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Fuzzy Systems, IEEE Transactions on

Issue 4 • Date Aug. 1999

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Displaying Results 1 - 13 of 13
  • Comment on "Combinatorial rule explosion eliminated by a fuzzy rule configuration" [with reply]

    Page(s): 475 - 478
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (75 KB)  

    The "curse of dimensionality" is one of the key problems facing fuzzy systems theory today. Fuzzy systems are based on a set of IF-THEN rules and the structure of these fuzzy rules causes an exponential growth in the number of rules when more inputs are added, resulting in unwieldy rulebases. Many strategies have been proposed to alleviate the curse of dimensionality. Combs and Andrews (ibid., vol.6, p.1-11, 1998) attempt to reduce the growth of the fuzzy rulebase by proposing a disjunctive form for fuzzy rules. In the current paper, we comment on this approach and show that it is mathematically invalid, as illustrated by an example. Combs replies that the authors are addressing 2 different issues; whether the union and intersection rules of configuration be equivalent in fuzzy logic, and whether the latter can overcome the curse of dimensionality. View full abstract»

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  • Author's reply

    Page(s): 477 - 478
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    First Page of the Article
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  • Comments on "A fuzzy neural network and its application to pattern recognition"

    Page(s): 479 - 480
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    This note analyzes the unsupervised fuzzy neural network (FNNU) of the original paper by Kwan and Cai (ibid., vol.2, p.185-93, 1994) and finds the following: the FNNU is a clustering net, not a classifier net, and the number of clusters the network settles to may be less or more than the actual number of pattern classes (sometimes it could even be equal to the number of training data points); the huge number of connections in the FNNU can be drastically reduced without degrading its performance; and the algorithm does not have any learning capability for its parameters. Computational experience shows that usually the performance of a multilayer perceptron (MLP) is comparable to that of even a supervised version of FNN (trained by gradient descent algorithm) in terms of recognition scores, but an MLP has a much faster convergence than the supervised version of FNN. View full abstract»

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  • A note on the Gustafson-Kessel and adaptive fuzzy clustering algorithms

    Page(s): 453 - 461
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    In this letter, we show that the Gustafson-Kessel (G-K) algorithm (1979) and the original adaptive fuzzy clustering (AFC) algorithm can be thought of as special cases of a more general algorithm. Our analysis shows that the G-K algorithm is better suited for ellipsoidal clusters of equal volume, whereas the original AFC algorithm is better suited for linear clusters. We also discuss a new variation of these algorithms, which can be used to improve the results of the G-K and AFC algorithms in some cases View full abstract»

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  • Hybrid state-space fuzzy model-based controller with dual-rate sampling for digital control of chaotic systems

    Page(s): 394 - 408
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    We develop a hybrid state-space fuzzy model-based controller with dual-rate sampling for digital control of chaotic systems. A Takagi-Sugeno (TS) fuzzy model is used to model the chaotic dynamic system and the extended parallel-distributed compensation technique is proposed and formulated for designing the fuzzy model-based controller under stability conditions. The optimal regional-pole assignment technique is also adopted in the design of the local feedback controllers for the multiple TS linear state-space models. The proposed design procedure is as follows: an equivalent fast-rate discrete-time state-space model of the continuous-time system is first constructed by using fuzzy inference systems. To obtain the continuous-time optimal state-feedback gains, the constructed discrete-time fuzzy system is then converted into a continuous-time system. The developed optimal continuous-time control law is finally converted into an equivalent slow-rate digital control law using the proposed intelligent digital redesign method. The main contribution of the paper is the development of a systematic and effective framework for fuzzy model-based controller design with dual-rate sampling for digital control of complex such as chaotic systems. The effectiveness and the feasibility of the proposed controller design method is demonstrated through numerical simulations on the chaotic Chua circuit View full abstract»

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  • On the asymptotic stability of free fuzzy systems

    Page(s): 467 - 468
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    It has been shown by Thathachar and Viswanath (ibid., vol.5, p.145-51, 1997) that the stability of Takagi and Sugeno's fuzzy system is equivalent to that of a corresponding switching system with finite number of characteristic matrices. In this correspondence, we shall correct a false proof of a result in Thathachar and Viswanath View full abstract»

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  • A note on the use of a fuzzy approach in adaptive partitioning algorithms for global optimization

    Page(s): 468 - 475
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    In global optimization, adaptive partitioning algorithms (APA) operate on the basis of partitioning the feasible region into subregions, sampling and evaluating each subregion, and selecting one or more subregions for repartitioning. The purpose of the repartitioning process is to locate a narrow neighborhood around the global optimum. In this correspondence, we propose to use a fuzzy approach in the assessment of subregions using random samples taken from these subregions. We discuss different types of uncertainties involved in APA and we conclude that the use of a fuzzy approach in the assessment of subregions is in concurrence with APA's convergence property. We provide numerical results for the fuzzy approach on 13 test functions from the literature View full abstract»

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  • Learning in the framework of fuzzy lattices

