Measure of operators associated with fuzzy automata. (English) Zbl 1504.68110
Summary: This paper is toward the study of measure of different operators in fuzzy automata theory, which determine the amount of preciseness of given \(L\)-valued subset endowed with an \(L\)-valued preorder induced by \(L\)-valued transition function of an \(M\)-valued automaton. Further, we study the algebraic and topological study of \(M\)-valued automata via different \(L\)-valued operators and on the basis of homomorphism we examine the behavior of operators associated with an \(M\)-valued automaton.
MSC:
| 68Q45 | Formal languages and automata |
Keywords:
\(M\)-valued automaton; \(L\)-valued operators; \(M\)-valued operators; measure of operators; \(ML\)-graded topology/co-topology; homomorphismReferences:
| [1] | Bavel, Z. and Thomas, J. W., On the decomposability of monadic algebras and automata, Proceedings of the 8th Annual Symposium on Switching and Automata Theory (1967) 322-335. |
| [2] | Holcombe, W. M. L., Algebraic Automata Theory (Cambridge University Press, 1982). · Zbl 0489.68046 |
| [3] | Ito, M., Algebraic structures of automata, Theoretical Computer Science429 (2012) 164-168. · Zbl 1238.68087 |
| [4] | Shukla, W. and Srivastava, A. K., A topology for automata: A note, Information and Control32 (1976) 163-168. · Zbl 0338.94028 |
| [5] | Srivastava, A. K. and Shukla, W., A topology for automata II, International Journal of Mathematics and Mathematical Sciences9 (1986) 425-428. · Zbl 0605.68042 |
| [6] | Bailador, G. and Trivino, G., Pattern recognition using temporal fuzzy automata, Fuzzy Sets and Systems61 (2009) 37-55. · Zbl 1185.68588 |
| [7] | Mordeson, J. N. and Malik, D. S., Fuzzy Automata and Languages: Theory and Applications (Chapman and Hall/CRC, London/Boca Raton, 2002). · Zbl 1046.68068 |
| [8] | Peeva, K., Fuzzy acceptors for syntactic pattern recognition, International Journal of Approximate Reasoning5 (1991) 291-306. · Zbl 0733.68068 |
| [9] | Zadeh, L. A., Fuzzy sets, Information and Control8 (1965) 338-353. · Zbl 0139.24606 |
| [10] | W. G. Wee, On generalizations of adaptive algorithm and application of the fuzzy sets concept to pattern classification, Ph.D. Thesis, Purdue University (1967). |
| [11] | Santos, E. S., Maximin automata, Information and Control12 (1968) 367-377. |
| [12] | Malik, D. S., Mordeson, J. N. and Sen, M. K., Submachines of fuzzy finite state machine, Journal of Fuzzy Mathematics2 (1994) 781-792. · Zbl 0824.68077 |
| [13] | Abolpour, K. and Zahedi, M. M., Isomorphism between two BL-general fuzzy automata, Soft Computing16 (2012) 729-736. · Zbl 1259.68136 |
| [14] | Abolpour, K. and Zahedi, M. M., BL-general fuzzy automata and accept behavior, Journal of Applied Mathematics and Computing38 (2012) 103-118. · Zbl 1297.68100 |
| [15] | Abolpour, K. and Zahedi, M. M., General fuzzy automata based on complete residuated lattice-valued, Iranian Journal of Fuzzy Systems14 (2017) 103-121. · Zbl 1398.68289 |
| [16] | Das, P., A fuzzy topology associated with a fuzzy finite state machine, Fuzzy Sets and Systems105 (1999) 469-479. · Zbl 0959.68071 |
| [17] | Horry, M. and Zahedi, M. M., Some (fuzzy) topologies on general fuzzy automata, Iranian Journal of Fuzzy Systems10 (2013) 73-89. · Zbl 1339.68148 |
| [18] | Ignjatović, J., Ćirić, M. and Bogdanović, S., Determinization of fuzzy automata with membership values in complete residuated lattices, Information Sciences178 (2008) 164-180. · Zbl 1128.68047 |
