The global optimization is supported by evolutionary computing (and particle swarm optimization, PSO, in particular) whereas the local optimization is realized by adopting some modified iterative schemes encountered in FCM. We show that this hybrid vehicle of optimization is of interest when dealing with comprehensive fitness functions which quantify a general view at the results of clustering (such as e.g., the one expressed by cluster validity indexes or the one articulating the mapping- reconstruction capabilities of the clusters).

A fuzzy inference-based algorithm with rules using the Nash solution is proposed for group decision making considering the finite discriminating abilities of real decision makers (DMs). It provides a solution that can capture and incorporate the imprecision of real people at declaring their preferences, and hence, it reflects more faithfully the DMs' opinions. The algorithm is applied to a purchase project of a storage area network with two DMs and three options. It shows how the algorithm can provide a unique solution whereas customary crisp methods are either unable to do it or reveal a risk of choosing, in 16.5% of the cases, an option that does not match with the preferences declared by the group of DMs as a whole. The algorithm aims for processes where the options are difficult to evaluate, circumstance that makes clear that human beings cannot provide unreal crisp values, and that the solution changes if preference information is only partially taken.

This study is concerned with a concept of structural expansion of fuzzy relations. Roughly speaking, when dealing with a finite family of highly dimensional fuzzy relations Ri, i = 1,2,…c, the intent is to provide a way of expressing them as Cartesian products of some fuzzy sets and “reduced” fuzzy relations of lower dimensionality. More descriptively, this expansion is regarded as a vehicle to isolate fuzzy sets which are easy to interpret and retain some relational “remainder” which is far less interpretable yet still effective in terms of processing. The expansion process can be performed stepwise by moving toward isolation of more fuzzy sets. We formulate the problem as a certain optimization task where the fuzzy sets obtained in the expansion process minimize an underlying performance index. Two main strategies of structural expansion are discussed. We distinguish between expansion relying on the use of individual variables and collections of variables. While the concept of structural expansion is of a substantial level of generality, in this study, we assume that fuzzy relations are formed through fuzzy clustering (Fuzzy C-Means, FCM to be brief) so that prototypes of the clusters can be directly used in the optimization procedure. Further refinement of fuzzy sets obtained as the result of the expansion is carried out through some logic transformation realized by means of uninorms. The links of structural expansion with rule-based computing with the related issue of interpretability and effectiveness of processing are discussed as well.

The vehicle dispatching problem for cooperative deliveries from multiple depots (VDP/CD/MD) is an important and difficult problem in the transport industries. To solve the VDP/CD/MD, A hierarchical multiplex structure (HIMS++) calculation model is proposed. The HIMS++ model takes advantage of object-oriented modeling, heuristic method, and fuzzy inference in (atomic, molecular, individual) three layers, so it can find a utility decision (vehicles plan) close to expert dispatcher. Furthermore, since the vital input parameters are few and the computational engine is packaged into a software component, the HIMS++ model is a convenient tool for the VDP/CD/MD. The HIMS++ model and its optimization algorithm are implemented as a software component using object-oriented paradigm, and through metaprogramming. The performance of the HIMS++ model is evaluated through experiments using 3-days oil delivery data taken from an actual dispatching center in Tokyo area. A total of 27 tank lorries are available for daily cooperative deliveries from three depots to about 30–60 destinations with different owners are used to save a running cost. The experimental results and the evaluations by human experts confirm that the HIMS++ model is better than the results of experienced dispatchers in six evaluation objectives, and can be applied to the planning support system for the VDP/CD/MD. The HIMS++ model will be able to cover similar transportation problems in the real world. © 2008 Wiley Periodicals, Inc.

