Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31900
Learning FCM by Tabu Search

Authors: Somayeh Alizadeh, Mehdi Ghazanfari, Mostafa Jafari, Salman Hooshmand


Fuzzy Cognitive Maps (FCMs) is a causal graph, which shows the relations between essential components in complex systems. 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 causal graph based on historical data and by using metaheuristic such Tabu Search (TS). The efficiency of the proposed method is shown via comparison of its results of some numerical examples with those of some other methods.

Keywords: Fuzzy Cognitive Map (FCM), Learning, Meta heuristic, Genetic Algorithm, Tabu search.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1713


[1] R.Axelrod, Structure of Decision: The Cognitive Maps of Political Elites, Princeton University Press, Princeton, NJ, 1976.
[2] M.A. Styblinski, B.D. Meyer, Signal flow graphs versus fuzzy cognitive maps in application to qualitative circuit analysis, Internet. J. Man Mach. Studies 35 (1991) 175-186.
[3] V.C. Georgopoulos, G.A. Malandraki, C.D. Stylios, A fuzzy cognitive map approach to differential diagnosis of specific language impairment, J. Artif. Intel. Med. 29 (3) (2003) 261-278.
[4] C.D. Stylios, P.P. Groumpos, The challenge of modeling supervisory systems using fuzzy cognitive maps, J.Intel. Manuf. 9 (4) (1998) 339- 345.
[5] C.D. Stylios, P.P. Groumpos, Fuzzy cognitive maps: a model for intelligent supervisory control systems, Comput. Ind. 39 (3) (1999) 229- 238.
[6] C.D. Stylios, P.P. Groumpos, Fuzzy cognitive map in modeling supervisory control systems, J. Intel. & Fuzzy Systems 8 (2) (2000) 83- 98.
[7] M. G. Bougon, "Congregate Cognitive Maps: a Unified Dynamic Theory of Organization and Strategy," Journal of Management Studies, 29:369-389, (1992)
[8] K.C. Lee,W.J. Lee, O.B. Kwon, J.H. Han, P.I.Yu, Strategic planning simulation based on fuzzy cognitive map knowledge and differential game, Simulation 71 (5) (1998) 316-327.
[9] D. Kardaras, G. Mentzas, Using fuzzy cognitive maps to model and analyze business performance assessment, in: J. Chen, A. Mital (Eds.), Advances in Industrial Engineering Applications and Practice II, 1997, pp. 63-68.
[10] W. Stach, L. Kurgan, Modeling software development project using fuzzy cognitive maps, Proc. 4th ASERC Workshop on Quantitative and Soft Software Engineering (QSSE-04), 2004, pp. 55-60.
[11] W. Stach, L. Kurgan,W. Pedrycz, M. Reformat, Parallel fuzzy cognitive maps as a tool for modeling software development project, Proc. 2004 North American Fuzzy Information Processing Society Conf. (NAFIPS-04), Banff, AB, 2004, pp. 28-33.
[12] A. R. Montazemi, D. W. Conrath, "The Use of Cognitive Mapping for Information Requirements Analysis," MIS Quarterly, 10:44-55, (1986)
[13] K. Gotoh, J. Murakami, T.Yamaguchi, Y.Yamanaka, Application of fuzzy cognitive maps to supporting for plant control, Proc. SICE Joint Symp. 15th Systems Symp. and Tenth Knowledge Engineering Symp., 1989, pp. 99-104.
[14] Carvalho, J.P.,Tomé, J.A.,"Rule Based Fuzzy Cognitive Maps and Fuzzy Cognitive Maps - A Comparative Study", Proceedings of the 18th International Conference of the North American Fuzzy Information Processing Society, NAFIPS99, New York
[15] Carvalho, J.P., Tomé, J.A.,"Rule Based Fuzzy Cognitive Maps- Fuzzy Causal Relations", Computational Intelligence for Modelling, Control and Automation, Edited by M. Mohammadian, 1999
[16] Carvalho, J.P., Tomé, J.A., "Fuzzy Mechanisms for Causal Relations", Proceedings of the Eighth International Fuzzy Systems Association World Congress, IFSA'99, Taiwan
[17] Carvalho,J.P.,Tomé, J.A.,"Rule Based Fuzzy Cognitive Maps - Qualitative Systems Dynamics", Proceedings of the 19th International Conference of the North American Fuzzy Information Processing Society, NAFIPS2000, Atlanta
[18] S.Alizadeh, M.Ghazanfari, M.Jafari, "An approach for solving fuzzy system dynamics problems", 21st International system dynamics conference, U.S.A, July 2003.
[19] D.E. Koulouriotis, I.E. Diakoulakis, D.M. Emiris, E.N. Antonidakis, I.A. Kaliakatsos, Efficiently modeling and controlling complex dynamic systems using evolutionary fuzzy cognitive maps (Invited Paper), Internat. J. Comput. Cognition 1 (2) (2003) 41-65.