| [19] | Ignjatović, J., Ćirić, M., Bogdanović, S. and Petković, T., Myhill-Nerode type theory for fuzzy languages and automata, Fuzzy Sets and Systems161 (2010) 1288-1324. · Zbl 1202.68261 |
| [20] | Ignjatović, J., Ćiric, M. and Simoović, V., Fuzzy relation equations and subsystems of fuzzy transition systems, Knowledge-Based Systems38 (2013) 48-61. |
| [21] | Jin, J. H., Li, Q. G. and Li, Y. M., Algebraic properties of \(L\)-fuzzy finite automata, Information Sciences234 (2013) 182-202. · Zbl 1284.68421 |
| [22] | Jun, Y. B., Intuitionistic fuzzy finite state machines, Journal of Applied Mathematics and Computing17 (2005) 109-120. · Zbl 1058.18002 |
| [23] | Jun, Y. B., Intuitionistic fuzzy finite switchboard state machines, Journal of Applied Mathematics and Computing20 (2006) 315-325. · Zbl 1084.18002 |
| [24] | Jun, Y. B., Quotient structures of intuitionistic fuzzy finite state machines, Information Sciences177 (2007) 4977-4986. · Zbl 1129.68040 |
| [25] | Kim, Y. H., Kim, J. G. and Cho, S. J., Products of \(T\)-generalized state machines and \(T\)-generalized transformation semigroups, Fuzzy Sets and Systems93 (1998) 87-97. · Zbl 0928.68079 |
| [26] | Kumbhojkar, H. V. and Chaudhari, S. R., On proper fuzzification of fuzzy finite state machines, International Journal of Fuzzy Mathematics8 (2008) 1019-1027. · Zbl 0969.68106 |
| [27] | Li, Y. and Pedrycz, W., Fuzzy finite automata and fuzzy regular expressions with membership values in lattice-ordered monoids, Fuzzy Sets and Systems156 (2005) 68-92. · Zbl 1083.68059 |
| [28] | Lihua, W. and Qiu, D., Automata theory based on complete residuated lattice-valued logic: Reduction and minimization, Fuzzy Sets and Systems161 (2010) 1635-1656. · Zbl 1192.68426 |
| [29] | Močko̧r, J., A category of fuzzy automata, International Journal of General Systems20 (1991) 73-82. · Zbl 0735.68063 |
| [30] | Močko̧r, J., Fuzzy and non-deterministic automata, Soft Computing3 (1999) 221-226. |
| [31] | Močko̧r, J., Semigroup homomorphisms and fuzzy automata, Soft Computing6 (2002) 423-427. · Zbl 1039.68080 |
| [32] | Peeva, K., Behaviour, reduction and minimization of finite \(L\)-automata, Fuzzy Sets and Systems28 (1988) 171-181. · Zbl 0663.68069 |
| [33] | Peeva, K., Finite \(L\)-fuzzy acceptors, regular \(L\)-fuzzy grammars and syntactic pattern recognition, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems12 (2004) 89-104. · Zbl 1074.68032 |
| [34] | Qiu, D., Automata theory based on complete residuated lattice-valued logic(I), Science in China Series F: Information Sciences44 (2001) 419-429. · Zbl 1125.68383 |
| [35] | Qiu, D., Automata theory based on complete residuated lattice-valued logic(II), Science in China Series F: Information Sciences45 (2002) 442-452. · Zbl 1161.68549 |
| [36] | Qiu, D., Automata theory based on quantum logic: Some characterizations, Information and Computation190 (2004) 179-195. · Zbl 1074.68020 |
| [37] | Qiu, D., Characterizations of fuzzy finite automata, Fuzzy Sets and Systems141 (2004) 391-414. · Zbl 1059.68069 |
| [38] | Srivastava, A. K. and Tiwari, S. P., A topology for fuzzy automata, Lecture Notes in Artificial Intelligence2275 (2002) 485-490. · Zbl 1053.68578 |
| [39] | Tiwari, S. P., Gautam, V. and Davvaz, B., On minimal realization for a fuzzy language and Brzozowski’s algorithm, Journal of Intelligent and Fuzzy Systems29 (2015) 1949-1956. · Zbl 1361.68126 |
| [40] | Tiwari, S. P. and Sharan, S., Fuzzy automata based on lattice-ordered monoids with algebraic and topological aspects, Fuzzy Information and Engineering4 (2012) 155-164. · Zbl 1256.68114 |
