×

Computing behavior of finite fuzzy machines – algorithm and its application to reduction and minimization. (English) Zbl 1170.68506

Summary: We define finite fuzzy machines and investigate their behavior. Algorithm and software are proposed for computing behavior, for establishing equivalence and redundancy of states and for solving reduction and minimization problems. Computational complexity of the algorithm is discussed. Testing examples are supplied. The results are valid for finite max-min, min-max and max-product fuzzy machines.

MSC:

68Q45 Formal languages and automata
68Q05 Models of computation (Turing machines, etc.) (MSC2010)
68Q25 Analysis of algorithms and problem complexity
Full Text: DOI

References:

[1] De Baets, B., Analytical solution methods for fuzzy relational equations, (Dubois, D.; Prade, H., Fundamentals of Fuzzy Sets. Fundamentals of Fuzzy Sets, The Handbooks of Fuzzy Sets Series, vol. 1 (2000), Kluwer Academic Publishers), 291-340 · Zbl 0970.03044
[2] Chaudhari, S. R., Homomorphisms of fuzzy recognizers, Kybernetes, 36, 5-6, 768-775 (2007) · Zbl 1193.93011
[3] Cheng, W.; Mo, Z. W., Minimization algorithm of fuzzy finite automata, Fuzzy Sets and Systems, 141, 439-448 (2004) · Zbl 1069.68563
[4] A. Di Nola, A. Lettieri, Relation Equations in Residuated Lattices, Rendiconti del Circolo Matematico di Palermo, s. II, XXXVIII, 1989, pp. 246-256.; A. Di Nola, A. Lettieri, Relation Equations in Residuated Lattices, Rendiconti del Circolo Matematico di Palermo, s. II, XXXVIII, 1989, pp. 246-256. · Zbl 0691.06002
[5] Di Nola, A.; Lettieri, A.; Perfilieva, I.; Novák, V., Algebraic analysis of fuzzy systems, Fuzzy Sets and Systems, 158, 1, 1-22 (2007) · Zbl 1110.93012
[6] Hájek, P., Metamathematics of Fuzzy Logic (1998), Kluwer: Kluwer Dordrecht · Zbl 0937.03030
[7] Klir, G.; Yuan, B., Fuzzy Sets and Fuzzy Logic: Theory and Applications (1995), Prentice Hall PTR: Prentice Hall PTR NJ · Zbl 0915.03001
[8] Konstantinidis, S.; Nikolae, S.; Yu, S., Fuzzification of rational and recognizable sets, Fundamenta Informaticae, 76, 4, 413-447 (2007) · Zbl 1123.68061
[9] Lei, H.; Li, Y., Reduction and minimization algorithm of synchronous lattice-valued automata, Computer Engineering and Applications, 42, 16, 57-60 (2006)
[10] Lei, H.; Li, S., Algorithm for determining equivalence between lattice-valued finite automata, Computer Engineering and Applications, 42, 22, 39-41 (2006), 45
[11] Lei, H.; Li, Y., Reduction and minimization algorithm of synchronous lattice-valued automata, Computer Engineering and Applications, 42, 16, 57-60 (2006)
[12] Lei, H. X.; Li, Y. M., Minimization of states in automata theory based on finite lattice-ordered monoids, Information Sciences, 177, 6, 1413-1421 (2007) · Zbl 1109.68058
[13] Li, Y., A categorical approach to lattice-valued fuzzy automata, Fuzzy Sets and Systems, 157, 6, 855-864 (2006) · Zbl 1090.18003
[14] Li, Z.; Li, P.; Li, Y., The relationships among several types of fuzzy automata, Information Sciences, 176, 15, 2208-2226 (2006) · Zbl 1110.68065
[15] Li, Y.; Pedrycz, W., Minimization of lattice finite automata and its application to the decomposition of lattice languages, Fuzzy Sets and Systems, 158, 1423-1436 (2007) · Zbl 1123.68063
[16] Li, Y.; Pedrycz, W., Fuzzy finite automata and regular expressions with membership values in lattice-ordered monoids, Fuzzy Sets and Systems, 156, 68-92 (2005) · Zbl 1083.68059
