A Simplified Form of Fuzzy Multiset Finite Automata

  • Pavel MartinekEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 464)


Fuzzy multiset finite automata represent fuzzy version of finite automata working over multisets. Description of these automata can be simplified to such a form where transition relation is bivalent and only the final states form a fuzzy set. In this paper it is proved that the simplified form preserves computational power of the automata and way of how to perform the corresponding transformation is described.


Fuzzy multiset finite automata Simplified fuzzy multiset finite automata 


  1. 1.
    Bělohlávek, R.: Determinism and fuzzy automata. Inf. Sci. 143, 205–209 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Blizard, W.D.: Multiset theory. Notre Dame J. Form. Log. 30(1), 36–66 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Blizard, W.D.: The development of multiset theory. Mod. Log. 1(4), 319–352 (1991)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Csuhaj-Varjú, E., Martín-Vide, C., Mitrana, V.: Multiset automata. In: Calude, C.S., Păun, G., Rozenberg, G., Salomaa, A. (eds.) Multiset Processing—Mathematical, Computer Science, and Molecular Computing Points of View. LNCS, vol. 2235, pp. 69–83. Springer, Berlin (2001)Google Scholar
  5. 5.
    Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York (1980)zbMATHGoogle Scholar
  6. 6.
    González de Mendívil, J.R., Garitagoitia, J.R.: Fuzzy languages with infinite range accepted by fuzzy automata: pumping lemma and determinization procedure. Fuzzy Sets Syst. 249, 1–26 (2014)Google Scholar
  7. 7.
    Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation, 2nd edn. Pearson Addison Wesley, Upper Saddle River (2003)zbMATHGoogle Scholar
  8. 8.
    Ignjatović, J., Ćirić, M., Bogdanović, S.: Determinization of fuzzy automata with membership values in complete residuated lattices. Inf. Sci. 178(1), 164–180 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Kudlek, M., Martín-Vide, C., Păun, G.: Toward a formal macroset theory. In: Calude, C.S., Păun, G., Rozenberg, G., Salomaa, A. (eds.) Multiset Processing—Mathematical, Computer Science, and Molecular Computing Points of View. LNCS, vol. 2235, pp. 123–133. Springer, Berlin (2001)Google Scholar
  10. 10.
    Kudlek, M., Totzke, P., Zetsche, G.: Multiset pushdown automata. Fund. Inf. 93, 221–233 (2009)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Kudlek, M., Totzke, P., Zetsche, G.: Properties of multiset language classes defined by multiset pushdown automata. Fund. Inf. 93, 235–244 (2009)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Li, Y., Pedrycz, W.: Minimization of lattice finite automata and its application to the decomposition of lattice languages. Fuzzy Sets Syst. 158(13), 1423–1436 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Martinek, P.: Fuzzy multiset finite automata: determinism, languages, and pumping lemma. In: Tang, Z., Du, J., Yin, S., He, L., Li, R. (eds.) 2015 12th International Conference on Fuzzy Systems and Knowledge Discovery, pp. 64–68. China, Zhangjiajie (2015)Google Scholar
  14. 14.
    Mordeson, J.N., Malik, D.S.: Fuzzy Automata and Languages: Theory and Applications. Chapman and Hall/CRC, Boca Raton (2002)CrossRefzbMATHGoogle Scholar
  15. 15.
    Sipser, M.: Introduction to the Theory of Computation, 2nd edn. Thomson Course Technology, Boston (2006)zbMATHGoogle Scholar
  16. 16.
    Wang, J., Yin, M., Gu, W.: Fuzzy multiset finite automata and their languages. Soft Comput. 17(3), 381–390 (2013)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsTomas Bata University in ZlinZlínCzech Republic

Personalised recommendations