Fuzzy Logic pp 147-167 | Cite as

On Self-Organization of Cooperative Systems and Fuzzy Logic

  • Victor Korotkich
Conference paper
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 81)


A collection of many systems that cooperatively solve an optimization problem is considered. The consideration aims to determine conditions for the systems to be self-organized demonstrating their best performance for the problem. A general framework based on a concept of structural complexity is proposed to determine the conditions. The main merit of this framework is that it allows to set up computational experiments revealing a condition of best performance. The experiments give evidence to suggest that the condition is realized when the structural complexity of cooperative systems equals the structural complexity of the optimization problem. Importantly, the key parameter involved in the condition is of fuzzy logic character and admits interpretation in terms of human perceptions. The results of the paper give a new perspective in the developing of optimization methods based on cooperative systems and show the relevance of fuzzy logic to self-organization.


Optimal Algorithm Fuzzy Logic Computational Experiment Complexity Space Travel Salesman Problem 
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.


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  1. 1.
    R. Axelrod, (1984) The Evolution of Cooperation, Basic Books, New York.Google Scholar
  2. 2.
    M. Mezard, G. Parisi and M. A. Virasoro, (1987) Spin Glass Theory and Beyond, World Scientific, Singapore.MATHGoogle Scholar
  3. 3.
    B. Huberman, (1990) The Performance of Cooperative Processes, Physica D, vol. 42, pp. 39–47.Google Scholar
  4. 4.
    J. Holland, (1998) Emergence: From Chaos to Order, Perseus Books, Massachusetts.MATHGoogle Scholar
  5. 5.
    E. Bonabeau, M. Dorigo and G. Theraulaz, (1999) Swarm Intelligence: From Natural to Artificial Systems, Oxford University Press, Oxford.MATHGoogle Scholar
  6. 6.
    L. Zadeh, (1996), Fuzzy Logic = Computing with Words, IEEE Transactions on Fuzzy Systems, vol. 4, No. 2, pp. 103–111.Google Scholar
  7. 7.
    V. Korotkich, (1999) A Mathematical Structure for Emergent Computation, Kluwer Academic Publishers, Dordrecht/Boston/London.MATHGoogle Scholar
  8. 8.
    V. Korotkich, (1995) Multicriteria Analysis in Problem Solving and Structural Complexity, in Advances in Multicriteria Analysis, edited by P. Pardalos, Y. Siskos and C. Zopounidis, Kluwer Academic Publishers, Dordrecht, pp. 81–90.CrossRefGoogle Scholar
  9. 9.
    E. Prouhet, (1851) Memoire sur Quelques Relations entre les Puissances des Nombres, C.R. Acad. Sci., Paris, vol. 33, p. 225.Google Scholar
  10. 10.
    A. Thue, (1906) Uber unendliche Zeichenreihen, Norske vid. Selsk. Skr. I. Mat. Nat. Kl. Christiana, vol. 7, p. 1.Google Scholar
  11. 11.
    M. Morse, (1921) Recurrent Geodesics on a Surface of Negative Curvature, Trans. Amer. Math. Soc., vol. 22, p. 84.Google Scholar
  12. 12.
  13. 13.
  14. 14.
    S. Weinberg, (1993) Dreams of a Final Theory, Vintage, London.Google Scholar
  15. 15.
    R. Monasson, R. Zecchina, S. Kirkpatrick, B. Selman and L. Troyansky, (1999) Determining Computational Complexity from Characteristic ‘Phase Transitions’, Nature, vol. 400, pp. 133–137.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Victor Korotkich
    • 1
  1. 1.Central Queensland UniversityMackayAustralia

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