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Fuzzy Preorder, Fuzzy Topology and Fuzzy Transition System

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Logic and Its Applications (ICLA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7750))

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Abstract

The purpose of this work is to show that the observations made regarding fuzzy transition systems can be easily obtained by using the fuzzy preordered and fuzzy topological concepts.

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References

  1. Blount, K., Tsinakis, C.: The structure of residuated lattices. International Journal of Algebra and Computation 13, 437–461 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  2. Das, P.: A fuzzy topology associated with a fuzzy finite state machine. Fuzzy Sets and Systems 105, 469–479 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dörfler, W.: The Direct Product of Automata and Quasiautomata. In: Mazurkiewicz, A. (ed.) MFCS 1976. LNCS, vol. 45, pp. 270–276. Springer, Heidelberg (1976)

    Chapter  Google Scholar 

  4. Guo, X.: Grammar theory based on lattice-order monoid. Fuzzy Sets and Systems 160, 1152–1161 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ignjatović, J., Ćiric, M., Bogdanović, S.: Determinization of fuzzy automata with membership values in complete residuated lattices. Information Sciences 178, 164–180 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Jun, Y.B.: Intuitionistic fuzzy finite state machines. Journal of Applied Mathematics and Computing 17, 109–120 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Jun, Y.B.: Intuitionistic fuzzy finite switchboard state machines. Journal of Applied Mathematics and Computing 20, 315–325 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Jun, Y.B.: Quotient structures of intuitionistic fuzzy finite state machines. Information Sciences 177, 4977–4986 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kim, Y.H., Kim, J.G., Cho, S.J.: Products of T-generalized state machines and T-generalized transformation semigroups. Fuzzy Sets and Systems 93, 87–97 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kumbhojkar, H.V., Chaudhri, S.R.: On proper fuzzification of fuzzy finite state machines. International Journal of Fuzzy Mathematics 4, 1019–1027 (2008)

    Google Scholar 

  11. Li, Y., Pedrycz, W.: Fuzzy finite automata and fuzzy regular expressions with membership values in lattice-orderd monoids. Fuzzy Sets and Systems 156, 68–92 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Lihua, W., Qiu, D.: Automata theory based on complete residuated lattice-valued logic: Reduction and minimization. Fuzzy Sets and Systems 161, 1635–1656 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lowen, R.: Fuzzy topological spaces and fuzzy compactness. Jour. Math. Anal. Appl. 56, 621–633 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  14. Mordeson, J.N., Malik, D.S.: Fuzzy Automata and Languages: Theory and Applications. Chapman and Hall/CRC, London, Boca Raton (2002)

    Book  MATH  Google Scholar 

  15. Malik, D.S., Mordeson, J.N., Sen, M.K.: Submachines of fuzzy finite state machine. Journal of Fuzzy Mathematics 2, 781–792 (1994)

    MathSciNet  MATH  Google Scholar 

  16. Qiu, D.: Automata theory based on quantum logic: Some characterizations. Information and Computation 190, 179–195 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  17. Qiu, D.: Automata theory based on quantum logic: Reversibilities and pushdown automata. Theoretical Computer Science 386, 38–56 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  18. Qiu, D.: Characterizations of fuzzy finite automata. Fuzzy Sets and Systems 141, 391–414 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  19. Qiu, D.: Automata theory based on complete residuated lattice-valued logic(I). Science in China 44, 419–429 (2001)

    Article  MATH  Google Scholar 

  20. Qiu, D.: Automata theory based on complete residuated lattice-valued logic(II). Science in China 45, 442–452 (2002)

    MATH  Google Scholar 

  21. Santos, E.S.: Maximin automata. Information and Control 12, 367–377 (1968)

    Article  Google Scholar 

  22. She, Y.H., Wang, G.J.: An axiomatic approach of fuzzy rough sets based on residuated lattices. Computer and Mathematics with Applications 58, 189–201 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  23. Srivastava, A.K., Tiwari, S.P.: A Topology for Fuzzy Automata. In: Pal, N.R., Sugeno, M. (eds.) AFSS 2002. LNCS (LNAI), vol. 2275, pp. 485–490. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  24. Srivastava, A.K., Tiwari, S.P.: On relationships among fuzzy approximation operators, fuzzy topology, and fuzzy automata. Fuzzy Sets and Systems 138, 197–204 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  25. Wee, W.G.: On generalizations of adaptive algorithm and application of the fuzzy sets concept to pattern classification. Ph. D. Thesis, Purdue University, Lafayette, IN (1967)

    Google Scholar 

  26. Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  27. Lai, H., Zhang, D.: Fuzzy preorder and fuzzy topology. Fuzzy Sets and Systems 157, 1865–1885 (2006)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Indian School of Mines, Dhanbad, 826004, India

    S. P. Tiwari & Anupam K. Singh

Authors
  1. S. P. Tiwari
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  2. Anupam K. Singh
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Editor information

Editors and Affiliations

  1. The Institute of Mathematical Sciences, CIT Campus, 600113, Chennai, India

    Kamal Lodaya

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Tiwari, S.P., Singh, A.K. (2013). Fuzzy Preorder, Fuzzy Topology and Fuzzy Transition System. In: Lodaya, K. (eds) Logic and Its Applications. ICLA 2013. Lecture Notes in Computer Science, vol 7750. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36039-8_19

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  • DOI: https://doi.org/10.1007/978-3-642-36039-8_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36038-1

  • Online ISBN: 978-3-642-36039-8

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