    Page(s): 422 - 440
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    A basis for rigorous versatile learning is introduced theoretically, that is the framework of fuzzy lattices or FL-framework for short, which proposes a synergetic combination of fuzzy set theory and lattice theory. A fuzzy lattice emanates from a conventional mathematical lattice by fuzzifying the inclusion order relation. Learning in the FL-framework can be effected by handling families of intervals, where an interval is treated as a single entity/block the way explained here. Illustrations are provided in a lattice defined on the unit-hypercube where a lattice interval corresponds to a conventional hyperbox. A specific scheme for learning by clustering is presented, namely σ-fuzzy lattice learning scheme or σ-FLL (scheme) for short, inspired from adaptive resonance theory (ART). Learning by the σ-FLL is driven by an inclusion measure σ of the corresponding Cartesian product to be introduced here. We delineate a comparison of the σ-FLL scheme with various neural-fuzzy and other models. Applications are shown to one medical data set and two benchmark data sets, where σ-FLL's capacity for treating efficiently real numbers as well as lattice-ordered symbols separately or jointly is demonstrated. Due to its efficiency and wide scope of applicability the σ-FLL scheme emerges as a promising learning scheme View full abstract»

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  • An efficient solution procedure for fuzzy relation equations with max-product composition

    Page(s): 441 - 445
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    We study a system of fuzzy relation equations with max-product composition and present an efficient solution procedure to characterize the whole solution set by finding the maximum solution as well as the complete set of minimal solutions. Instead of solving the problem combinatorially, the procedure identifies the “nonminimal” solutions and eliminates them from the set of minimal solutions View full abstract»

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  • Qualitative robust fuzzy control with applications to 1992 ACC benchmark

    Page(s): 409 - 421
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    Robust control has long been the purview of quantitative linear control techniques, while qualitative symbolic control has been deemed more suitable to obtaining complex control objectives that require only low-output precision. The intelligent techniques of fuzzy control have, however, shown promise in obtaining results comparable to those obtained from H and H2 robust control techniques. Often though, these fuzzy control techniques ignore the original intent of fuzzy logic: implementation of symbolic linguistic control laws based on qualitative models of the plant and control behaviors. We show that robust control objectives, even for simple plants, can be achieved by first developing qualitative behaviors that stabilize the plant and then superimposing tracking behaviors that achieve control objectives. Specifically, by superimposing qualitative stability and tracking behaviors, we can achieve robustness and tracking stability comparable to the best published linear compensators for the 1992 ACC robust control benchmark View full abstract»

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  • Decision making with fuzzy probability assessments

    Page(s): 462 - 467
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (184 KB)  

    We discuss the idea of a fuzzy probability assessment, the association a collection of fuzzy probabilities with the outcomes of a random experiment. Fuzzy probability assessments often result from the linguistic specification of probabilities as provided by human experts. The question of consistency of the fuzzy probability assessment is considered. Finally, the problem of decision-making, selecting a best alternative action, in the face of a fuzzy probability assessment is investigated. Here we focus on the issue of obtaining the expected payoff of alternatives in the face of a fuzzy probability assessment. In the course of solving this problem we develop a representation of an effective probability distribution in the face of a fuzzy probability assessment View full abstract»

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  • Alternating cluster estimation: a new tool for clustering and function approximation

    Page(s): 377 - 393
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    Many clustering models define good clusters as extrema of objective functions. Optimization of these models is often done using an alternating optimization (AO) algorithm driven by necessary conditions for local extrema. We abandon the objective function model in favor of a generalized model called alternating cluster estimation (ACE). ACE uses an alternating iteration architecture, but membership and prototype functions are selected directly by the user. Virtually every clustering model can be realized as an instance of ACE. Out of a large variety of possible instances of non-AO models, we present two examples: 1) an algorithm with a dynamically changing prototype function that extracts representative data and 2) a computationally efficient algorithm with hyperconic membership functions that allows easy extraction of membership functions. We illustrate these non-AO instances on three problems: a) simple clustering of plane data where we show that creating an unmatched ACE algorithm overcomes some problems of fuzzy c-means (FCM-AO) and possibilistic c-means (PCM-AO); b) functional approximation by clustering on a simple artificial data set; and c) functional approximation on a 12 input 1 output real world data set. ACE models work pretty well in all three cases View full abstract»

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  • A fuzzy k-modes algorithm for clustering categorical data

    Page(s): 446 - 452
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    This correspondence describes extensions to the fuzzy k-means algorithm for clustering categorical data. By using a simple matching dissimilarity measure for categorical objects and modes instead of means for clusters, a new approach is developed, which allows the use of the k-means paradigm to efficiently cluster large categorical data sets. A fuzzy k-modes algorithm is presented and the effectiveness of the algorithm is demonstrated with experimental results View full abstract»

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Aims & Scope

The IEEE Transactions on Fuzzy Systems (TFS) is published quarterly. TFS will consider papers that deal with the theory, design or an application of fuzzy systems ranging from hardware to software.

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Meet Our Editors

Editor-in-Chief
Chin-Teng Lin
National Chiao-Tung University