Optimization in Genetically Evolved Fuzzy Cognitive Maps Supporting Decision-Making: The Limit Cycle Case

ANDREOU, A.S. and MATEOU, N.H and Zombanakis, George A. (2004): Optimization in Genetically Evolved Fuzzy Cognitive Maps Supporting Decision-Making: The Limit Cycle Case. Published in: Proceedings of the 1st IEEE International Conference on Information & Communication Technologies: from Theory to Applications ICTTA'04, , Vol. 1, No. 1 (19 April 2004): pp. 1-6.

Abstract

This paper presents the dynamic behavior of a hybrid system comprising Fuzzy Cognitive Maps and Genetic Algorithms, and focuses on the behavior observed when the system reaches equilibrium at fixed points or limit cycle. More specifically, the present works examines the theoretical background of the equilibrium and limit cycle behaviors and proposes a defuzzification method to handle the latter case. The proposed method calculates the mean value of a limit cycle and uses this value in the defuzzification process along with a confidence rate, which indicates the reliability of the results.

• Item Type: MPRA Paper
• Language: English
• Keywords: Fuzzy Cognitive Maps, Optimisation
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C65 - Miscellaneous Mathematical Tools; H - Public Economics > H5 - National Government Expenditures and Related Policies > H56 - National Security and War

References

[1] Aleksander I, Morton H., An Introduction to Neural Computing, 1st edn Int. Th. Comp. Press, London, 1995.

[2] Axelrod R., Structure of Decision, The Cognitive Maps of Political Elite, 1st edn Princeton University Press, 1976.

[3] Andreou, A.S., Mateou N.H. and Zombanakis, G.A,Evolutionary Fuzzy Cognitive Maps: A Hybrid System for Crisis Management and Political Decision-Making. Proceedings of the International Conference on Computational Intelligent for Modeling, Control & Automation CIMCA’ 2003, 2003, pp.732-743.

[4] Andreou A.S., Mateou N.H. and Zombanakis, G.A., “Soft Computing for Crisis Management and Political Decision Making: The Use of Genetically Evolved Fuzzy Cognitive Maps” Soft Computing Journal, forthcoming.

[5] Cox E. The Fuzzy Systems Handbook - A Practitioners Guide to Building Using and Maintaining Fuzzy Systems, 1st edn. Academic Press Incorporation, London, 1994.

[6] Harth E. Order and chaos in Neural Systems: An Approach to the dynamics of Higher Brain Functions, IEEE Transactions on Systems, Man and Cybernetics, Vol. SMC-13, No. 5, USA,1983, pp. 782-789.

[7] Kartakopoullos S.V, Understanding Neural Nets works and Fuzzy Logic. 1st edn IEEE Press, New York 1996.

[8] Kosko B, Fuzzy Cognitive Maps. International Journal of Man-Machine Studies Vol. 24, 1986, pp.65-75.

[9] Kosko B, Neural Networks and Fuzzy Systems, A dynamic systems approach to Machine Intelligence, 2nd edn.,Prentice Hall, London,1992.

[10] Kosko B, Fuzzy Thinking, the New Science of fuzzy logic, 2nd edn. Harper Collins, London, 1995.

[11] Lipo W, Edgar E.P., Ross J., Oscillations and Chaos in Neural Networks: An exactly solvable model, Proc. National Academe Science, Vol. 87,USA,1997, pp. 9467-9471.

[12] Michalewicz Z, Genetic Algorithms + Data Structures = Evolution Programs, 1st edn. Springer Berlin Heidelberg, 1994.

[13] Rangarajan K., A First Course in Optimization Theory, Cambridge University Press, New York, 1996.

[14] Taber WR, Siegel M, Estimation of Expert Weights and Fuzzy Cognitive Maps. 1st IEEE International Conference on Neural Networks Vol.2, 1987, pp. 319-325.

[15] Tsadiras AK, Margaritis KG, Using Certainly Neurons in Fuzzy Cognitive Maps. Neural Network World, Vol.6, 1996, pp.719-728.

[16] Tsadiras AK, Kouskouvelis I, Margaritis KG, Cognitive Mapping and Certainty Neuron Fuzzy Cognitive Map, Information Science 101, 1997, pp. 109-130.

[17] Zadeh LA, An introduction to fuzzy logic applications in intelligent systems, 1st edn. Kluwer Academic Publisher, Boston, 1992.

[18] Grantham, W.J. and Lee, B., "A Chaotic Limit Cycle Paradox," Dynamics and Control Vol. 3, 1993, pp.157-171.

[19] Sergei Oychikov, Max-Min Representation of Piecewise Linear Functions, Contributions to Algebra and Geometry, Vol 43, No. 1, 2002, pp. 297-302.

[20] B. Radunovi´c and J.-Y. Le Boudec. A Unified Framework for Max-Min and Min-Max Fairness with Application, Technical report IC-200248, EPFL, July 2002.

[21] J. L. GELUK, A renewal theorem in finite-mean case ,Proceedings of the American mathematical society, Vol 125, 1996, pp. 3407-3413.