An objects detection algorithm for color dynamic images from two cameras is proposed for a real surveillance system under low illumination. It provides automatic calculation of a Fuzzy Corresponding Map and color similarity for lower luminance conditions, which detects small chromatic regions in CCD camera images under lower illumination. Experimental detection results for two dynamic images from real surveillance cameras in a downtown area in Japan under low luminance conditions show that the proposed algorithm has 15% improved accuracy compared with the independent detection algorithm in the same false alarm rate, which implementability for severe surveillance situation is discussed. The proposed algorithm is being considered for use in a low cost surveillance system at a relatively poor security downtown (shopping mall) area in Japan.

A detection algorithm with color information for two dynamic images in a real surveillance system is proposed. It considers input region of frame as a detected region or the region behind other objects based on fuzzy corresponding map which describes common regions between input two dynamic images. Detection experimental results for the real surveillance situation show that the proposed algorithm improves 30% of accuracy compared with the independent detection algorithm. The algorithm will be installed in a basis unit for the real surveillance systems.

In order to visualize the whole structure of concept lattice obtained by formal concept analysis with respect to the image/video databases, a hierarchical representation method based on fuzzy clustering (especially, FCM) is proposed. In the case of proposed method, the FCM is firstly performed with respect to vast amount of objects of image/video databases, and the number of objects is reduced into suitable numbers for visualization under the environmental constrains. Each object of updated information table corresponds to each centroid of cluster. Furthermore, a flexible formal concept analysis can be formulated since the FCM can treat with multiple cluster information with respect to each object. Experiments using real image/video databases ('Corel Gallery 1000a' (1,000 color images) and a video selected from standard motion database (150 frames)) are performed to confirm the effectiveness of the proposed method. Through the investigation of the concept lattice obtained by the proposed method, it is confirmed that the proposed method is helpful to do video clipping and grasp the whole structure of image database.

Recently it has been shown that sum and product are not the only operations that can be used in order to define concrete approximation operators but several operations provided by fuzzy logic can be used. In this sense, in the present paper, pseudo-linear approximation operators of Shepard-type are studied from the practical point of view, in function approximation. It is shown that in several cases these outperform classical approximation operators based on sum and product operations.

A wavelet transformation based on max-plus algebra is proposed, where analysis and synthesis operations are defined by max (or min) and standard sum and they treat with 9 channel multi resolution images. The proposed wavelets especially can reserve edge information on compressed images due to the non-linear operations (max and min); therefore, they are efficient for the compression of predictive frames used in video compression and reconstruction. Through video compression and reconstruction experiments using standard video database, it is confirmed that effectiveness of the proposed wavelets.

A telecontrol laboratory for controlling a nonlinear robot arm online through the Internet is presented. The implementation of the scheme encompasses three major steps. The first step is to set up an approximately linear model after analyzing the experimental data of motor tests. The robot arm is controlled with a newly proposed generalized minimum variance self-adapted control (GMVSC) algorithm in the second step. In the third step, a client Web site with indicated IP address is developed to allow robot arm control with a correct login process. The experiments demonstrate that the robot arm is modeled and telecontrolled online with different weight parameter settings in GMVSC. And more benefit, with the GMVSC, the control value and the model of robot arm will be self adapted, adjusted, and identified. It is viewed in the second square of input pulse clearly, the same responsibility in output is obtained in the control system. This work results in a useful platform for researchers to carry out cooperative studies and facilitates the educational activities through the Internet.

Generalized non-linear wavelets are proposed by using weight coefficients in the analysis/synthesis operations. The proposed wavelets can generate various types of mother wavelets by adjusting the weight coefficients, in the setting of non-linear signal processing. Through experiment using real images extracted from standard image database (SIBDA), image analysis results (sub-band decomposition) are represented by the proposed method. Furthermore, the proposed method is applied to preprocessing of the chest lung X-ray images diagnosis based on standard digital image database created by Japanese society of radiological technology, and results of suspicious regions detection are shown

In order to generate various eigen fuzzy sets with respect to an image, an algorithm based on a permutation fuzzy matrix is proposed. The proposed algorithm is based on a rotation of the original fuzzy relation by using permutation fuzzy matrix, and the periodicity of the permutation matrix is studied in the setting of the fuzzy relational calculus. Through an experiment using the images extracted from the 'view sphere database', the properties of various eigen fuzzy sets obtained by the proposed algorithm are shown.