| [41] | Tiwari, S. P., Singh, A. K., Sharan, Shambhu and Yadav, V. K., Bifuzzy core of fuzzy automata, Iranian Journal of Fuzzy Systems12 (2015) 63-73. · Zbl 1336.68157 |
| [42] | Tiwari, S. P. and Srivastava, A. K., On a decomposition of fuzzy automata, Fuzzy Sets and Systems151 (2005) 503-511. · Zbl 1064.68060 |
| [43] | Tiwari, S. P., Yadav, V. K. and Singh, A. K., Construction of a minimal realization and monoid for a fuzzy language: A categorical approach, Journal of Applied Mathematics and Computing47 (2015) 401-416. · Zbl 1315.68171 |
| [44] | Zhang, Q. and Huang, Y., Intuitionistic fuzzy automata based on complete residuated lattice-valued logic, International Journal of Materials and Product Technology45 (2012) 108-118. |
| [45] | Han, S. E. and Šostak, A., \(M\)-valued measure of roughness for approximation of \(L\)-fuzzy sets and its topological interpretation, Computational Intelligence620 (2016) 251-266. · Zbl 1462.03022 |
| [46] | Han, S. E. and Šostak, A., On the measure of \(M\)-rough approximation of \(L\)-fuzzy sets, Soft Computing22 (2018) 3843-3855. · Zbl 1398.03178 |
| [47] | Li, F. and Yue, Y., L-valued fuzzy rough sets, Iranian Journal of Fuzzy Systems16 (2019) 111-127. · Zbl 1429.03175 |
| [48] | Höhle, U., \(M\)-valued sets and sheaves over integral commutative cl-monoids, in Applications of Category Theory to Fuzzy Sets (Kluwer Academic Press, 1992). · Zbl 0766.03037 |
| [49] | Höhle, U., Commutative, Residuated L-Monoids, Nonclassical Logics and Their Applications to Fuzzy Sets (Kluwer Academic Publications, Dodrecht, 1995). |
| [50] | Rosenthal, K. I., Quantales and their Applications, , Vol. 234 (Longman Scientific and Technical, 1990). · Zbl 0703.06007 |
| [51] | Ward, M., Structure residuation, The Annals of Mathematics39 (1938) 558-568. · Zbl 0019.28902 |
| [52] | Ward, M. and Dilworth, R. P., Residuated lattices, Transactions of the American Mathematical Society45 (1939) 335-354. · Zbl 0021.10801 |
| [53] | Brown, L. M. and Šostak, A., Categories of fuzzy topologies in the context of graded ditopologies, Iranian Journal of Fuzzy Systems11 (2014) 1-20. · Zbl 1419.54007 |
| [54] | Chen, P., Lai, H. and Zhang, D., Coreflective hull of finite strong \(L\)-topological spaces, Fuzzy Sets and Systems182 (2011) 79-92. · Zbl 1250.54008 |
| [55] | Chen, P. and Zhang, D., Alexandroff \(L\)-co-topological spaces, Fuzzy Sets and Systems161 (2010) 2505-2514. · Zbl 1207.54014 |
| [56] | Lowen, R., Fuzzy topological spaces and fuzzy compactness, Journal of Mathematical Analysis and Applications56 (1976) 621-633. · Zbl 0342.54003 |
| [57] | Gierz, G., Hoffman, K. H., Keimel, K., Lawson, J. D., Mislove, M. W. and Scott, D. S., Continuous Lattices and Domains (Cambridge University Press, Cambridge, 2003). · Zbl 1088.06001 |
| [58] | Šostak, A. and Elkins, A., \( L^M\)-valued equalities, \( L^M\)-rough approximation operators and \(ML\)-graded ditopologies, Hacettepe Journal of Mathematics and Statistics46 (2017) 15-32. · Zbl 1372.54011 |
| [59] | Bavel, Z., Structure and transition preserving functions of finite automata, Journal of the Association for Computing Machinery15 (1968) 135-158. · Zbl 0175.28001 |
| [60] | Prather, R. E., On categories of infinite automata, Mathematical Systems Theory4 (1970) 295-305. · Zbl 0208.02102 |
| [61] | Watanabe, T. and Noguchi, S., The amalgamation of automata, Journal of Computer and System Sciences15 (1977) 1-16. · Zbl 0357.94058 |
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