Advertisement

Algebraic Fuzzy Automata

  • Davender S. Malik
  • John N. Mordeson
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 58)

Abstract

A fuzzy finite state machine (ffsm) is a triple M = (Q, X, µ), where Q and X are finite nonempty sets and µ is a fuzzy subset of Q × X × Q, i.e., µ : Q × X × Q → [0, 1] . Let X* denote the set of all words of elements of X of finite length.

Keywords

Finite State Machine Exchange Property Finite Index Fuzzy Subset Congruence Relation 
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.
    Arbib, M.A., Algebraic Theory of Machines, Languages, and Semigroups, Academic Press, New York, 1968.MATHGoogle Scholar
  2. 2.
    Bavel, Z., Introduction to the Theory of Automata, Reston Publishing Co., Inc., Reston Virginia, A Prentice Hall Company, 1983.MATHGoogle Scholar
  3. 3.
    Comer, S. D., Polygroups derived from cogroups, J. Alg., 89 (1984), 397- 405.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Dörfler, W., The cartesian composition of automata, Math. Systems Theory, 11 (1978) 239–257.MATHCrossRefGoogle Scholar
  5. 5.
    Eilenberg, S., Automata, Languages and Machines, Vol. A, B, Academic Press, New York, 1974, 1976.MATHGoogle Scholar
  6. 6.
    Holcombe, W.M.L., Algebraic Automata Theory, Cambridge University Press, New York, 1982.MATHCrossRefGoogle Scholar
  7. 7.
    Jantosciak, J., Homomorphisms, Equivalences and reductions in hypergroups, Rivista Di Matematica Pura Ed Applicata 9 (1991) 23 - 47.MathSciNetMATHGoogle Scholar
  8. 8.
    Kandel, A. and Lee, S. C., Fuzzy Switching and Automata: Theory and Applications, Crane Russak, 1980.Google Scholar
  9. 9.
    Malik, D.S. and Mordeson, J.N., On fuzzy recognizers, Kybernets, 28 (1999) 47–60.MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Malik, D.S. and Mordeson, J.N., Minimal fuzzy recognizers, J. Fuzzy Math., 7 (1999) 381–389.MathSciNetMATHGoogle Scholar
  11. 11.
    Malik, D. S., Mordeson, J. N. and Sen, M. K., Semigroups of fuzzy finite state machines, Advances in Fuzzy Theory and Techonology, Edited by P.P. Wang, Vol II, 1994, 87–98.Google Scholar
  12. 12.
    Malik, D. S., Mordeson, J. N. and Sen, M. K., Submachines of fuzzy finite state machines, J. Fuzzy Math, 2 (1994) 781–792.MathSciNetMATHGoogle Scholar
  13. 13.
    Malik, D. S., Mordeson, J. N. and Sen, M. K., On subsystems of a fuzzy finite state machine, Fuzzy Sets and Systems, 68 (1994) 83–92.MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Malik, D. S., Mordeson, J. N. and Sen, M. K., The cartesian composition of fuzzy finite state machines, Kybernets, 24 (1995).Google Scholar
  15. 15.
    Malik, D. S., Mordeson, J. N. and Sen, M. K., On fuzzy regular languages, Inform. Sci., 88 (1996) 263–273.MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Malik, D. S., Mordeson, J. N. and Sen, M. K., Products of fuzzy finite state machines, Fuzzy Sets and Systems, 92 (1997) 95–102.MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Steimann, F. and Adlassnig, K., Clinical monotoring with fuzzy automata, Fuzzy Sets and Systems, 61 (1994) 37–42.MathSciNetCrossRefGoogle Scholar
  18. 18.
    Wee, W. G., On generalizations of adaptive algorithm and application of the fuzzy sets concept to pattern classification, Ph, D. Thesis, Purdue University, June, 1967.Google Scholar
  19. 19.
    Zadeh, L. A., Fuzzy sets, Inform. Control, 8 (1965) 338 - 353.MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Zadeh, L. A., Fuzzy sets and systems, Proc. Symp. System Theory, Polytechnic Institute of Brooklyn, 29 - 37 (1965).Google Scholar
  21. 21.
    Zariski, O. and Samuel, P., Commutative Algebra Vol I, D. Van Nostrand Company, Inc 1958.MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Davender S. Malik
    • 1
  • John N. Mordeson
    • 1
  1. 1.Creighton UniversityOmahaUSA

Personalised recommendations