We examine the effect of the fuzzy aggregation operators on the image retrieval performance, by empirically comparing 67 operators, applied to the problem of computing the image similarity, given a collection of feature similarities of the image regions. While majority of the existing image similarity models express the image similarity as an aggregation of feature similarities, no study presents a systematic comparison of the different operators. We compare the 67 operators by: (1) incorporating each operator into a hierarchical, region-based similarity model, which expresses the image similarity as an aggregation of region similarities, and each region similarity as an aggregation of the corresponding feature similarities; and (2) evaluating the obtained model(s) on five test databases, containing 64,339 general-purpose images, in 749 semantic categories. Results show that the retrieval performance strongly depends on the operator(s) incorporated in the similarity model - the difference in the average retrieval precision between the best and the worst performing of the 67 operators is up to 50%.

A color motion compression/reconstruction method based on fuzzy relational equations (C-MCF) is proposed. The C-MCF divides a motion sequence into intra-pictures (I-pictures) and predictive-pictures (P-pictures), respectively, and these pictures furthermore are divided into R, G, and B pictures that are equivalent to fuzzy relations. The fuzzy relations are compressed/reconstructed by fuzzy relational equations, where I-pictures and P-pictures are compressed/reconstructed by using uniform and non-uniform coders, respectively. In order to perform efficient compression/reconstruction of P-pictures, a design method of non-uniform coders is proposed. The proposed design method is based on a fuzzy entropy function and an overlap level of fuzzy sets and a fuzzy equalization. An experiment using 10 P-pictures confirms that the root means square errors of the proposed method is decreased to 77.2% of that of the uniform coders, under the compression rate 0.00198. An experiment of motion compression and reconstruction is also presented to confirm the effectiveness of the C-MCF based on the non-uniform coders.

We introduce a logic-driven clustering in which prototypes are formed and evaluated in a sequential manner. The way of revealing a structure in data is realized by maximizing a certain performance index (objective function) that takes into consideration an overall level of matching (to be maximized) and a similarity level between the prototypes (the component to be minimized). The prototypes identified in the process come with the optimal weight vector that serves to indicate the significance of the individual features (coordinates) in the data grouping represented by the prototype. Since the topologies of these groupings are in general quite diverse the optimal weight vectors are reflecting the anisotropy of the feature space, i.e., they show some local ranking of features in the data space. Having found the prototypes we consider an inverse similarity problem and show how the relevance of the prototypes translates into their granularity.

Local similarity pattern (LSP) is proposed as a new method for computing image similarity. Similarity of a pair of images is expressed in terms of similarities of the corresponding image regions, obtained by uniform partitioning of the image area. Different from the conventional methods, each region-wise similarity is computed using a different combination of image features (color, shape, and texture). In addition, a method for optimizing LSP, based on genetic algorithm, is proposed, and incorporated in the relevance feedback process, allowing the user to automatically specify LSP-based queries. LSP is evaluated on four test databases totalling over 2,000 images. Compared with six conventional methods, and SIMPLIcity, an advanced image retrieval system, LSP brings between 15% and 24% increase in the average retrieval precision. LSP, allowing comparison of different image regions using different similarity criteria, is more suited for modeling human perception of image similarity than the conventional methods.

A fuzzy logic based similarity measure is introduced as a criterion for the identification of structure in data. An important characteristic of the proposed approach is that cluster prototypes are formed and evaluated in the course of the optimization without any a-priori assumptions about the number of clusters. The intuitively straightforward compound optimization criterion of maximizing the overall similarity between data and the prototypes while minimizing the similarity between the prototypes is adopted. It is shown that the partitioning of the pattern space obtained in the course of the optimization is more intuitive than the one obtained for the standard FCM. The local properties of clusters (in terms of the ranking order of features in the multidimensional pattern space) are captured by the weight vector associated with each cluster prototype. The weight vector is then used for the construction of interpretable information granules.

