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Showing papers on "Fuzzy associative matrix published in 2000"


Journal ArticleDOI
TL;DR: Two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems that relax the existing conditions reported in the previous literatures.
Abstract: This paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures. Two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems. The first one employs the S-procedure to utilize information regarding the premise parts of the fuzzy systems. The next one enlarges the class of fuzzy control systems, whose stability is ensured by representing the interactions among the fuzzy subsystems in a single matrix and solving it by linear matrix inequality. The relationships between the suggested stability conditions and the conventional well-known stability conditions reported in the previous literatures are also discussed, and it is shown in a rigorous manner that the second condition of this paper includes the conventional conditions. Finally, some examples and simulation results are presented to illustrate the effectiveness of the stability conditions.

783 citations


Journal ArticleDOI
TL;DR: The TS fuzzy models with time delay are presented and the stability conditions are derived using Lyapunov-Krasovskii approach and a stabilization approach for nonlinear time-delay systems through fuzzy state feedback and fuzzy observer-based controller is presented.
Abstract: Takagi-Sugeno (TS) fuzzy models (1985, 1992) can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input/output (I/O) submodels. In this paper, the TS fuzzy model approach is extended to the stability analysis and control design for both continuous and discrete-time nonlinear systems with time delay. The TS fuzzy models with time delay are presented and the stability conditions are derived using Lyapunov-Krasovskii approach. We also present a stabilization approach for nonlinear time-delay systems through fuzzy state feedback and fuzzy observer-based controller. Sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain are derived through the numerical solution of a set of coupled linear matrix inequalities. An illustrative example based on the CSTR model is given to design a fuzzy controller.

768 citations


Book
26 Apr 2000
TL;DR: This book about fuzzy classifier design briefly introduces the fundamentals of supervised pattern recognition and fuzzy set theory and some theoretical properties thereof are studied.
Abstract: This book about fuzzy classifier design briefly introduces the fundamentals of supervised pattern recognition and fuzzy set theory. Fuzzy if-then classifiers are defined and some theoretical properties thereof are studied. Popular training algorithms are detailed. Non if-then fuzzy classifiers include relational, k-nearest neighbor, prototype-based designs, etc. A chapter on multiple classifier combination discusses fuzzy and non-fuzzy models for fusion and selection.

486 citations


Journal ArticleDOI
Yaochu Jin1
TL;DR: This paper proposes an effective approach to data-based fuzzy modeling of high-dimensional systems by generating an initial fuzzy rule system based on the conclusion that optimal fuzzy rules cover extrema using a genetic algorithm and the gradient method.
Abstract: Fuzzy modeling of high-dimensional systems is a challenging topic. This paper proposes an effective approach to data-based fuzzy modeling of high-dimensional systems. An initial fuzzy rule system is generated based on the conclusion that optimal fuzzy rules cover extrema. Redundant rules are removed based on a fuzzy similarity measure. Then, the structure and parameters of the fuzzy system are optimized using a genetic algorithm and the gradient method. During optimization, rules that have a very low firing strength are deleted. Finally, interpretability of the fuzzy system is improved by fine training the fuzzy rules with regularization. The resulting fuzzy system generated by this method has the following distinct features: (1) the fuzzy system is quite simplified; (2) the fuzzy system is interpretable; and (3) the dependencies between the inputs and the output are clearly shown. This method has successfully been applied to a system that has 11 inputs and one output with 20 000 training data and 80 000 test data.

