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The shape of fuzzy sets in adaptive function approximation

IEEE TRANSACTIONS ON fuzzy SYSTEMS 2001年第4期9卷 637-656页

作者： Mitaim, S Kosko, B Thammasat Univ Dept Elect Engn Pathum Thani 12121 Thailand Univ So Calif Dept Elect Engn Syst Signal & Image Proc Inst Los Angeles CA 90089 USA

The shape of if-part fuzzy sets affects how well feedforward fuzzy systems approximate continuous functions. We explore a wide range of candidate if-part sets and derive supervised learning laws that tune them. Then we test how well the resulting adaptive fuzzy systems approximate a battery of test functions. No one set shape emerges as the best shape. The sinc function often does well and has a tractable learning law. But its undulating sidelobes may have no linguistic meaning. This suggests that the engineering goal of function-approximation accuracy may sometimes have to outweigh the linguistic or philosophical interpretations of fuzzy sets that have accompanied their use in expert systems. We divide the if-part sets into two large classes. The first class consists of n-dimensional joint sets that factor into n scalar sets as found in almost all published fuzzy systems. These sets ignore the correlations among vector components of input vectors. fuzzy systems that use factorable if-part sets suffer in general from exponential rule explosion in high dimensions when they blindly approximate functions without knowledge of the functions. The factorable fuzzy sets themselves also suffer from what we call the second curse of dimensionality: The fuzzy sets tend to become binary spikes in high dimension. The second class of if-part sets consists of the more general but less common n-dimensional joint sets that do not factor into n scalar fuzzy sets. We present a method for constructing such unfactorable joint sets from scalar distance measures. fuzzy systems that use unfactorable if-part sets need not suffer from exponential rule explosion but their increased complexity may lead to intractable learning laws and inscrutable if-then rules. We prove that some of these unfactorable joint sets still suffer the second curse of dimensionality of spikiness. The search for the best if-part sets in fuzzy function approximation has just begun.

关键词： adaptive fuzzy system curse of dimensionality fuzzy function approximation fuzzy sets

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Reducing the number of parameters of a fuzzy system using scaling functions

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SOFT COMPUTING 2006年第9期10卷 749-756页

作者： Klawonn, F Univ Appl Sci Braunschweig Wolfenbuettel Dept Comp Sci D-38302 Wolfenbuettel Germany

Learning techniques are tailored for fuzzy systems in order to tune them or even for deriving fuzzy rules from data. However, a compromise between accuracy and interpretability has to be found. Flexible fuzzy systems with a large number of parameters and high degrees of freedom tend to function as black boxes. In this paper, we introduce an interpretation of fuzzy systems that enables us to work with a small number of parameters without loosing flexibility or interpretability. In this way, we can provide a learning algorithm that is efficient and yields accuracy as well as interpretability. Our fuzzy system is based on extremely simple fuzzy sets and transformations using interpretable scaling functions of the input variables.

关键词： fuzzy function approximation alternating optimization gradient descend

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Optimizing the Performance of Rule-Based fuzzy Routing Algorithms in Wireless Sensor Networks

Optimizing the Performance of Rule-Based Fuzzy Routing Algor...

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IEEE International Conference on fuzzy Systems (FUZZ-IEEE)

作者： Sert, Seyyit Alper Yazici, Adnan Supreme Headquarters Allied Powers Europe SHAPE Strateg Dev & Preparat Directorate Mons Belgium Nazarbayev Univ Sch Sci & Technol Dept Comp Sci Astana Kazakhstan

