Fuzzy model tuning using simulated annealing

This paper presents the use of simulated annealing metaheuristic for tuning Mamdani type fuzzy models. Structure of the Mamdani fuzzy model is learned from input-output data pairs using Wang and Mendel's method and fuzzy c-means clustering algorithm. Then, parameters of the fuzzy system are tuned through simulated annealing. In this paper, we perform experiments to examine effects of (a) initial solution generated by Wang and Mendel's method and fuzzy c-means clustering method, (b) membership function update procedure, (c) probability parameter for the calculation of the initial temperature, (d) temperature update coefficient used for cooling schedule, and (e) randomness level in the disturbance mechanism used in simulated annealing algorithm on the tuning of Mamdani type fuzzy models. Experiments are performed with Mackey-Glass chaotic time series. The results indicate that Wang and Mendel's method provides better starting configuration for simulated annealing compared to fuzzy c-means clustering method, and for the membership function update parameter, MFChangeRate@? (0,1], and the probability parameter for the calculation of the initial temperature, P"0@? (0,1), values close to zero produced better results.

[1]  Francisco Herrera,et al.  Analysis and guidelines to obtain a good uniform fuzzy partition granularity for fuzzy rule-based systems using simulated annealing , 2000, Int. J. Approx. Reason..

[2]  Magne Setnes,et al.  GA-fuzzy modeling and classification: complexity and performance , 2000, IEEE Trans. Fuzzy Syst..

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

[4]  V. Cerný.  Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm , 1985 .

[5]  Jyh-Shing Roger Jang,et al.  ANFIS: adaptive-network-based fuzzy inference system , 1993, IEEE Trans. Syst. Man Cybern..

[6]  Francisco Herrera,et al.  Hybridizing genetic algorithms with sharing scheme and evolution strategies for designing approximate fuzzy rule-based systems , 2001, Fuzzy Sets Syst..

[7]  J. Yen,et al.  Fuzzy Logic: Intelligence, Control, and Information , 1998 .

[8]  J. C. Dunn,et al.  A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters , 1973 .

[9]  E. Bonomi,et al.  The N-City Travelling Salesman Problem: Statistical Mechanics and the Metropolis Algorithm , 1984 .

[10]  Rudolf Kruse,et al.  Neuro-fuzzy systems for function approximation , 1999, Fuzzy Sets Syst..

[11]  Andrew A. Goldenberg,et al.  Development of a systematic methodology of fuzzy logic modeling , 1998, IEEE Trans. Fuzzy Syst..

[12]  Derek A. Linkens,et al.  Rule-base self-generation and simplification for data-driven fuzzy models , 2004, Fuzzy Sets Syst..

[13]  John Yen,et al.  Application of statistical information criteria for optimal fuzzy model construction , 1998, IEEE Trans. Fuzzy Syst..

[14]  Brigitte Charnomordic,et al.  Generating an interpretable family of fuzzy partitions from data , 2004, IEEE Transactions on Fuzzy Systems.

[15]  Serge Guillaume,et al.  Designing fuzzy inference systems from data: An interpretability-oriented review , 2001, IEEE Trans. Fuzzy Syst..

[16]  Francisco Herrera,et al.  Cooperative Evolutionary Learning of Linguistic Fuzzy Rules and Parametric Aggregation Connectors for Mamdani Fuzzy Systems , 2007, IEEE Transactions on Fuzzy Systems.

[17]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[18]  Ehl Emile Aarts,et al.  Statistical cooling : a general approach to combinatorial optimization problems , 1985 .

[19]  G. T. Timmer,et al.  Stochastic global optimization methods part II: Multi level methods , 1987, Math. Program..

[20]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[21]  Yan Shi,et al.  A new approach of neuro-fuzzy learning algorithm for tuning fuzzy rules , 2000, Fuzzy Sets Syst..

[22]  Hamid Mohamadi,et al.  Data mining with a simulated annealing based fuzzy classification system , 2008, Pattern Recognit..

[23]  Bruce E. Hajek,et al.  Cooling Schedules for Optimal Annealing , 1988, Math. Oper. Res..

[24]  Yaochu Jin,et al.  Fuzzy modeling of high-dimensional systems: complexity reduction and interpretability improvement , 2000, IEEE Trans. Fuzzy Syst..

[25]  C. L. Liu,et al.  A New Algorithm for Floorplan Design , 1986, DAC 1986.

[26]  Magne Setnes,et al.  Compact and transparent fuzzy models and classifiers through iterative complexity reduction , 2001, IEEE Trans. Fuzzy Syst..

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

[28]  H. D. Cheng,et al.  Automatically Determine the Membership Function Based on the Maximum Entropy Principle , 1997, Inf. Sci..

[29]  Ebrahim H. Mamdani,et al.  An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller , 1999, Int. J. Hum. Comput. Stud..

[30]  Zuhal Akyürek,et al.  The enhancement of the cell-based GIS analyses with fuzzy processing capabilities , 2006, Inf. Sci..

[31]  Patrick Siarry,et al.  Fuzzy rule base learning through simulated annealing , 1999, Fuzzy Sets Syst..

[32]  B. Hajek,et al.  Simulated annealing—to cool or not , 1989 .

[33]  Guixi Liu,et al.  Learning and tuning of fuzzy membership functions by simulated annealing algorithm , 2000, IEEE APCCAS 2000. 2000 IEEE Asia-Pacific Conference on Circuits and Systems. Electronic Communication Systems. (Cat. No.00EX394).

[34]  Francisco Herrera,et al.  Generating the knowledge base of a fuzzy rule-based system by the genetic learning of the data base , 2001, IEEE Trans. Fuzzy Syst..

[35]  Beatrice Lazzerini,et al.  Learning concurrently partition granularities and rule bases of Mamdani fuzzy systems in a multi-objective evolutionary framework , 2009, Int. J. Approx. Reason..

[36]  L. Glass,et al.  Oscillation and chaos in physiological control systems. , 1977, Science.

[37]  G. T. Timmer,et al.  Stochastic global optimization methods part I: Clustering methods , 1987, Math. Program..

[38]  Dimitris E. Koulouriotis,et al.  Comparing simulated annealing and genetic algorithm in learning FCM , 2007, Appl. Math. Comput..

[39]  D. D. Nauck,et al.  Learning Algorithms for Neuro-Fuzzy Systems , 2005 .