[20] D.E. Koulouriotis, I.E. Diakoulakis, D.M. Emiris, C.D.Zopounidis, Development of dynamic cognitive networks as complex systems approximators: validation in financial time series, Applied Soft Computing 5 (2005) 157-179
[21] C.D. Stylios, P.P. Groumpos, Modeling complex systems using fuzzy cognitive maps, IEEE Trans. Systems Man, Cybern. Part A: Systems Humans 34 (1) (2004).
[22] D.E. Koulouriotis, I.E. Diakoulakis, D.M. Emiris, Anamorphosis of fuzzy cognitive maps for operation in ambiguous and multi-stimulus real world environments, 10th IEEE Internet. Conf. on Fuzzy Systems, 2001, pp. 1156-1159.
[23] B. Kosko, Hidden patterns in combined and adaptive knowledge networks, Internet. J.Approx. Reason.2 (1988) 377-393.
[24] B. Kosko, Fuzzy cognitive maps, Internat. J. Man-Mach. Studies 24 (1986) 65-75.
[25] B. Kosko, Neural Networks and Fuzzy Systems, Prentice-Hall, Englewood Cliffs, NJ, 1992.
[26] B. Kosko, Fuzzy Engineering, Prentice-Hall, Englewood Cliffs, NJ, 1997.
[27] M. Khan, M.Quaddus, Group decision support using fuzzy cognitive maps for causal reasoning, Group Decision Negotiation J. 13 (5) (2004) 463-480.
[28] Wojciech Stach, Lukasz Kurgan,Witold Pedrycz, Marek Reformat Genetic learning off uzzy cognitive maps, Fuzzy Sets and Systems 153 (2005) 371-401
[29] E Papageorgiou, C.Stylios P. Groumpos, Unsupervised learning techniques for fine-tuning fuzzy cognitive map causal links, Int. J. Human-Computer Studies 64 (2006) 727-743
[30] Lee C. C, Fuzzy logic in control systems: Fuzzy logic controller, Part 1, 2 IEEE Trans.Syst.Man Cybernet, 20 (2), 404-435.
[31] M. Schneider, E. Shnaider, A. Kandel, G. Chew, Automatic construction of FCMs, Fuzzy Sets and Systems 93 (2) (1998) 161-172.
[32] Kun Chang Lee , Jin Sung Kim, Nam Ho Chung, Soon Jae Kwon, Fuzzy cognitive map approcha to web mining inference amplification, Expert System with Applications 22 (2002) 197-211
[33] D. Kardaras, B. Karakostas "The use of fuzzy cognitive maps to simulate the information systems strategic planning process". Information and Software Technology 41 (1999) 197-210
[34] J.A. Dickerson, B. Kosko, Fuzzy virtual worlds, Artif.Intel. Expert 7 (1994) 25-31.
[35] A. Vazquez, A balanced differential learning algorithm in fuzzy cognitive maps, Technical Report, Departament de Llenguatges I Sistemes Informatics, Universitat Politecnica de Catalunya (UPC), 2002.
[36] E. Papageorgiou, C.D. Stylios, P.P. Groumpos, Fuzzy cognitive map learning based on nonlinear Hebbian rule, Australian Conf. on Artificial Intelligence, 2003, pp. 256-268.
[37] E. Papageorgiou, C.D. Stylios, P.P. Groumpos, Active Hebbian learning algorithm to train fuzzy cognitive maps, Internat. J.Approx.Reason.37 (3) (2004) 219-249.
[38] D.E. Koulouriotis, I.E. Diakoulakis, D.M. Emiris, Learning fuzzy cognitive maps using evolution strategies: a novel schema for modeling and simulating high-level behavior, IEEE Congr. On Evolutionary Computation (CEC2001), 2001, pp. 364-371.
[39] E. Papageorgiou, K.E. Parsopoulos, C.D. Stylios, P.P. Groumpos, M.N. Vrahatis, Fuzzy cognitive maps learning using particle swarm optimization, J. Intel. Inform.Systems. 2005
[40] K.E. Parsopoulos, E.I. Papageorgiou, P.P. Groumpos, M.N. Vrahatis, A first study of fuzzy cognitive maps learning using particle swarm optimization, Proc. IEEE 2003 Congr. On Evolutionary Computation, 2003, pp. 1440-1447.
[41] M. Khan, A. Chong, Fuzzy cognitive map analysis with genetic algorithm, Proc. 1st Indian Internat. Conf. on Artificial Intelligence (IICAI-03), 2003
[42] Amit Konar, Uday K. Chakraborty , Reasoning and unsupervised learning in a fuzzy cognitive map , Information Sciences 170 (2005) 419-441
[43] M.Ghazanfari, S.Alizadeh,M.Fathian,D.E.Koulouriotis, Comparing Simulated Annealing and Genetic Algorithm in Learning FCM, Applied Mathematics and Computation (2007), doi:10.1016/ j.amc.2007.02.144
[44] Hussein Aly Abbass, Ruhul Amin, Sarker, Charles S. Newton. Data mining : a heuristic approach , 2002, Idea Group Publishing.
[45] Marc Pirlot, General local search methods, European journal of operational research 92, 1996 , 493-511
[46] R.Tavakkoli-Moghaddam, M.B. Aryanezhad, N.Safaei, A. Azaron, Solving a dynamic cell formation problem using metaheuristics, Applied Mathematics and Computation 170 (2005) 761-780