A digital watermarking method using image compression based on a fuzzy relational equation (ICF) is proposed. The method is based on least significant bit modification. If the coding system of ICF is not designed appropriately, the fuzzy relational equation will be unsolvable due to the watermarking (modification of compressed image). In order to avoid this problem, a condition for appropriate coding system design is represented in terms of the solvability degree of the fuzzy relational equation. Image compression and reconstruction experiments using 100 images (extracted from Corel Gallery) are performed, and it is confirmed that the signed image is indistinguishable from the unsigned one.

A new fuzzy controller for anti-swing and positioning control of an overhead traveling crane is proposed based on the SIRMs (single input rule modules) dynamically connected fuzzy inference model. The trolley position and velocity, the rope swing angle and angular velocity are selected as input items, and the trolley acceleration as output item. With a simple structure, the controller can autonomously adjust the influence of each input item. The control system is further proved to be asymptotically stable near destination. Control simulation results show that the controller is robust to different rope lengths and has generalization ability for different initial positions. Compared with linear state feedback controller, the fuzzy controller can drive the crane to destination in short time with small swing angle.

WWW information visualization system based on the plastic clustering is introduced, which assists the user to obtain the background knowledge of the unknown topics through a series of information retrieval. The keyword-based clustering is employed for the plastic clustering, which stocks the generated clusters and reuses them for the subsequent retrieval. The keyword set extraction based on the immune network model is also described with the analysis of its network dynamics.

Aircraft behavior can be described by a set of parameters that represent their aerodynamic properties and flight conditions. They are measured in aerodynamic tunnels under some special laboratory conditions. However, they do not fully describe all possible flight situations. Their accuracy is also limited. As considerable changes of the description occur during a flight, the use of non-adaptive autopilots, especially in combat aircraft, is strongly limited. The removal of this obstacle is possible only by means of a continuous on-line adaptation of the aircraft model and by a consecutive adaptation of the autopilot. The paper deals with the design of a performance-adaptive, so-called self-organizing, fuzzy controller as an autopilot. The structure of such a controller as well as the modified adaptation principle with some experiments are described.

A stability analysis approach for a class of fuzzy controllers based on the single input rule modules (SIRMs) dynamically connected fuzzy inference model is proposed. It is proved that such a fuzzy controller can be approximately changed into a linear state feedback controller near an equilibrium point if each SIRM has a property of linear input-output mapping. Then linear state feedback control theories can be used to solve the stability problem. The proposed approach is applied to stabilization control of inverted pendulum system and the stability analysis results agree completely with the control results.

A fuzzy controller for backing up control of truck-trailer system is proposed based on the single input rule modules dynamically connected fuzzy inference model. The relative angle of the truck with the trailer, trailer angle, and trailer vertical position are selected as the input items. The dynamic importance degrees are set up such that the relative angle takes control priority when it becomes big. Simulation results demonstrate that the fuzzy controller backs up the truck-trailer system successfully even from a jackknife situation.

A systematic method to construct stabilization fuzzy controllers for a single pendulum system and a series-type double pendulum system is presented based on the single input rule modules (SIRMs) dynamically connected fuzzy inference model. The angle and angular velocity of each pendulum and the position and velocity of the cart are selected as the input items. Each input item is given with a SIRM and a dynamic importance degree. All the SIRMs have the same rule setting. The dynamic importance degrees use the absolute value(s) of the angle(s) of the pendulum(s) as the antecedent variable(s). The dynamic importance degrees are designed such that the upper pendulum angular control takes the highest priority and the cart position control takes the lowest priority when the upper pendulum is not balanced upright. The control priority orders are automatically adjusted according to control situations. The simulation results show that the proposed fuzzy controllers have high generalization ability to completely stabilize a wide range of single pendulum systems and series-type double pendulum systems in short time. By extending the architecture, a stabilization fuzzy controller for a series-type triple pendulum system is even possible. © 2001 John Wiley & Sons, Inc.