470 citations


Book
26 Apr 2000
TL;DR: Fuzzy Subsets: Fuzzy Relations.- FuzzY Equivalence Relations.- Pattern Classification.- Similarity Relations.- References.- fuzzy Graphs: Paths and Connectedness.
Abstract: Fuzzy Subsets: Fuzzy Relations.- Fuzzy Equivalence Relations.- Pattern Classification.- Similarity Relations.- References.- Fuzzy Graphs: Paths and Connectedness. Bridges and Cut Vertices. Forests and Trees. Trees and Cycles. A Characterization of Fuzzy Trees. (Fuzzy) Cut Sets. (Fuzzy Chords, (Fuzzy) Cotrees, and (Fuzzy) Twigs. (Fuzzy) 1-Chain with Boundary 0, (Fuzzy) Coboundary, and (Fuzzy) Cocycles. (Fuzzy) Cycle Set and (Fuzzy) Cocycle Set.- Fuzzy Line Graphs.- Fuzzy Interval Graphs. Fuzzy Intersection Graphs. Fuzzy Interval Graphs. The Fulkerson and Gross Characterization. The Gilmore and Hoffman Characterization.- Operations on Fuzzy Graphs: Cartesian Product and Composition. Union and Join.- On Fuzzy Tree Definition.- References.- Applications of Fuzzy Graphs: Clusters.- Cluster Analysis. Cohesiveness. Slicing in Fuzzy Graphs.- Application to Cluster Analysis.- Fuzzy Intersection Equations. Existence of Solutions.- Fuzzy Graphs in Database Theory. Representation of Dependency Structure r(X,Y) by Fuzzy Graphs.- A Description of Strengthening and Weakening Members of a Group. Connectedness Criteria. Inclusive Connectedness Categories. Exclusive Connectedness Categories.- An Application of Fuzzy Graphs to the Problem Concerning Group Structure. Connectedness of a Fuzzy Graph. Weakening and Strenghtening Points of a Fuzzy Directed Graph.- References.- Fuzzy Hypergraphs: Fuzzy Hypergraphs.- Fuzzy Transversals of Fuzzy Hypergraphs. Properties of Tr(H). Construction of H3.- Coloring of Fuzzy Hypergraphs. beta-degree Coloring Procedures. Chromatic Values of Fuzzy Colorings.- Intersecting Fuzzy Hypergraphs. Characterization of Strongly Intersecting Hypergraphs. Simply Ordered Intersecting Hypergraphs. H-dominant Transversals.- Hebbian Structures.- Additional Applications.- References.

468 citations


Journal ArticleDOI
01 Apr 2000
TL;DR: Using this Symbiotic-Evolution-based Fuzzy Controller (SEFC) design method, the number of control trials, as well as consumed CPU time, are considerably reduced when compared to traditional GA-based fuzzy controller design methods and other types of genetic reinforcement learning schemes.
Abstract: An efficient genetic reinforcement learning algorithm for designing fuzzy controllers is proposed in this paper. The genetic algorithm (GA) adopted in this paper is based upon symbiotic evolution which, when applied to fuzzy controller design, complements the local mapping property of a fuzzy rule. Using this Symbiotic-Evolution-based Fuzzy Controller (SEFC) design method, the number of control trials, as well as consumed CPU time, are considerably reduced when compared to traditional GA-based fuzzy controller design methods and other types of genetic reinforcement learning schemes. Moreover, unlike traditional fuzzy controllers, which partition the input space into a grid, SEFC partitions the input space in a flexible way, thus creating fewer fuzzy rules. In SEFC, different types of fuzzy rules whose consequent parts are singletons, fuzzy sets, or linear equations (TSK-type fuzzy rules) are allowed. Further, the free parameters (e.g., centers and widths of membership functions) and fuzzy rules are all tuned automatically. For the TSK-type fuzzy rule especially, which put the proposed learning algorithm in use, only the significant input variables are selected to participate in the consequent of a rule. The proposed SEFC design method has been applied to different simulated control problems, including the cart-pole balancing system, a magnetic levitation system, and a water bath temperature control system. The proposed SEFC has been verified to be efficient and superior from these control problems, and from comparisons with some traditional GA-based fuzzy systems.

230 citations


Journal ArticleDOI
TL;DR: A new fuzzy Delphi method that employs the fuzzy statistics and technique of the conjugate gradient search to fit membership functions to fit fuzzy forecasts for managerial talent assessment for a company located in Taiwan is proposed.

177 citations


Journal ArticleDOI
TL;DR: This paper investigates the existence of a solution of duality fuzzy linear equation systems and two necessary and sufficient conditions for the solution existence are given.

175 citations


01 Jan 2000
TL;DR: Methods for extracting fuzzy rules for both function approximation and pattern classification are presented, based on estimating clusters in the data, which corresponds to a fuzzy rule that relates a region in the input space to an output region.
Abstract: Extracting fuzzy rules from data allows relationships in the data to be modeled by "if-then" rules that are easy to understand, verify, and extend. This paper presents methods for extracting fuzzy rules for both function approximation and pattern classification. The rule extraction methods are based on estimating clusters in the data; each cluster obtained corresponds to a fuzzy rule that relates a region in the input space to an output region (or, in the case of pattern classification, to an output class). After the number of rules and initial rule parameters are obtained by cluster estimation, the rule parameters are optimized by gradient descent. Applications to a function approximation problem and to a pattern classification problem are also illustrated.

