Big Bang – Big Crunch Learning Method for Fuzzy Cognitive Maps

Modeling of complex dynamic systems, which are very complicated to establish mathematical models, requires new and modern methodologies that will exploit the existing expert knowledge, human experience and historical data. Fuzzy cognitive maps are very suitable, simple, and powerful tools for simulation and analysis of these kinds of dynamic systems. However, human experts are subjective and can handle only relatively simple fuzzy cognitive maps; therefore, there is a need of developing new approaches for an automated generation of fuzzy cognitive maps using historical data. In this study, a new learning algorithm, which is called Big Bang-Big Crunch, is proposed for the first time in literature for an automated generation of fuzzy cognitive maps from data. Two real-world examples; namely a process control system and radiation therapy process, and one synthetic model are used to emphasize the effectiveness and usefulness of the proposed methodology. Keywords—Big Bang-Big Crunch optimization, Dynamic Systems, Fuzzy Cognitive Maps, Learning.

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

[2]  Siamak Talatahari,et al.  Optimal design of Schwedler and ribbed domes via hybrid Big Bang–Big Crunch algorithm , 2010 .

[3]  Somayeh Alizadeh,et al.  Learning FCM by chaotic simulated annealing , 2009 .

[4]  Y. Istefanopulos,et al.  OPTIMAL NONLINEAR CONTROLLER DESIGN FOR FLEXIBLE ROBOT MANIPULATORS WITH ADAPTIVE INTERNAL MODEL , 2007 .

[5]  Charles V. Camp.  DESIGN OF SPACE TRUSSES USING BIG BANG–BIG CRUNCH OPTIMIZATION , 2007 .

[6]  Alberto Vázquez Huerga.  A Balanced Differential Learning algorithm in Fuzzy Cognitive Maps , 2002 .

[7]  Bart Kosko,et al.  Virtual Worlds as Fuzzy Cognitive Maps , 1994, Presence: Teleoperators & Virtual Environments.

[8]  Jose Aguilar,et al.  A Survey about Fuzzy Cognitive Maps Papers (Invited Paper) , 2005 .

[9]  Shigeo Abe,et al.  Neural Networks and Fuzzy Systems , 1996, Springer US.

[10]  Ibrahim Eksin,et al.  A new optimization method: Big Bang-Big Crunch , 2006, Adv. Eng. Softw..

[11]  Osman Kaan Erol,et al.  A Genetic Programming Classifier Design Approach for Cell Images , 2007, ECSQARU.

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

[13]  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..

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

[15]  H.M. Genc,et al.  Bearing-Only Target Tracking Based on Big Bang – Big Crunch Algorithm , 2008, 2008 The Third International Multi-Conference on Computing in the Global Information Technology (iccgi 2008).

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

[17]  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.

[18]  Chrysostomos D. Stylios,et al.  Modelling supervisory control systems using fuzzy cognitive maps , 2000 .

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

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

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

[22]  Engin Yesil,et al.  Big Bang Big Crunch Optimization Method Based Fuzzy Model Inversion , 2008, MICAI.

[23]  A. Kaveh,et al.  Size optimization of space trusses using Big Bang-Big Crunch algorithm , 2009 .

[24]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[25]  Ricardo J. G. B. Campello,et al.  Towards true linguistic modelling through optimal numerical solutions , 2003, Int. J. Syst. Sci..

[26]  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).

[27]  Michael N. Vrahatis,et al.  Evolutionary Computation Techniques for Optimizing Fuzzy Cognitive Maps in Radiation Therapy Systems , 2004, GECCO.

[28]  Michael N. Vrahatis,et al.  Improving fuzzy cognitive maps learning through memetic particle swarm optimization , 2008, Soft Comput..

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