This study is concerned with a decomposition of fuzzy relations, that is their representation with the aid of a certain number of fuzzy sets. We say that some fuzzy sets decompose an original fuzzy refraction if the sum of their Cartesian products approximate the given fuzzy relation. The theoretical underpinnings of the problem are presented along with some linkages with Boolean matrices (such as a Schein rank). Subsequently, we reformulate the decomposition of fuzzy relations as a problem of numeric optimizing and propose a detailed learning scheme leading to a collection of decomposing fuzzy sets. The role of the decomposition in a general class of data compression problems (including those of image compression and rule-based system condensation) is formulated and discussed in detail.

Differentiation of a Choquet integral for a nonnegative measurable function taken with respect to a fuzzy measure over a real fuzzy measure space is proposed. It is applied to the capital investment decision making problem. Kaino and Hirota (1999) proposed the X axis real interval limited Choquet integral for a preparation to define a fuzzy measure shift differentiation of the Choquet integral. Here, the upper differential coefficient, the lower differential coefficient, the differential coefficient, and the derived function of the X axis real interval limited Choquet integral for a nonnegative measurable function over a real fuzzy measure space along the domain (a subset of real numbers) are defined by the limitation process of the X axis real interval limited Choquet integral. Two examples of differentiation are given, where the nonnegative measurable functions are either a simple function or a triangular function. Moreover, they are applied to the automobile factory capital investment decision making problem. Assume that an automobile company has a sales plan of a new car. The current factory line has a capacity to manufacture 3,200 new cars, additional to the current car lines. Then, it is easy to make a decision to invest or not using the differentiation of the X axis real interval limited Choquet integral over X, which give us the increase or decrease rate of the expected sales revenue (also profit) per new car.

A major issue in the field of fuzzy applications is the complexity of the algorithms used. In order to obtain efficient methods, it is necessary to reduce complexity without losing the easy interpretability of the components. One of the possibilities to achieve complexity reduction is to combine fuzzy rule interpolation with the use of hierarchical structured fuzzy rule bases, as proposed by Sugeno et al. (1991). For interpolation, the method of Koczy and Hirota (1993) is used, but other techniques are also suggested. The difficulty of applying this method is that it is often impossible to determine a partition of any subspace of the original state space so that in all elements of the partition the number of variables can be locally reduced. Instead of this, a sparse fuzzy partition is searched for and so the local reduction of dimensions will be usually possible. In this case however, interpolation in the sparse partition itself, i.e. interpolation in the meta-rule level is necessary. This paper describes a method how such a multilevel interpolation is possible.

In pattern processing, it is difficult for all features to be extracted correctly. For a system using fuzzy inference, if input datum is lacking, the system does not work well. In the paper, a framework of a modified fuzzy inference method with lack of input data is introduced, and experimental results are provided. In the proposed method that is modified from Mamdani's fuzzy inference, a result of each rule is the adjustment for the purpose of protection from influence of lacking input data. The adjustment of the resulting fuzzy labels at each rule is used as the degree of importance which is set up in the rules by humans. In the results of a simple experiment, the system can infer well with lack of input data using this method. In results of simple experiments using a set of five fuzzy rules (three input and three output), when one or two input data are lacking, the system infers correctly.

A systematical approach to constructing stabilization fuzzy controllers for single and series-type double inverted pendulum systems is presented based on the SIRMs (single input rule modules) dynamically connected fuzzy inference model. The common architecture of the controllers is discussed. The simulation results show that the fuzzy controllers have high generalization ability to stabilize a wide range of the single and double pendulum systems in about 6.0 and 10.0 seconds.