[17] Mordeson, J. N.; Malik, D. S., Fuzzy Automata and Languages - Theory and Applications (2002), Chapman & Hall/CRC: Chapman & Hall/CRC London · Zbl 1046.68068
[18] Peeva, K., Equivalence, reduction and minimization of finite automata over semirings, Theoretical Computer Science, 88, 269-285 (1991) · Zbl 0737.68063
[19] Peeva, K., Behaviour, reduction and minimization of finite L-automata, Fuzzy Sets and Systems, 28, 2, 171-181 (1988) · Zbl 0663.68069
[20] Peeva, K., Finite L-fuzzy machines, Fuzzy Sets and Systems, 141, 3, 415-437 (2004) · Zbl 1059.68066
[21] Peeva, K.; Kyosev, Y.; calculus-theory, Fuzzy relational, Applications and software (with CD-ROM), (Advances in Fuzzy Systems - Applications and Theory, vol. 22 (2004), World Scientific: World Scientific Publishing Company), CD-ROM · Zbl 1083.03048
[22] Peeva, K.; Kyosev, Y., Algorithm for solving max-product fuzzy relational equations, Soft Computing, 11, 7, 593-605 (2007) · Zbl 1113.65042
[23] K. Peeva, Zl. Zahariev, Linear dependence in fuzzy algebra, in: Proceedings of 31st International Conference AME, Sozopol, June 2005, Softrade, 2006, pp. 71-83.; K. Peeva, Zl. Zahariev, Linear dependence in fuzzy algebra, in: Proceedings of 31st International Conference AME, Sozopol, June 2005, Softrade, 2006, pp. 71-83. · Zbl 1102.68144
[24] K. Peeva, Zl. Zahariev, Software for testing linear dependence in fuzzy algebra, in: Second International Scientific Conference Computer Science, Chalkidiki, 30 September-2 October 2005, Part I, 2006, pp. 294-299.; K. Peeva, Zl. Zahariev, Software for testing linear dependence in fuzzy algebra, in: Second International Scientific Conference Computer Science, Chalkidiki, 30 September-2 October 2005, Part I, 2006, pp. 294-299. · Zbl 1102.68144
[25] I. Perfilieva, L. Nosková, System of fuzzy relation equations with inf-→; composition: complete set of solutions, Fuzzy Sets and Systems, in press. doi:10.1016/j.fss.2007.12.012.; I. Perfilieva, L. Nosková, System of fuzzy relation equations with inf-→; composition: complete set of solutions, Fuzzy Sets and Systems, in press. doi:10.1016/j.fss.2007.12.012.
[26] Rahonis, G., Infinite fuzzy computations, Fuzzy Sets and Systems, 153, 2, 275-288 (2005) · Zbl 1138.68433
[27] Ray, A. K.; Chattererjee, B.; Majumdar, A. K., A formal power series approach to the construction of minimal fuzzy automata, Information Sciences, 55, 1-3, 189-207 (1991) · Zbl 0717.68059
[28] Sanchez, E., Resolution of composite fuzzy relation equations, Information and Control, 30, 38-48 (1976) · Zbl 0326.02048
[29] Santos, E. S., Maximin automata, Information and Control, 13, 363-377 (1968) · Zbl 0174.03601
[30] Santos, E. S., Maximin, minimax and composite sequential machines, Journal of Mathematical Analysis and Applications, 24, 246-259 (1968) · Zbl 0187.28103
[31] Santos, E. S., On reduction of maxi-min machines, Journal of Mathematical Analysis and Applications, 40, 60-78 (1972) · Zbl 0245.94041
[32] Santos, E. S., Max-product machines, Journal of Mathematical Analysis and Applications, 37, 677-686 (1972) · Zbl 0245.94040
[33] Santos, E. S.; Wee, W. G., General formulation of sequential machines, Information and Control, 12, 1, 5-10 (1968) · Zbl 0162.02501
[34] Xing, H.; Qui, D.; Liu, Fuchun; Fan, Z., Equivalence in automata theory based on complete residuated lattice-valued logic, Fuzzy Sets and Systems, 158, 13, 1407-1422 (2007) · Zbl 1152.68463
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.