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.
[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
[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
@article{"International Journal of Information, Control and Computer Sciences:61479", author = "Somayeh Alizadeh and Mehdi Ghazanfari and Mostafa Jafari and Salman Hooshmand", title = "Learning FCM by Tabu Search", abstract = "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.", volume = "1", number = "9", pages = "2840-8", }