A fuzzy controller for stabilizing parallel-type double inverted pendulum system is presented, based on the single input rule modules (SIRMs) dynamically connected fuzzy inference model. By using the SIRMs and the dynamic importance degrees, the angular controls of the two pendulums and the position control of the cart are done entirely in parallel and the priority orders of the three controls are automatically adjusted according to control situations. Simulation results show that the fuzzy controller with a simple and intuitive structure can stabilize completely a parallel-type double inverted pendulum system within 10 seconds. This is the first result for a fuzzy controller to realize complete stabilization of a parallel-type double inverted pendulum system.

A fast solving method of the solution for max continuous t-norm composite fuzzy relational equation of the type G(i, j)=(R/sup T//spl square/A/sub i/)/sup T//spl square/B/sub j/, i=1, 2, ..., I, j=1, 2, ..., J, where A/sub i//spl isin/F(X)X={x/sub 1/, x/sub 2/, ..., x/sub M/}, Bj/spl isin/F(Y) Y={y/sub 1/, y/sub 2/, ..., y/sub N/}, R/spl isin/F(X/spl times/Y), and /spl square/: max continuous t-norm composition, is proposed. It decreases the computation time IJMN(L+T+P) to JM(I+N)(L+P), where L, T, and P denote the computation time of min, t-norm, and relative pseudocomplement operations, respectively, by simplifying the conventional reconstruction equation based on the properties of t-norm and relative pseudocomplement. The method is applied to a lossy image compression and reconstruction problem, where it is confirmed that the computation time of the reconstructed image is decreased to 1/335.6 the compression rate being 0.0351, and it achieves almost equivalent performance for the conventional lossy image compression methods based on discrete cosine transform and vector quantization.

A method of multimedia information data acquisition is proposed based on fuzzy rules, where multimedia mean the five human senses. Observed information is characterized by VAGOT (visual, acoustic, gustatory, olfactory and tactile) time series data and the goal is to extract an appropriate subset of VAGOT data based on a given instruction. Here, Multimedia Information centers on image and sound, represented by membership functions. Fuzzy rules based on visual and acoustic information are used to identify the appropriate time interval in three experiments: various cars on a general road, sunny-side-up eggs and fireworks multimedia information.

The study is devoted to linguistic data mining, an endeavor that exploits the concepts, constructs, and mechanisms of fuzzy set theory. The roles of information granules, information granulation, and the techniques therein are discussed in detail. Particular attention is given to the manner in which these information granules are represented as fuzzy sets and manipulated according to the main mechanisms of fuzzy sets. We introduce unsupervised learning (clustering) where optimization is supported by the linguistic granules of context, thereby giving rise to so-called context-sensitive fuzzy clustering. The combination of neuro, evolutionary, and granular computing in the context of data mining is explored. Detailed numerical experiments using well-known datasets are also included and analyzed.

This study concentrates on fuzzy relational calculus regarded as a basis of data compression. In this setting, images are represented as fuzzy relations. We investigate fuzzy relational equations as a basis of image compression. It is shown that both compression and decompression (reconstruction) phases are closely linked with the way in which fuzzy relational equations are being usually set and solved. The theoretical findings encountered in the theory of these equations are easily accommodated as a backbone of the relational compression. The character of the solutions to the equations make them ideal for reconstruction purposes as they specify the extremal elements of the solution set and in such a way help establish some envelopes of the original images under compression. The flexibility of the conceptual and algorithmic framework arising there is also discussed. Numerical examples provide a suitable illustrative material emphasizing the main features of the compression mechanisms.

The "fuzzy hierarchical pattern recognition using fixation feedback" method is proposed and it is applied to recognize kinds, i.e., groups of trade names, of cars. In the experiments, image data of fourteen kinds of minicars taken from several directions are used. By comparing the results of the "non fixation feedback" method, it has been confirmed that the proposed method could increase efficiency without decreasing accuracy rates of recognition.

Proposed is a certain generalization of nonmonotonic fuzzy set operators introduced originally by R. R. Yager. By introducing a modulating function one can effectively model situations in which available information interacts (overlaps) with a given default fuzzy set. Discussed is a complete learning environment in which the default values (sets) can be derived based upon some experimental data. The role of the nonmonotonic operations is also revealed in the setting of reasoning carried out in the presence of fuzzy data. ©1997 John Wiley & Sons, Inc.