156 citations


Journal Article
TL;DR: The paper gave the principle and procedure of fuzzy analytical hierarchy process and studied the properties of fuzzy consistent judgement matrix and the rationality to denote the important comparision of elements by fuzzy consistency judgement matrix.
Abstract: Firstly the paper pointed out the defects of AHP. Then,the paper introduced the concept of fuzzy consistent judgement matrix,and studied the properties of fuzzy consistent judgement matrix and the rationality to denote the important comparision of elements by fuzzy consistent judgement matrix,and the relation between the fuzzy consistent judgement matrix denoting the important comparision and the weigtht denoting the level of importance of element. On the basis of the research,the paper gave the principle and procedure of fuzzy analytical hierarchy process.

137 citations


Journal ArticleDOI
TL;DR: The results of FUSICO-project have indicated that the fuzzy traffic signal control can be the potential control method for signalized intersections.

Journal ArticleDOI
TL;DR: A method based on Simulated Annealing (SA) is presented in order to obtain a good uniform fuzzy partition granularity that improves the FRBS behaviour and is an efficient granularity search method for finding a good number of labels per variable.

Proceedings ArticleDOI
07 May 2000
TL;DR: Through computer simulations, it is shown that fuzzy rule-based systems with high classification performance can be designed without modifying the membership functions of antecedent linguistic values when the authors use fuzzy rules with certainty grades.
Abstract: This paper examines the effect of rule weights in fuzzy rule-based classification systems. Each fuzzy rule in our classification system has antecedent linguistic values and a single consequent class. We use a fuzzy reasoning method based on a single winner rule in the classification phase. The winner rule for a new pattern is the fuzzy rule that has the maximum compatibility grade with the new pattern. When we use fuzzy rules with certainly grades, the winner is determined as the rule with the maximum product of the compatibility grade and the certainty grade. In this paper, the effect of rule weights is illustrated by drawing classification boundaries using fuzzy rules with/without certainty grades. It is also shown that certainly grades play an important role when a fuzzy rule-based classification system is a mixture of general rules and specific rules. Through computer simulations, we show that fuzzy rule-based systems with high classification performance can be designed without modifying the membership functions of antecedent linguistic values when we use fuzzy rules with certainty grades.

Book
01 Dec 2000
TL;DR: Fuzzy Logic Approaches to Human-Consistent Systems: Toward aa Logic of Perceptions Based on Fuzzy logic Uncertainty-Based Information: A Critical Review.
Abstract: Fuzzy Logic Approaches to Human-Consistent Systems: Toward aa Logic of Perceptions Based on Fuzzy Logic Uncertainty-Based Information: A Critical Review- Structure of Truth Values: Triangular Norms - Basic Properties and Representation Theorems Semantic for Fuzzy Logic Supporting Truth Functionality States on Perfect MV-Algebras A Glance at Implication and T-Conditional Functions- Metamathematical Aspects of Fuzzy Logic: On the Metamathematics of Fuzzy Logic Fuzzy Metalogic for Crisp Logics Degrees of Truth and Degrees of Validity- Formal Systems of Fuzzy Logic: Fuzzy Propositional Logic Some Consequences of Herbrand and McNaughton Theorems in Fuzzy Logic- Fuzzy Quantifiers: Many On T-Quantifiers and S-Quantifiers- Reasoning in Impreciseness: Reasoning on Imprecisely Defined Functions Similarity-Based Reasoning- Relational Systems in Fuzzy Logic:Generalized Solvability Behaviour for Systems of Fuzzy Equations Fuzzy Points Fuzzy Relations and Fuzzy Functions- Extensions and Departures from Fuzzy Logic: Fuzzy Galois Connections and Fuzzy Concept Lattices A Unified Compilation Style Labelled Deductive System for Modal, Substructural and Fuzzy Logics

