Learning fuzzy inference systems using an adaptive membership function scheme

An adaptive membership function scheme for general additive fuzzy systems is proposed in this paper. The proposed scheme can adapt a proper membership function for any nonlinear input-output mapping, based upon a minimum number of rules and an initial approximate membership function. This parameter adjustment procedure is performed by computing the error between the actual and the desired decision surface. Using the proposed adaptive scheme for fuzzy system, the number of rules can be minimized. Nonlinear function approximation and truck backer-upper control system are employed to demonstrate the viability of the proposed method.

[1]  Edward E. Smith,et al.  Conceptual Combination with Prototype Concepts , 1984, Cogn. Sci..

[2]  E. Rosch ON THE INTERNAL STRUCTURE OF PERCEPTUAL AND SEMANTIC CATEGORIES1 , 1973 .

[3]  Chuen-Chien Lee,et al.  Fuzzy logic in control systems: fuzzy logic controller. II , 1990, IEEE Trans. Syst. Man Cybern..

[4]  John A. Bernard,et al.  Use of a rule-based system for process control , 1988 .

[5]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[6]  E. Rosch,et al.  Family resemblances: Studies in the internal structure of categories , 1975, Cognitive Psychology.

[7]  A. Tversky,et al.  Judgment under Uncertainty: Heuristics and Biases , 1974, Science.

[8]  Richard Bellman,et al.  On the Analytic Formalism of the Theory of Fuzzy Sets , 1973, Inf. Sci..

[9]  A. Tsoi,et al.  Importance of membership functions: a comparative study on different learning methods for fuzzy inference systems , 1994, Proceedings of 1994 IEEE 3rd International Fuzzy Systems Conference.

[10]  Douglas L. Medin,et al.  Context theory of classification learning. , 1978 .

[11]  M. Tomizuka,et al.  Stability of fuzzy linguistic control systems , 1990, 29th IEEE Conference on Decision and Control.

[12]  B. Widrow,et al.  Neural networks for self-learning control systems , 1990, IEEE Control Systems Magazine.

[13]  Jyh-Shing Roger Jang,et al.  Self-learning fuzzy controllers based on temporal backpropagation , 1992, IEEE Trans. Neural Networks.

[14]  E. Sapir Grading, A Study in Semantics , 1944, Philosophy of Science.

[15]  Masaharu Mizumoto,et al.  Fuzzy controls under various fuzzy reasoning methods , 1988, Inf. Sci..

[16]  Brian R. Gaines,et al.  Fuzzy and Probabilistic Uncertainty Logics , 1978, Inf. Control..

[17]  A. Tversky Features of Similarity , 1977 .

[18]  I. Turksen Measurement of membership functions and their acquisition , 1991 .

[19]  Chuen-Chien Lee FUZZY LOGIC CONTROL SYSTEMS: FUZZY LOGIC CONTROLLER - PART I , 1990 .

[20]  Bart Kosko,et al.  Adaptive fuzzy systems for backing up a truck-and-trailer , 1992, IEEE Trans. Neural Networks.

[21]  Lotfi A. Zadeh,et al.  Outline of a New Approach to the Analysis of Complex Systems and Decision Processes , 1973, IEEE Trans. Syst. Man Cybern..

[22]  Derrick H. Nguyen,et al.  Neural networks for self-learning control systems , 1990 .

[23]  Edward E. Smith,et al.  On the adequacy of prototype theory as a theory of concepts , 1981, Cognition.

[24]  Pei Wang,et al.  Belief Revision in Probability Theory , 1993, UAI.

[25]  G. Oden Fuzziness in semantic memory: Choosing exemplars of subjective categories , 1977, Memory & cognition.

[26]  Jerry M. Mendel,et al.  Generating fuzzy rules by learning from examples , 1992, IEEE Trans. Syst. Man Cybern..

[27]  Philippe Smets,et al.  Varieties of ignorance and the need for well-founded theories , 1991, Inf. Sci..

[28]  Shaorong Liu,et al.  A method of generating control rule model and its application , 1992 .

[29]  Bart Kosko,et al.  Adaptive fuzzy systems for target tracking , 1992 .