Fuzzy finite automata and fuzzy regular expressions with membership values in lattice-ordered monoids

Fuzzy Sets and Systems

Volumn 156, Issue 1, 2005, Pages 68-92

  Li, Yongming ^a,b   Pedrycz, Witold ^c  

^a SHAANXI NORMAL UNIVERSITY   (China)

^b NORTHWESTERN POLYTECHNICAL UNIVERSITY   (China)

^c UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Closure property; Fuzzy finite automaton; Fuzzy language; Fuzzy regular expression; Lattice order monoid; Level structure

Indexed keywords

ALGEBRA; AUTOMATA THEORY; COMPUTER SIMULATION; FUNCTIONS; THEOREM PROVING;

CLOSURE PROPERTY; FUZZY FINITE AUTOMATA; FUZZY LANGUAGE; FUZZY REGULAR EXPRESSION; LATTICE-ORDER MONOIDS;

FUZZY SETS;

EID: 24944554023     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2005.04.004     Document Type: Article

References (43)

1. P.R.J. Asveld, A bibliography on fuzzy automata, grammars and languages, Bull. European Assoc. Theoret. Comput. Sci. (58) (1996) 187-196 [ISSN 0252-9742].
2. P.R.J. Asveld Algebraic aspects of families of fuzzy languages Theoret. Comput. Sci. 293 2003 417 445
3. R. Balbes, and P. Dwinger Distributive Lattices 1974 University of Mossouri Press Columbia, Missouri
4. R. Bělohlávek Determinism and fuzzy automata Inform. Sci. 142 2002 205 209
5. G. Birkhoff, Lattice Theory (1940), (3rd) Ed., American Mathematical Society, Providence, RI, USA, 1973.
6. S. Eilenberg Automata, Languages, and Machines vol. A, B 1974 Academic Press New York
7. G. Grätzer General Lattice Theory 1978 Academic Press New York, San Franciso
8. U. Höhle On the fundamentals of fuzzy set theory J. Math. Anal. Appl. 201 1996 786 826
9. J.E. Hopcroft, and J.D. Ullman Introduction to Automata Theory, Languages and Computation 1979 Addison-Wesley New York
10. A. Kandel, and S.C. Lee Fuzzy Switching and Automata: Theory and Applications 1980 Arnold London
11. W. Kuich, and A. Salomaa Semiring, Automata, Language 1986 Springer Berlin, Heidelberg, New York
12. H.V. Kumbhojkar, and S.R. Chaudhari Fuzzy recognizers and recognizable sets Fuzzy Sets and Systems 131 2002 381 392
13. E.T. Lee, and L.A. Zadeh Note on fuzzy languages Inform. Sci. 1 1969 421 434
14. Y.M. Li, and Z.H. Li Free semilattices and strongly free semilattices generated by partially ordered sets Northeastern Math. J. 9 3 1993 359 366
15. Y.M. Li, and Z.H. Li Quantales and the process semantics of bisimulation Acta Math. Sinica 42 2 1999 313 320 (in Chinese)
16. Y.M. Li Dual quantales and their properties J. Shaanxi Normal Univ. (Natural Science Edition) 29 1 2001 1 5 (in Chinese)
17. Y.M. Li, Noncommutative linear logic and its quantale semantics, J. Shaanxi Normal Univ. (Natural Science Edition) 29 (12) (2001) 1-5 (in Chinese).
18. Y.M. Li, M. Zhou, and Z.H. Li Projective objects and injective objects in the category of quantales J. Pure Appl. Algebra 176 2002 249 258
19. Y.M. Li, and Z.K. Shi Remarks on uninorm aggregation operators Fuzzy Sets and Systems 114 2000 377 380
20. F. Lin, and H. Ying Modeling and control of fuzzy discrete event systems IEEE Trans. Systems Man Cybernet. - part B: Cybernet. 32 4 2002 408 415
21. D.S. Malik, and J.N. Mordeson On fuzzy regular languages Inform. Sci. 88 1996 263 273
22. D.S. Malik, and J.N. Mordeson Fuzzy Discrete Structures 2000 Physica-Verlag New York
23. A. Mateescu, A. Salomaa, K. Salomaa, and Sh. Yu Lexical analysis with a simple finite-fuzzy-automaton model J. Universal Comput. Sci. 1 1995 292 311
24. J.N. Mordeson, and D.S. Malik Fuzzy Automata and Languages: Theory and Applications 2002 Chapman & Hall/CRC Boca Raton, London
25. J. Močkoř Semigroup homomorphisms and fuzzy automata Soft Comput. 6 2002 423 427
26. W. Pedrycz, and A. Gacek Learning of fuzzy automata Internat. J. Comput. Intell. Appl. 1 1 2001 19 33
27. K. Peeva Equivalence, reduction and minimization of finite automata over semirings Theoret. Comput. Sci. 88 1991 269 285
28. D.W. Qiu Automata theory based on complete residuated lattice-valued logic Sci. China Ser. F 44 6 2001 419 429
29. D.W. Qiu Automata theory based on complete residuated lattice-valued logic Sci. China Ser. F 45 6 2002 442 452
30. K.L. Rosenthal Quantales and their Applications 1990 Longman Scientific and Technical London
31. E.S. Santos Maximin automata Inform. Control 12 1968 367 377
32. E.S. Santos On reduction of max-min machines J. Math. Anal. Appl. 37 1972 677 686
33. E.S. Santos Fuzzy automata and languages Inform. Sci. 10 1976 193 197
34. E.S. Santos Regular fuzzy expressions M.M. Gupta G.N. Saridis B.R. Gaines Fuzzy Automata and Decision Processes 1977 North-Holland Amsterdam 169 175
35. J.Z. Shen Fuzzy language on free monoid Inform. Sci. 88 1996 149 168
36. M.G. Thomason, and P.N. Marinos Deterministic acceptors of regular fuzzy languages IEEE Trans. Systems Man Cybernet. 4 1974 228 230
37. V. Topencharov, and K. Peeva Equivalence, reduction and minimization of finite fuzzy automata J. Math. Anal. Appl. 84 1981 270 281
38. W. Wechler The Concept of Fuzziness in Automata and Language Theory 1978 Addison-Wesley Reading, MA, USA
39. W.G. Wee, On generalizations of adaptive algorithm and application of the fuzzy sets concept to pattern classification, Ph.D. Thesis, Purdue University, June 1967.
40. W.G. Wee, and K.S. Fu A formulation of fuzzy automata and its application as a model of learning systems IEEE Trans. Systems Man Cybernet. 5 1969 215 223
41. R.R. Yager Aggregation operators and fuzzy systems modeling Fuzzy Sets and Systems 67 1994 129 145
42. M.S. Ying A formal model of computing with words IEEE Trans. Fuzzy Systems 10 5 2002 640 652
43. L.A. Zadeh, Fuzzy languages and their relation to human and machine intelligence, Electron. Research Laboratory University California, Berkeley, CA, Technical Report ERL-M302, 1971.