Proceedings ArticleDOI
07 May 2000
TL;DR: A convenient fusion of natural-language processing and fuzzy logic techniques for analyzing affect content in free text and shows a very good correspondence of affect sets with human judgments of affect content.
Abstract: We propose a convenient fusion of natural-language processing and fuzzy logic techniques for analyzing affect content in free text; our main goals are fast analysis and visualization of affect content for decision-making. The primary linguistic resource for fuzzy semantic typing is the fuzzy affect lexicon, from which other important resources are generated, notably the fuzzy thesaurus and affect category groups. Free text is tagged with affect categories from the lexicon, and the affect categories' centralities and intensities are combined using techniques from fuzzy logic to produce affect sets fuzzy sets that represent the affect quality of a document. We show different aspects of affect analysis using news stories and movie reviews. Our experiments show a very good correspondence of affect sets with human judgments of affect content. We ascribe this to the effective representation of ambiguity in our fuzzy affect lexicon, and the ability of fuzzy logic to deal successfully with the ambiguity of words in natural language. Planned extensions of the system include personalized profiles for Web-based content dissemination, fuzzy retrieval, clustering and classification.

Book
15 Jan 2000
TL;DR: Fuzzy Lyapunov synthesis fuzzy Lyap unov synthesis and stability analysis adaptive fuzzy controller design inverse optimality for fuzzy controllershyperbolic approach to fuzzy modelling fuzzy controllers for the hyperbolic state-space model.
Abstract: Fuzzy Lyapunov synthesis fuzzy Lyapunov synthesis and stability analysis adaptive fuzzy controller design inverse optimality for fuzzy controllers hyperbolic approach to fuzzy modelling fuzzy controllers for the hyperbolic state-space model.

Journal ArticleDOI
TL;DR: It is shown that with a modified fuzzy least square method proposed for solution of a type of problem with crisp input and fuzzy output, the predictability in the new model is better than Tanaka’s and its computation efficiency isbetter than the conventional fuzzy leastsquare method.

Journal ArticleDOI
TL;DR: An explicit fuzzy supervised classification method which consists of three steps, a MIN fuzzy reasoning rule followed by a rescaling operation are applied to deduce the fuzzy outputs, or in other words, the fuzzy classification of the pixel.
Abstract: Fuzzy classification has become of great interest because of its capacity to provide more useful information for geographic information systems. This paper describes an explicit fuzzy supervised classification method which consists of three steps. The explicit fuzzyfication is the first step where the pixel is transformed into a matrix of membership degrees representing the fuzzy inputs of the process. Then, in the second step, a MIN fuzzy reasoning rule followed by a rescaling operation are applied to deduce the fuzzy outputs, or in other words, the fuzzy classification of the pixel. Finally, a defuzzyfication step is carried out to produce a hard classification. The classification results on Landsat TM data demonstrate the promising performances of the method and comparatively short classification time.

Journal ArticleDOI
TL;DR: A novel approach is presented to use the finite element analysis as a “numerical experiment” tool, and to find directly, by fuzzy linear regression method, the statistical property of the structure stress.

Book ChapterDOI
01 Jan 2000
TL;DR: The classical Srikant and Agrawal’s algorithm is extended to allow discovering the relationships between data attributes upon all levels of fuzzy taxonomic structures, and it is revealed that the extended algorithm is at the same level of computational complexity in the number of the transactions as that of the classical algorithm.
Abstract: Data mining is a key step of knowledge discovery in databases. Classically, mining generalized association rules is to discover the relationships between data attributes upon all levels of presumed exact taxonomic structures. In many real-world applications, however, the taxonomic structures may not be crisp but fuzzy. This paper focuses on the issue of mining generalized association rules with fuzzy taxonomic structures. First, fuzzy extensions are made to the notions of the degree of support, the degree of confidence, and the R-interest measure. The computation of these degrees takes into account the fact that there may exist a partial belonging between any two itemsets in the taxonomy concerned. Then, the classical Srikant and Agrawal’s algorithm (including the Apriori algorithm and the Fast algorithm) is extended to allow discovering the relationships between data attributes upon all levels of fuzzy taxonomic structures. In this way, both crisp and fuzzy association rules can be discovered. Finally, the extended algorithm is run on the synthetic data with up to 106 transactions. It reveals that the extended algorithm is at the same level of computational complexity in the number of the transactions as that of the classical algorithm.

Journal ArticleDOI
TL;DR: A simplified fuzzy logic control for loop controllers is presented using a fixed control table with mapping parameters and is shown to be suitable for a loop controller with regard to the computation time and the required memory.

