Determinization of fuzzy automata with membership values in complete residuated lattices

Information Sciences

Volumn 178, Issue 1, 2008, Pages 164-180

  Ignjatović, Jelena ^a   Ćirić, Miroslav ^a   Bogdanović, Stojan ^a  

^a UNIVERSITY OF NI   (Serbia)

Author keywords

Complete residuated lattice; Deterministic automaton; Deterministic fuzzy recognizer; Fuzzy automaton; Fuzzy right congruence; Locally finite semiring; Nerode's fuzzy relation

Indexed keywords

COMPUTER SIMULATION; FUZZY CLUSTERING; INFORMATION SCIENCE; MATHEMATICAL MODELS; PROBLEM SOLVING;

COMPLETE RESIDUATED LATTICE; DETERMINISTIC AUTOMATON; DETERMINISTIC FUZZY RECOGNIZER; FUZZY AUTOMATA; FUZZY FINITE AUTOMATA; FUZZY RIGHT CONGRUENCE; LOCALLY FINITE SEMIRING; NERODE'S FUZZY RELATION; RESIDUATED LATTICES;

FUZZY SYSTEMS;

EID: 35148813934     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2007.08.003     Document Type: Article

References (39)

1. Bělohlávek R. Fuzzy Relational Systems: Foundations and Principles (2002), Kluwer, New York
2. Bělohlávek R. Determinism and fuzzy automata. Information Sciences 143 (2002) 205-209
3. Bozapalidis S., and Louscou-Bozapalidou O. On the recognizability of fuzzy languages I. Fuzzy Sets and Systems 157 (2006) 2394-2402
4. Ćirić M., Ignjatović J., and Bogdanović S. Fuzzy equivalence relations and their equivalence classes. Fuzzy Sets and Systems 158 (2007) 1295-1313
5. M. Ćirić, A. Stamenković, J. Ignjatović, T. Petković, Factorization of fuzzy automata, in: E. Csuhaj-Varju, Z. Ésik (Eds.), FCT 2007, Lecture Notes in Computer Science, vol. 4639, 2007, pp. 213-225.
6. de Luca A., and Varricchio S. Finiteness and Regularity in Semigroups and Formal Languages (1999), Springer-Verlag, Berlin Heidelberg
7. M. Droste, P. Gastin, Weighted automata and weighted logics, in: L. Caires et al. (Eds.), ICALP 2005, Lecture Notes in Computer Science, vol. 3580, 2005, pp. 513-525.
8. Droste M., and Gastin P. Weighted automata and weighted logics. Theoretical Computer Science 380 (2007) 69-86
9. Esteva F., Godo L., and Garcia-Cerdaña A. On the hierarchy of t-norm based residuated fuzzy logics. In: Orlowska E., and Fitting M. (Eds). Beyond Two: Theory and Applications of Multiple-valued Logic (2003), Physica-Verlag, Heidelberg 251-272
10. Hájek P. Mathematics of Fuzzy Logic (1998), Kluwer, Dordrecht
11. Höhle U. Commutative, residuated ℓ-monoids. In: Höhle U., and Klement E.P. (Eds). Non-classical Logics and Their Applications to Fuzzy Subsets (1995), Kluwer Academic Publishers, Boston, Dordrecht 53-106
12. J. Ignjatović, M. Ćirić, S. Bogdanović, T. Petković, Myhill-Nerode type theory for fuzzy languages and automata, Fuzzy Sets and Systems, submitted for publication.
13. Lawson M.V. Finite Automata (2004), Chapman & Hall/CRC, Boca Raton, London
14. Lei H.X., and Li Y.M. Minimization of states in automata theory based on finite lattice-ordered monoids. Information Sciences 177 (2007) 1413-1421
15. Li P., and Li Y.M. Algebraic properties of LA-languages. Information Sciences 176 (2006) 3232-3255
16. Li Y.M. A categorical approach to lattice-valued fuzzy automata. Fuzzy Sets and Systems 157 (2006) 855-864
17. Li Y.M. Approximation and robustness of fuzzy finite automata. International Journal of Approximate Reasoning (2007) 10.1016/j.ijar.2007.05.004
18. Li Y.M., and Pedrycz W. Fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids. Fuzzy Sets and Systems 156 (2005) 68-92
19. Li Y.M., and Pedrycz W. The equivalence between fuzzy Mealy and fuzzy Moore machines. Soft Computing 10 (2006) 953-959
20. Li Y.M., and Pedrycz W. Minimization of lattice finite automata and its application to the decomposition of lattice languages. Fuzzy Sets and Systems 158 (2007) 1423-1436
21. Li Z.H., Li P., and Li Y.M. The relationships among several types of fuzzy automata. Information Sciences 176 (2006) 2208-2226
22. Lin F., and Ying H. Modeling and control of fuzzy discrete event systems. IEEE Transaction on Systems, Man, and Cybernetics B 32 4 (2002) 408-415
23. Močkoř J. Fuzzy and non-deterministic automata. Soft Computing 3 (1999) 221-226
24. Malik D.S., Mordeson J.N., and Sen M.K. On fuzzy regular languages. Information Sciences 88 (1996) 263-273
25. Mordeson J.N., and Malik D.S. Fuzzy Automata and Languages: Theory and Applications (2002), Chapman & Hall/CRC, Boca Raton, London
26. Mordeson J.N., Malik D.S., and Kuroki N. Fuzzy Semigroups (2003), Springer
27. Petković T. Congruences and homomorphisms of fuzzy automata. Fuzzy Sets and Systems 157 (2006) 444-458
28. Qiu D.W. Automata theory based on completed residuated lattice-valued logic (I). Science in China, Series F 44 6 (2001) 419-429
29. Qiu D.W. Automata theory based on completed residuated lattice-valued logic (II). Science in China, Series F 45 6 (2002) 442-452
30. Qiu D.W. Characterizations of fuzzy finite automata. Fuzzy Sets and Systems 141 3 (2004) 391-414
31. Qiu D.W. Supervisory control of fuzzy discrete event systems: a formal approach. IEEE Transactions on Systems, Man and Cybernetics - Part B 35 1 (2005) 72-88
32. Qiu D.W. Pumping lemma in automata theory based on complete residuated lattice-valued logic: A note. Fuzzy Sets and Systems 157 (2006) 2128-2138
33. Qiu D.W. A note on Trillas CHC models. Artificial Intelligence 171 (2007) 239-254
34. Shen J. Fuzzy language on free monoid. Information Sciences 88 (1996) 149-168
35. Sheng L., and Li Y.M. Regular grammars with truth values in lattice-ordered monoid and their languages. Soft Computing 10 (2006) 79-86
36. Valverde L. On the structure of F-indistinguishability operators. Fuzzy Sets and Systems 17 (1985) 313-328
37. Wang H., and Qiu D.W. Computing with words via Turing machines: a formal approach. IEEE Transactions on Fuzzy Systems 11 6 (2003) 707-718
38. Xing H.G., Qiu D.W., Liu F.C., and Fan Z.J. Equivalence in automata theory based on complete residuated lattice-valued logic. Fuzzy Sets and Systems 158 (2007) 1407-1422
39. Yu S. Regular languages. In: Rozenberg G., and Salomaa A. (Eds). Handbook of Formal Languages vol. 1 (1999), Springer-Verlag, Berlin Heidelberg 41-110