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The equivalence between fuzzy Mealy and fuzzy Moore machines

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Abstract

We study the relationships between fuzzy Mealy and fuzzy Moore machines in the frame of truth values in a lattice-ordered monoid. In particular, we show that lattice-valued sequential-like machines and lattice-valued finite Moore machines are equivalent in the sense they exhibit the same input–output characteristics.

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References

  • Basak NC, Gupta A (2002) On quotient machines of a fuzzy automata and the minimal machine. Fuzzy Sets Syst 125:223–229

    Article  MathSciNet  MATH  Google Scholar 

  • Birkhoff G (1973) Lattice theory (1940), 3rd edn. American Mathematical Society, Providence, Rhode Island

    Google Scholar 

  • Booth TL (1967) Sequential machines and automata theory. John Wiley, New York

    MATH  Google Scholar 

  • Cheng W, Mo ZW (2004) Minimization algorithm of fuzzy finite automata. Fuzzy Sets Syst 141:439–448

    Article  MathSciNet  MATH  Google Scholar 

  • Grätzer G (1978) General lattice theory. Academic, New York

    Google Scholar 

  • Hopcroft JE, Ullman JD (1979) Introduction to automata theory, languages and computation. Addison-Wesley, New York

    MATH  Google Scholar 

  • Kandel A, Lee SC (1980) Fuzzy switching and automata: theory and applications. Arnold, London

    Google Scholar 

  • Li YM, Li ZH (1999) Quantales and the process semantics of bisimulation. Acta Math Sinica 42(2):313–320 (in Chinese)

    Google Scholar 

  • Li YM (2001) Dual quantales and their properties, J. Shaanxi Normal University (Natural Science edn), 29(1):1–5 (in Chinese)

    Google Scholar 

  • Li YM (2001) Noncommutative linear logic and its quantale semantics, J. Shaanxi Normal University (Natural Science Edn), 29(12):1–5 (in Chinese)

    Google Scholar 

  • Li YM, Zhou M, Li ZH (2002) Projective objects and injective objects in the category of quantales. J Pure Appl Alg 176(2–3):249–258

    Article  MathSciNet  MATH  Google Scholar 

  • Li YM, Shi ZK (2000) Remarks on uninorm aggregation operators. Fuzzy Sets Syst 114(3):377–380

    Article  MathSciNet  MATH  Google Scholar 

  • Malik DS, Mordeson JN, Sen MK, Minimization of fuzzy finite automata. Inf Sci 113:323–330

  • Malik DS, Mordeson JN (2000) Fuzzy discrete structures. Physica-Verlag, New York

    MATH  Google Scholar 

  • Mordeson JN, Malik DS (2002) Fuzzy automata and languages: theory and applications. Chapman & Hall/CRC, Boca Raton

    MATH  Google Scholar 

  • Močkoř J (2002) Semigroup homomorphisms and fuzzy automata. Soft Comput 6:423–427

    Google Scholar 

  • Paz A (1971) Introduction to probabilistic automata. Academic, New York

    MATH  Google Scholar 

  • Pedrycz W, Gacek A (2001) Learning of fuzzy automata. Inter J Comput Intell Appl 1(1):19–33

    Article  Google Scholar 

  • Peeva K (1991) Equivalence, reduction and minimization of finite automata over semirings. Theor Comput Sci 88:269–285

    Article  MathSciNet  MATH  Google Scholar 

  • Peeva K (2004) Finite L-fuzzy machines. Fuzzy Sets Syst 141(3):415–437

    Article  MathSciNet  MATH  Google Scholar 

  • Rosenthal KL (1990) Quantales and their applications. Longman, London

    MATH  Google Scholar 

  • Santos ES (1968) Maximin automata. Inf Control 12:367–377

    Article  Google Scholar 

  • Santos ES (1972) Max-product machines. J Math Anal Appl 37:677–686

    Article  MathSciNet  MATH  Google Scholar 

  • Santos ES (1972) On reduction of max-min machines. J Math Anal Appl 40:60–78

    Article  MathSciNet  MATH  Google Scholar 

  • Santos ES, Wee WG (1968) General formulation of sequential machines. Inf Control 12(1):5–10

    Article  MathSciNet  MATH  Google Scholar 

  • Starke P (1998) Abstract automata, 2nd edn. Birkhaeuser, Basel

    Google Scholar 

  • Topencharov V, Peeva K (1981) Equivalence, reduction and minimization of finite fuzzy automata. J Math Anal Appl 84:270–281

    Article  MathSciNet  MATH  Google Scholar 

  • Wee WG (1967) On generalizations of adaptive algorithm and application of the fuzzy sets concept to pattern classification, PhD Thesis, Purdue University

  • Wee WG, Fu KS (1969) A formulation of fuzzy automata and its application as a model of learning systems. IEEE Trans Syst Man Cybern 5:215–223

    Article  Google Scholar 

  • Yager RR (1994) Aggregation operators and fuzzy systems modeling. Fuzzy Sets Syst 67:129–145

    Article  MathSciNet  MATH  Google Scholar 

  • Ying MS (2002) A formal model of computing with words. IEEE Trans Fuzzy Syst 10(5):640–652

    Article  Google Scholar 

  • Zadeh LA (1971) Fuzzy languages and their relation to human and machine intelligence. Electronic Research Laboratory, University of California, Berkeley. Tech.Rep.ERL-M302

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Authors and Affiliations

  1. College of Computer Science, Shaanxi Normal University, Xi’an, 710062, China

    Yongming Li

  2. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, T6G2V4, Canada

    Witold Pedrycz

Authors
  1. Yongming Li
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  2. Witold Pedrycz
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Correspondence to Yongming Li.

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Li, Y., Pedrycz, W. The equivalence between fuzzy Mealy and fuzzy Moore machines. Soft Comput 10, 953–959 (2006). https://doi.org/10.1007/s00500-005-0022-x

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