This paper proposes a connection admission control (CAC) method for asynchronous transfer mode (ATM) networks based on the possibility distribution of cell loss ratio (CLR). The possibility distribution is estimated in a fuzzy inference scheme by using observed data of the CLR. This method makes possible secure CAC, thereby guaranteeing the allowed CLR. First, a fuzzy inference method is proposed, based on a weighted average of fuzzy sets, in order to estimate the possibility distribution of the CLR. In contrast to conventional methods, the proposed inference method can avoid estimating excessively large values of the CLR. Second, the learning algorithm is considered for tuning fuzzy rules for inference. In this, energy functions are derived so as to efficiently achieve higher multiplexing gain by applying them to CAC. Because the upper bound of the CLR can easily be obtained from the possibility distribution by using this algorithm, CAC can be performed guaranteeing the allowed CLR. The simulation studies show that the proposed method can well extract the upper bound of the CLR from the observed data. The proposed method also makes possible self-compensation in real time for the case where the estimated CLR is smaller than the observed CLR. It preserves the guarantee of the CLR as much as possible in operation of ATM switches. Third, a CAC method which uses the fuzzy inference mentioned above is proposed. In the area with no observed CLR data, fuzzy rules are automatically generated from the fuzzy rules already tuned by the learning algorithm with the existing observed CLR data. Such areas exist because of the absence of experience in connections. This method can guarantee the allowed CLR in the CAC and attains a high multiplex gain as is possible. The simulation studies show its feasibility. Finally, this paper concludes with some brief discussions.

Fuzzy control is at present still the most important area of real applications for fuzzy theory. It is a generalized form of expert control using fuzzy sets in the definition of vague/linguistic predicates, modeling a system by If...then rules. In the classical approaches it is necessary that observations on the actual state of the system partly match (fire) one or several rules in the model (fired rules), and the conclusion is calculated by the evaluation of the degrees of matching and the fired rules. Interpolation helps reduce the complexity as it allows rule bases with gaps. Various interpolation approaches are shown. It is proposed that dense rule bases should be reduced so that only the minimal necessary number of rules remain still containing the essential information in the original base, and all other rules are replaced by the interpolation algorithm that however can recover them with a certain accuracy prescribed before reduction. The interpolation method used for demonstration is the Lagrange method supplying the best fitting minimal degree polynomial. The paper concentrates on the reduction technique that is rather independent from the style of the interpolation model, but cannot be given in the form of a tractable algorithm. An example is shown to illustrate possible results and difficulties with the method.

In the domain of law, various real situations are expressed as relations and/or combinations of legal knowledge items (legal concepts, articles of law, etc). Such knowledge items (legal facts, events) cannot be precisely defined. Legal judgement is performed based on resemblance of legal knowledge and facts. In our system, vague legal knowledge is saved in the fuzzy relational database, and legal inference is realized as fuzzy inference. The target law for this system is the United Nations Convention on Contracts for the International Sale of Goods (CISG).

International Journal of Uncertainty, Fuzziness and Knowledge-Based SystemsVol. 04, No. 06, pp. 495 (1996) No AccessGUEST EDITORS' INTRODUCTION: APPLICATIONS OF FUZZY THEORY TO COMPLEX SYSTEMSJonathan Lee, Kaoru Hirota, and Laszlo KoczyJonathan LeeNational Central University, Taiwan, ROC, Kaoru HirotaTokyo Institute of Technology, Japan, and Laszlo KoczyTechnical University of Budapest, Hungaryhttps://doi.org/10.1142/S0218488596000457Cited by:0 Next AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Remember to check out the Most Cited Articles! Check out our titles on Fuzzy Logic & Z-Numbers With a wide range of areas, you're bound to find something you like. FiguresReferencesRelatedDetails Recommended Vol. 04, No. 06 Metrics History PDF download

