Learning FCM by chaotic simulated annealing

Abstract Fuzzy cognitive map (FCM) is a directed graph, which shows the relations between essential components in complex systems. It is a very convenient, simple, and powerful tool, which is used in numerous areas of application. Experts who are familiar with the system components and their relations can generate a related FCM. There is a big gap when human experts cannot produce FCM or even there is no expert to produce the related FCM. Therefore, a new mechanism must be used to bridge this gap. In this paper, a novel learning method is proposed to construct FCM by using Chaotic simulated annealing (CSA). The proposed method not only is able to construct FCM graph topology but also is able to extract the weight of the edges from input historical data. The efficiency of the proposed method is shown via comparison of its results of some numerical examples with those of Simulated annealing (SA) method.

[1]  D. E. Koulouriotis,et al.  Learning fuzzy cognitive maps using evolution strategies: a novel schema for modeling and simulating high-level behavior , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[2]  Abraham Kandel,et al.  Automatic construction of FCMs , 1998, Fuzzy Sets Syst..

[3]  Amir Azaron,et al.  Solving a dynamic cell formation problem using metaheuristics , 2005, Appl. Math. Comput..

[4]  M. Quaddus,et al.  Group Decision Support Using Fuzzy Cognitive Maps for Causal Reasoning , 2004 .

[5]  M. Mohammadian.  Computational Intelligence for Modelling, Control and Automation '99 , 1999 .

[6]  M. A. Styblinski,et al.  Signal Flow Graphs vs Fuzzy Cognitive Maps in Application to Qualitative Circuit Analysis , 1991, Int. J. Man Mach. Stud..

[7]  W. Stach,et al.  Parallel fuzzy cognitive maps as a tool for modeling software development projects , 2004, IEEE Annual Meeting of the Fuzzy Information, 2004. Processing NAFIPS '04..

[8]  Bart Kosko,et al.  Fuzzy Cognitive Maps , 1986, Int. J. Man Mach. Stud..

[9]  Michael N. Vrahatis,et al.  A first study of fuzzy cognitive maps learning using particle swarm optimization , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[10]  Michel G. Bougon,et al.  CONGREGATE COGNITIVE MAPS: A UNIFIED DYNAMIC THEORY OF ORGANIZATION AND STRATEGY , 1992 .

[11]  Kun Chang Lee,et al.  Strategic Planning Simulation Based on Fuzzy Cognitive Map Knowledge and Dif ferential Game , 1998, Simul..

[12]  Huanwen Tang,et al.  Application of chaos in simulated annealing , 2004 .

[13]  Amit Konar,et al.  Reasoning and unsupervised learning in a fuzzy cognitive map , 2005, Inf. Sci..

[14]  Chrysostomos D. Stylios,et al.  Fuzzy Cognitive Map Learning Based on Nonlinear Hebbian Rule , 2003, Australian Conference on Artificial Intelligence.

[15]  Ioannis Antoniou,et al.  Cellular automata study of high burn-up structures , 2003 .

[16]  Chrysostomos D. Stylios,et al.  Fuzzy cognitive maps: a model for intelligent supervisory control systems , 1999 .

[17]  Chrysostomos D. Stylios,et al.  The challenge of modelling supervisory systems using fuzzy cognitive maps , 1998, J. Intell. Manuf..

[18]  Alex Chong,et al.  Fuzzy Cognitive Map Analysis with Genetic Algorithm , 2003, IICAI.

[19]  Chrysostomos D. Stylios,et al.  Modeling complex systems using fuzzy cognitive maps , 2004, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[20]  David W. Conrath,et al.  The Use of Cognitive Mapping for Information Requirements Analysis , 1986, MIS Q..

[21]  Chrysostomos D. Stylios,et al.  Unsupervised learning techniques for fine-tuning fuzzy cognitive map causal links , 2006, Int. J. Hum. Comput. Stud..

[22]  Chrysostomos D. Stylios,et al.  Fuzzy Cognitive Maps in modeling supervisory control systems , 2000, J. Intell. Fuzzy Syst..

[23]  Bart Kosko,et al.  Fuzzy Engineering , 1996 .

[24]  Michael N. Vrahatis,et al.  Fuzzy Cognitive Maps Learning Using Particle Swarm Optimization , 2005, Journal of Intelligent Information Systems.

[25]  Emile H. L. Aarts,et al.  Simulated Annealing: Theory and Applications , 1987, Mathematics and Its Applications.

[26]  Dimitris E. Koulouriotis,et al.  Development of dynamic cognitive networks as complex systems approximators: validation in financial time series , 2005, Appl. Soft Comput..

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

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

[29]  Yanbin Yuan,et al.  A hybrid chaotic genetic algorithm for short-term hydro system scheduling , 2002, Math. Comput. Simul..

[30]  Ahmad Harb,et al.  Controlling Hopf bifurcation and chaos in a small power system , 2003 .

[31]  Chrysostomos D. Stylios,et al.  Active Hebbian learning algorithm to train fuzzy cognitive maps , 2004, Int. J. Approx. Reason..

[32]  Dimitris E. Koulouriotis,et al.  Anamorphosis of fuzzy cognitive maps for operation in ambiguous and multi-stimulus real world environments , 2001, 10th IEEE International Conference on Fuzzy Systems. (Cat. No.01CH37297).

[33]  Witold Pedrycz,et al.  Genetic learning of fuzzy cognitive maps , 2005, Fuzzy Sets Syst..

[34]  Chen Tian-Lun,et al.  Application of Chaos in Genetic Algorithms , 2002 .

[35]  Voula C. Georgopoulos,et al.  A fuzzy cognitive map approach to differential diagnosis of specific language impairment , 2003, Artif. Intell. Medicine.

[36]  Bart Kosko,et al.  Neural networks and fuzzy systems , 1998 .

[37]  D. Kardaras,et al.  Using Fuzzy Cognitive Maps to Model and Analyse Business Performance Assessment , 1997 .

[38]  José Tomé,et al.  Fuzzy Mechanisms For Causal Relations , 2002 .

[39]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[40]  Guanrong Chen,et al.  From Chaos To Order Methodologies, Perspectives and Applications , 1998 .

[41]  Bart Kosko,et al.  Hidden patterns in combined and adaptive knowledge networks , 1988, Int. J. Approx. Reason..

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

[43]  José Tomé,et al.  Rule Based Fuzzy Cognitive Maps: Fuzzy Causal Relations , 2002 .

[44]  J.A.B. Tome,et al.  Rule based fuzzy cognitive maps and fuzzy cognitive maps-a comparative study , 1999, 18th International Conference of the North American Fuzzy Information Processing Society - NAFIPS (Cat. No.99TH8397).

[45]  M. Pirlot.  General local search methods , 1996 .

[46]  J.A.B. Tome,et al.  Rule based fuzzy cognitive maps-qualitative systems dynamics , 2000, PeachFuzz 2000. 19th International Conference of the North American Fuzzy Information Processing Society - NAFIPS (Cat. No.00TH8500).