Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

INTERVAL-VALUED FUZZY REGULAR LANGUAGE

  • Ravi, K.M. (Department of Mathematics, JSS Academy of Technical Education) ;
  • Alka, Choubey (Department of Mathematics, Jaypee Institute of Information Technology University)
  • Received : 2009.07.27
  • Accepted : 2009.12.14
  • Published : 2010.05.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, a definition of interval-valued fuzzy regular language (IVFRL) is proposed and their related properties studied. A model of finite automaton (DFA and NDFA) with interval-valued fuzzy transitions is proposed. Acceptance of interval-valued fuzzy regular language by the finite automaton (DFA and NDFA) with interval-valued fuzzy transitions are examined. Moreover, a definition of finite automaton (DFA and NDFA) with interval-valued fuzzy (final) states is proposed. Acceptance of interval-valued fuzzy regular language by the finite automaton (DFA and NDFA) with interval-valued fuzzy (final) states are also discussed. It is observed that, the model finite automaton (DFA and NDFA) with interval-valued fuzzy (final) states is more suitable than the model finite automaton (DFA and NDFA) with interval-valued fuzzy transitions for recognizing the interval-valued fuzzy regular language. In the end, interval-valued fuzzy regular expressions are defined. We can use the proposed interval-valued fuzzy regular expressions in lexical analysis.

Keywords

References

  1. Marian B. Gorzalczany, A method of inference in approximate reasoning based on intervalvalued fuzzy sets, Fuzzy Sets and Systems, 21 (1987), 1-17. https://doi.org/10.1016/0165-0114(87)90148-5
  2. J.E. Hopcroft, J.D. Ullman, Introduction to Automata Theory, Languages and Computation, Addison-Wesley, New York, 1979.
  3. E. T. Lee and L. A. Zadeh, Note on fuzzy languages, Information Sciences 1 (1969), 421-434. https://doi.org/10.1016/0020-0255(69)90025-5
  4. Y. Li, Witold Petrycz, Fuzzy finite automata and fuzzy regular expressions with membership values in lattice-ordered monoids, Fuzzy Sets and Systems 156 (2005), 68-92. https://doi.org/10.1016/j.fss.2005.04.004
  5. D. S. Malik, J. N. Mordeson, Fuzzy Automata and Languages: Theory and Applications, Chapman Hall, CRC Boca Raton, London, New York, Washington DC, 2002.
  6. A. Mateescu, A. Salomaa, Kai Salomaa, S. Yu, Lexical Analysis with a Simple Finite-Fuzzy-Automaton Model, Jr. Of Uni.Comp. Sci 5 (1995), 292-311.
  7. Ioannis K. Vlachos, George D. Sergiadis, Subsethood, entropy and cardinality for intervalvalued fuzzy sets-An algebraic derivation, Fuzzy Sets and Systems 158 (2007), 1384-1396. https://doi.org/10.1016/j.fss.2006.12.018
  8. L. A. Zadeh, Fuzzy sets, Inform. And Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X