The paper introduces a design methodology for developing fuzzy systems with the aid of fuzzy J K flip-flops. The network representation of the flip-flops expressed with the aid of generic AND and OR neurons is provided. Detailed design algorithms that essentially exploit a parametric learning of the flip-flops are studied. Numerical examples are given as well.>

The paper introduces a neural network-based model of logical connectives. The basic processing unit consists of two types of generic OR and AND neurons structured into a three layer topology. Due to the functional integrity we will be referring to it as an OR/AND neuron. The specificity of the logical connectives is captured by the OR/AND neuron within its supervised learning. Further analysis of the connections of the neuron obtained in this way provides a better insight into the nature of the connectives applied in fuzzy sets by emphasizing their features of "locality" and interactivity. Afterward, we will study several architectures of neural networks comprising these neurons treated as their basic functional components. The numerical studies embrace both the structures formed by single OR/AND neurons and aimed at modeling logical connectives (including the Zimmermann-Zysno data set, 1980) and the networks representing various decision-making architectures. We will also propose a realization of a pseudo median filter in which the OR/AND neurons play an ultimate role.>

Concept formation contrives one among vital issues in all fields of science. It can be stated that, to a significant degree, a scientific discovery is related to various aspects of creation of general categories out of a mass of raw empirical data analyzed from a suitable perspective. Thus, as it is seen now, the concept of any notion is constructed on the basis of a significant amount of previous experience. Despite a lot of research completed, there still exists a number of open questions about diverse features of the constructed concepts. In this article we develop a framework for concept formation making use of a logical platform of fuzzy sets combined with mechanisms of neurocom-putations. It will be indicated how for a given naming of the concept its description can be derived. Moreover, a particular attention will be devoted to mechanisms justifying a relevance of the concepts with respect to a collection of available empirical facts. This may play a primordial role in recognizing some limitations of a character of the concept (i.e., its generality or specificity) which cannot be exceeded simultaneously not losing consistency with the family of collected objects utilized within the process of concept formation.

A characteristic approach of approximate reasoning is the partial matching of observations to prototypes. This analysis is cast in the framework of fuzzy set theory and brings another dimension to the fuzzy matching criterion; this dimension is the measure of uncertainty through the concept of subjective entropy. While a similarity measure, in the matching process, activates relevant prototypes, the entropy formalism derived provides a measure of uncertainty in the partial matching to each prototype. The novel approach formalizes an entropy weights activation of prototypes for fuzzy partial matching. A methodology is developed for matching of observation to a set of prototypes making use of a suitable aggregation done with a framework of fuzzy integrals. A method of dealing with compound hypothesis is also developed.>

The authors propose and define a fuzzy flip-flop that is an extended form of an ordinary binary flip-flop, specifically, a J-K flip-flop. A truth table for a J-K flip-flop is fuzzified, extending binary NOT, AND, and OR operations to fuzzy negation, t-norm and s-norm, respectively. Two types of fundamental characteristic equations of the fuzzy flip-flop are introduced: the reset- and the set-type equations, both of which are fuzzy extensions of a characteristic equation of a J-K flip-flop. Their characteristics are demonstrated graphically, especially in the case in which fuzzy negation, t-norm and s-norm relate to complementation, min, and max operations, respectively. Other fundamental fuzzy operations are examined, and their characteristics are demonstrated graphically. Both of the above types are unified in the case of complementation, min, and max operations, and a fundamental characteristic equation for a min-max-type fuzzy flip-flop negation, t-norm and s-norm gates is proposed. A circuit is presented and tested.>

The results of different fuzzy clustering algorithms are dealt with collectively in a formal framework of probabilistic set theory in order to interpret the structure of data. Special attention is paid to calculation of entropy of the fuzzy clusters detected by various grouping methods. Two numerical examples illustrate applicability of the proposed way of cluster evaluation.