Fuzzy cognitive maps in multi-agent environments

  • Paulo Camargo Silva
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 992)


In the last years we have seen a large development about fuzzy cognitive maps (FCMs). The theoretical base of FCM is connected with the neural networks theory (differential hebbian learning) and fuzzy sets and systems theory. There are applications of the FCM in the following fields of research: adaptive network cognitive processor, analyze and extend graph theoretical behavior, plant control, information requirement analysis, analysis electrical circuit, model gastric-appetite behavior and popular political development. Our interest in this work is to show the importance of combination of FCM with the multi-agent modal logic of knowledge and belief to model structures of complex design in multiagent environments. We make an application to plant control. The model that we introduce can be used to model popular political development, social systems, and military strategy, and others. In Goto and Yamaguchi [1991] is shown as FCMs can model plant control. In our point of view an ideal model of plant control must not involve the opinion of an expert about a plant control, but the opinion of a group of experts. If each expert of a group makes a FCM on a plant control, it is interesting to investigate what signifies the common knowledge of group about this plant control. Moreover is interesting to know what each agent of group knows about the FCM made by others agents. This can be much important in the design of plant control and to build political model, social systems, and military strategy. With reference to multi-agent modal logic of knowledge and belief, we make a generalization of work of Friedman and Halpern [1994a], Friedman and Halpern [1994b], by using of fuzzy measures. The multi-agent modal logic of knowledge and belief with fuzzy measures allows interpret fuzzy statements with linguistic fuzzy quantifiers such as developed in FCM.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. HALPERN, J., & MOSES, Y. [1992]-A Guide to Completeness and Complexity for for Modal Logic of Knowledge and Belief, Artificial Intelligence Vol. 54, No. 3, april 319–379.Google Scholar
  2. TABER, W. R. [1991]-Knowledge Processing with Fuzzy Cognitive Maps, Expert Systems with Applications, Vol. 2, 83–87.Google Scholar
  3. EDSON, B., TURNER, C., MEYERS, M., & SIMPSON, P.[1988]-The Adaptive Networks Cognitive Processor, Proceedings of the 1988 Aerospace Applications of Artificial Intelligence (AAAIC 88), Vol.II.Google Scholar
  4. MYERS, M., TURNER, C., KUCZEWSKI, R., & SIMPSON, P. [1988]-ANCP Adaptive Network Cognitive Processor: Vols I & II, TRW MEAD, Final Report Prepared for Air Force Wright Aeronautical LaboratoriesGoogle Scholar
  5. STYBLINSKI, M. & MEYER, B. [1988]-Fuzzy Cognitive Map, Signal Flow Graphs, and Qualitative Circuit Analysis, Proceedings of the IEEE International Conference on Neural Network: Vol. II, (pp. 549–556). San Diego: IEEE.Google Scholar
  6. MENTAZENI, A. & CONRATH, D. [1986]-The Use of Cognitive Mapping for Information Requirement Analysis, Management Information Systems Quarterly.Google Scholar
  7. SUGENO, M.[1977]-Fuzzy Measures and Fuzzy Integrals — a survey, in Gupta, M.M., Saridis, G.N., and Gaines, B.R.[1977].Google Scholar
  8. GUPTA, M.M., et. al.[1977]-Fuzzy Automata and Decision Processes, North-Holland, New York.Google Scholar
  9. DUBOIS, H. & PRADE, D. [1982]-A Class of Fuzzy Measures based on Triangular Norms, International, J. of General Systems, 8.Google Scholar
  10. KOSKO, B. [1992]-Neural Networks and Fuzzy Systems: A Dynamical Systems Approach to Machine Intelligence, Prentice Hall, New York.Google Scholar
  11. STYBLINSKI, M. & MEYER, B. [1991]-Signal Flow Graphs vs Fuzzy Cognitive in Application to Qualitative Circuit Analysis, International Journal of Man-Machine Studies, 35, 175–186.Google Scholar
  12. GOTO, K., & MURAKAMI, J., YAMAGUCHI, T., & YAMANAKA, Y., [1989]-Application of Fuzzy Cognitive Maps to Supporting for Plant Control, (in Japanese) 10th Knowledge Engineering Symposium, 99–104.Google Scholar
  13. GOTO, K., & YAMAGUCH. T.[1991]-Fuzzy Associative Memory Application to a Plant Modeling, in Kohonen, K., Makisara, O. Simula, O., and Kangas, J. [1991]Google Scholar
  14. KOHONEN, K., MAKISARA, O. SIMULA, O., & KANGAS, J. [1991]-Artificial Neural Networks, Vol.2, North-Holland.Google Scholar
  15. ZHANG, W., & CHEN, S. [1988]-A Logical Architecture for Cognitive Maps, Proceedings of the 2nd IEEE International Conference on Neural Network, Vol. I, 231–238, july.Google Scholar
  16. FRIEDMAN, N. & HALPERN, J.[1994a]-A knowledge-Based Framework For Belief Change Part I: Foundations, Proceedings of Theoretical Aspects of Reasoning about Knowledge, Morgan Kaufman.Google Scholar
  17. FRIEDMAN, N. & HALPERN, J.[1994b]-A Knowledge-Based Framework For Belief Change Part II: Revision and Update, Principles of Knowledge Representation and Reasoning: Proc. Fourth International Conference (KR'94)Google Scholar
  18. FRIEDMAN, N. & HALPERN, J.[1994c]-On the Complexity of Conditional Logics, in Principles of Knowledge Representation and Reasoning: Proc. Fourth International Conference (KR'94).Google Scholar
  19. ZADEH, L.A.[1978]-Fuzzy sets as a Basis for a Theory of Possibility, Fuzzy Sets and Systems, Vol. 1, No. 1, pp. 3–28.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Paulo Camargo Silva
    • 1
  1. 1.University of Erlangen-NuernbergErlangenGermany

Personalised recommendations