Advertisement

Fuzzy Cognitive Maps: Analysis and Extensions

  • Zhi-Qiang Liu
Part of the Computer Science Workbench book series (WORKBENCH)

Abstract

Fuzzy cognitive map (FCM) [5] was a modification of the cognitive map of Axelrod [1]. FCMs can be used in knowledge representation and inference which are essential to any intelligent system. FCM encodes rules in its networked structure in which all concepts are causally connected. Rules are fired based on a given set of initial conditions and the structure of the FCM. The resulting map pattern represents the causal inference of the FCM. In FCMs, we are able to represent all concepts and arcs (edges) connecting the concepts by symbols or numerical values. Moreover, in such a framework it is possible to handle different types of uncertainties effectively and to combine readily several FCMs into a single FCM that takes the knowledge from different experts into consideration [6]. FCM provides a mechanism for handling causality between events/objects in a more natural fashion. Indeed, FCM is a flexible and realistic representation scheme for dealing with knowledge. This scheme is potentially useful in the development of human-centered systems that require soft-knowledge in the sense that system concepts, their relationships, and the meta-system knowledge can be represented only to a certain degree. In addition, subtle (spatial and temporal) variations in the knowledge base can often result in completely different outcomes or decisions [25]. Many recently developed systems and successful applications have shown that fuzzy cognitive maps represent a promising paradigm for the development of functional intelligent systems [10, 15, 19, 20].