ISBN: (纸本)9781538617281

Effective data routing is one of the crucial themes for energy-efficient communication in wireless sensor networks (WSN). In the WSN research domain, fuzzy approaches are in most cases superior to well-defined methodologies, especially where boundaries between clusters are unclear. For this reason, a significant number of studies have recently proposed fuzzy-based solutions for the problems encountered in WSNs. Rule-based fuzzy systems are part of these widespread fuzzy-based solutions that often involve some field experts for identification and derivation of fuzzy rules as well as fuzzy membership functions;thus, a considerable amount of time is devoted to the realization of the final system. Nevertheless, it is almost impossible or not feasible to realize a fuzzy system with an optimality property. In this study, we utilize the modified clonal selection algorithm (CLONALG-M) to improve the performance of rule-based fuzzy routing algorithms. Although previous studies have been devoted to fuzzy optimization in general, to the best of our knowledge, improving the efficiency of rule-based fuzzy routing algorithms has not yet been considered. For this reason, CLONALG-M is applied to determine the approximate form of the output membership functions that improve the overall performance of fuzzy routing algorithms, whose rule base and shapes of membership functions are initially known. Experimental analysis and evaluations of the approach used in this study are performed on selected fuzzy rule-based routing algorithms and the obtained results verify that our approach performs and scales well to improve fuzzy routing performance.

关键词： fuzzy routing performance tuning fuzzy function approximation optimization

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Discussion on Accuracy of approximation with Smooth fuzzy Models

Discussion on Accuracy of Approximation with Smooth Fuzzy Mo...

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IEEE Canadian Conference on Electrical and Computer Engineering (CCECE)

作者： Sadjadi, Ebrahim Navid Ebrahimi, Maryam Gachloo, Zahra Univ Carlos III Madrid Madrid Spain Shahid Beheshti Univ Tehran Iran Damghan Univ Damghan Iran

ISBN: (纸本)9781728154428

The structure of fuzzy model impacts how well it approximates the nonlinear function, and how many rules are required to gain the desired accuracy. The most of the earlier works rely on diminishing the higher derivation of the fuzzy model in front of the higher derivatives of the real system. However, the smooth compositions are m-time differentiable and will not diminish. This has motivated to derive the relation of required fuzzy rules with the arbitrary accuracy for function approximation through the smooth fuzzy model. The originality of the work is that the approximation error and the number of required fuzzy rules in this paper, rely on the structure of the fuzzy model and the involved s-t compositions, beside the nonlinear properties of the real plant, through a reliable mathematical formulation. Hence, we have presented a prediction-correction algorithm to include all the main factors. It is proved that number of the required rules are lower than those of the earlier works to gain the same level of model accuracy.

关键词： fuzzy function approximation fuzzy modeling Smooth functions Theoretical results

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Increasing energy efficiency of rule-based fuzzy clustering algorithms using CLONALG-M for wireless sensor networks

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APPLIED SOFT COMPUTING 2021年 109卷 107510-107510页

作者： Sert, Seyyit Alper Yazici, Adnan Supreme Headquarters Allied Powers Europe SHAPE Strateg Dev & Preparat Directorate B-7010 Mons Belgium Nazarbayev Univ Sch Sci & Technol Dept Comp Sci Nur Sultan 010000 Kazakhstan Middle East Tech Univ Dept Comp Engn TR-06800 Ankara Turkey

Because of its efficiency, clustering is used for effective communication in Wireless Sensor Networks (WSNs). In the WSN clustering area, fuzzy approaches are found to be superior to crisp cluster counterparts when the boundaries between clusters are unclear. As a result, many studies have proposed some fuzzy-based solutions to the cluster problem in WSNs. Most rule-based fuzzy clustering systems employ field experts in trial and error processes, identifying and defining fuzzy rules as well as the forms of membership functions at the output;thus, considerable time has been allocated to realize and define these functions. Therefore, it is almost impossible or impractical to achieve a fuzzy system optimally. In this study, we propose a modified clonal selection algorithm (CLONALG-M) to improve the energy efficiency of rule-based fuzzy clustering algorithms. Although some studies in the literature focus on fuzzy optimization in general, to the best of our knowledge, performance improvement of rule-based fuzzy clustering algorithms is not taken into account. The CLONALG-M algorithm based on the Clonal Selection Principle is used to elucidate the basic principles of an adaptive immune system. In this study, we apply this principle to determine the approximate deployment of outputbased membership functions that increase the performance of rule-based fuzzy clustering algorithms, whose rule base and shape of membership functions are previously known. Experimental analysis and evaluations of the proposed approach have been performed on selected fuzzy clustering approaches, and obtained results show that our approach performs and adapts well for improving performance of fuzzy output functions. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Clonal selection principle Performance tuning fuzzy function approximation fuzzy clustering algorithms Wireless sensor networks

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