Journal ArticleDOI
TL;DR: The fuzzy modeling of large collections of noisy data described in this paper achieves a very high degree of compression with a relatively low computational complexity both for maintenance and interrogation of the model itself.

Journal ArticleDOI
TL;DR: Methods in fuzzy logic applied to serve as secondary classifier for a hierarchical classification model and the use of this model in interpretation of mammograms is discussed and the inevitability of using a fuzzy approach in the problem is discussed.

Journal ArticleDOI
TL;DR: Stabilization of the closed-loop fuzzy system using local parallel distributed compensators is investigated, and connective stability of the open loop and closed loop of the interconnected system is analyzed via the concepts of vector Lyapunov functions and M-matrices.
Abstract: This paper discusses decentralized parallel distributed compensator design for Takagi-Sugeno fuzzy systems. The fuzzy system is viewed as an interconnection of subsystems some of which are strongly connected, while others being weakly connected. The necessary theory is developed so that one can associate this fuzzy system with another one in a higher dimensional space, the so-called expanded space, design decentralized parallel distributed compensators in the expanded space, then contract the solution for implementation on the original fuzzy system. In this respect, connective stability of the open loop and closed loop of the interconnected system is analyzed via the concepts of vector Lyapunov functions and M-matrices. Different Lyapunov functions generate different results for the discrete-time fuzzy system, quadratic Lyapunov generating the superior of the two. Following a similar approach, stabilization of the closed-loop fuzzy system using local parallel distributed compensators is investigated.

Journal ArticleDOI
TL;DR: A class of smooth associative, increasing binary operations on a chain that also satisfy weak boundary conditions is completely characterize by the help of this equivalent form, which is the intermediate-value theorem.
Abstract: An intuitive notion of smoothness introduced by Godo et al. (1988) on finite chains is investigated and formulated in a more useful mathematical way. By the help of this equivalent form, which is the intermediate-value theorem, we completely characterize a class of smooth associative, increasing binary operations on a chain that also satisfy weak boundary conditions. Some important subclasses of such operations are also described.

Journal ArticleDOI
01 Dec 2000
TL;DR: The work of Chen, Ke and Chang (1990) is extended to present a fuzzy backward reasoning algorithm for rule-based systems using fuzzy Petri nets, where the fuzzy production rules of a rule- based system are represented by fuzzyPetri nets.
Abstract: Chen, Ke and Chang (1990) have presented a fuzzy forward reasoning algorithm for rule-based systems using fuzzy Petri nets. In this paper, we extend the work of Chen, Ke and Chang (1990) to present a fuzzy backward reasoning algorithm for rule-based systems using fuzzy Petri nets, where the fuzzy production rules of a rule-based system are represented by fuzzy Petri nets. The system can perform fuzzy backward reasoning automatically to evaluate the degree of truth of any proposition specified by the user. The fuzzy backward reasoning capability allows the computers to perform reasoning in a more flexible manner and to think more like people.

Journal ArticleDOI
TL;DR: A new approach of neuro-fuzzy learning algorithm for tuning fuzzy rules by using training input–output data, based on the gradient descent method is developed, which can be well avoided in the case of non-f firing or weak-firing.

Journal ArticleDOI
TL;DR: It is proved that fuzzy polynomial regression can model the extension principle extension of continuous real-valued functions.

Journal ArticleDOI
01 Dec 2000
TL;DR: The proposed method can find an appropriate fuzzy system with a low number of rules to approach an identified system under the condition that the constructed fuzzy system must satisfy a predetermined acceptable performance.
Abstract: A method based on the concepts of genetic algorithm (GA) and recursive least-squares method is proposed to construct a fuzzy system directly from some gathered input-output data of the discussed problem. The proposed method can find an appropriate fuzzy system with a low number of rules to approach an identified system under the condition that the constructed fuzzy system must satisfy a predetermined acceptable performance. In this method, each individual in the population is constructed to determine the number of fuzzy rules and the premise part of the fuzzy system, and the recursive least-squares method is used to determine the consequent part of the constructed fuzzy system described by this individual. Finally, three identification problems of nonlinear systems are utilized to illustrate the effectiveness of the proposed method.

Journal ArticleDOI
TL;DR: The general theory of fuzzy stochastic differential systems is discussed, including the existence and uniqueness of a solution, the continuity of the solution with respect to the initial value and the stability of systems when there are perturbations of the coefficients and the initial conditions.