Keywords

Fuzzy System Vertex Function Connection Matrix Inference Pattern Input Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R. Axelrod, Structure of Decision: the Cognitive Maps of Political Elites, Princeton, NJ:Princeton University Press, 1976.Google Scholar
  2. [2]
    J. A. Dickerson and B. Kosko, “Virtual Worlds as Fuzzy Cognitive Maps,” pp.471–477, 1993.Google Scholar
  3. [3]
    M. Hagiwara, “Extended Fuzzy Cognitive Maps,” Proceedings of International Conference on Fuzzy Systems, pp.795–801, 1992.Google Scholar
  4. [4]
    S.H. Kim and K.S. Park, “Fuzzy Cognitive Maps Considering Time Relationships,” International Journal of Human Computer Studies, Vol.42, Issue 2, pp.157–168, 1995.CrossRefGoogle Scholar
  5. [5]
    B. Kosko, “Fuzzy Cognitive Maps,” International Journal Manmachine Studies, Vol.24, pp.65–75, 1986.MATHCrossRefGoogle Scholar
  6. [6]
    B. Kosko, “Adaptive Inference in Fuzzy Knowledge Networks,” Proceedings of the First Int. Conf. on Neural Networks, Vol.2, pp261–268, 1987.Google Scholar
  7. [7]
    B. Kosko, “Fuzzy System as Universal Approximators,” Proceedings of the 1st IEEE International Conference on Fuzzy Systems, pp.1153–1162, 1992.Google Scholar
  8. [8]
    B. Kosko, Neural Networks and Fuzzy Systems: A Dynamical Systems Approach to Machine Intelligence, Prentice-Hall, Englewood Cliffs, 1992.Google Scholar
  9. [9]
    Z.Q. Liu, Fuzzy Cognitive Networks: Theory and Applications, Spriner Verlag, Berling, (to appear) Dec. 2000.Google Scholar
  10. [10]
    Z.Q. Liu and R. Satur, “Contextual Fuzzy Cognitive Map for Decision Support in Geographic Information Systems,” (to appear) IEEE Trans. Fuzzy Systems, Sept. 1999.Google Scholar
  11. [11]
    Z.Q. Liu and Y. Miao, “Fuzzy Cognitive Map and Its Causal Inferences,” Proceedings of IEEE International Conference on Fuzzy Systems, Vol.3, pp.1540–1545, FUZZ-IEEE’1999, Seoul, S. Korea, Aug.22-25, 1999.Google Scholar
  12. [12]
    Y. Miao and Z.Q. Liu, “On Causal Inference in Fuzzy Cognitive Maps,” (to appear) IEEE Tran. Fuzzy Systems, Nov. 1999.Google Scholar
  13. [13]
    Y. Miao and Z.Q. Liu, “Dynamical Cognitive Network as an Extension of Fuzzy Cognitive Map,” (in press) Proceedings of International Conference on Tools in Artificial Intelligence, Chicago, IL, USA, Nov. 9-11, 1999.Google Scholar
  14. [14]
    Y. Miao and Z.Q. Liu, “Dynamical Cognitive Networks,” submitted to IEEE Tran. Fuzzy Systems, 1999.Google Scholar
  15. [15]
    T. D. Ndousse and T. Okuda, “Computational Intelligence for Distributed Fault Management in Networks Using Fuzzy Cognitive Maps,” Proceedings of IEEE International Conference on Communications Converging Technologies for Tomorrow’s Application, IEEE New York, Vol.3, pp.1558–1562, 1996.Google Scholar
  16. [16]
    C. E. Pelaez and J. B. Bowles, “Applying Fuzzy Cognitive Maps Knowledge-Representation to Failure Modes Effects Analysis,” Proceedings of Annual Reliability and Maintainability Symposium, pp.450–456, 1995.Google Scholar
  17. [17]
    K. Perusich, “Fuzzy Cognitive Maps for Policy Analysis,” Proceedings of International Symposium on Technology and Society Technical Expertise and Public Decisions, IEEE New York, pp.369–373, 1996.Google Scholar
  18. [18]
    R. Satur, Z.Q. Liu, and M. Gahegan, “Multi-layered Fuzzy Cognitive Map Applied to Context Dependent Learning,” Proceedings of Interntational Joint Conference of 4th IEEE International Conference on Fuzzy Systems and 2nd International Fuzzy Engineering Symposium IEEE FUZZ-IEEE/IFES’95, Yokohama, Japan, pp.561–568, March 20-24, 1995.Google Scholar
  19. [19]
    R. Satur and Z.Q. Liu, “A Context-driven Intelligent Database Processing System Using Object Oriented Fuzzy Cognitive Maps,” International Journal of Intelligent Systems, Vol.11, No.9, pp.671–689, 1996.CrossRefGoogle Scholar
  20. [20]
    R. Satur and Z.Q. Liu, “A Contextual Fuzzy Cognitive Map Framefwork for Geographic Information Systems,” (to appear) IEEE Trans. Fuzzy Systems, Sept. 1999.Google Scholar
  21. [21]
    M. Schneider, E. Shnaider, A. Kandel, and G. Chew, “Constructing Fuzzy Cognitive Maps,” Proceedings of IEEE International Conference on Fuzzy Systems, IEEE New York, pp.2281–2288, 1995.Google Scholar
  22. [22]
    P.C. Silva, “New Forms of Combinated Matrices in Fuzzy Cognitive Maps,” Proceedings of International Conference on Neural Networks, Vol.2, pp.771–776, 1995.Google Scholar
  23. [23]
    R.W. Taber and M.A. Siegel, “Estimation of Expert Weights Using Fuzzy Cognitive Maps,” Proceedings of 1st International Conference on Neural Networks, Vol.2, pp.319–325, 1987.Google Scholar
  24. [24]
    R.W. Taber, “Knowledge Processing with Fuzzy Cognitive Maps,” Expert Systems with Applications, Vol. 2, Issue 1, pp.83–87, 1991.CrossRefGoogle Scholar
  25. [25]
    W.A. Woods, “Important Issues in Knowledge Representation,” Knowledge-Based Systems: Fundamentals and Tools, O. N. Garcia and Y. Chien (Eds), IEEE Computer Society Press, 1991.Google Scholar

Copyright information

© Springer-Verlag Tokyo 2000

Authors and Affiliations

  • Zhi-Qiang Liu

There are no affiliations available

Personalised recommendations