آمار
| تعداد نشریات | 26 |
| تعداد شمارهها | 447 |
| تعداد مقالات | 4,557 |
| تعداد مشاهده مقاله | 5,380,003 |
| تعداد دریافت فایل اصل مقاله | 3,580,074 |
Kleen’s Theorem for BL-general L-fuzzy automata | ||
| Journal of Mahani Mathematical Research | ||
| دوره 10، شماره 2، دی 2021، صفحه 125-144 اصل مقاله (607.51 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmrc.2021.17171.1134 | ||
| نویسندگان | ||
| Marzieh Shamsizadeh* 1؛ Mohammad Mehdi Zahedi2؛ Khadijeh Abolpour3 | ||
| 1Behbahan Khatam Alanbia University of Technology, Khouzestan, Iran | ||
| 2Department of Mathematics Graduate University of Advanced Technology, Kerman, Iran | ||
| 3Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran | ||
| چکیده | ||
| The contribution of generl fuzzy automata to neural networks has been considerable, and dynamical fuzzy systems are becoming more and more popular and useful. Basic logic, or BL for short, has been introduced by Hájek [5] in order to provide a general framework for formalizing statements of fuzzy nature. In this note, some of the closure properties of the BL-general fuzzy automaton based on lattice valued such as union, intersection, connection and a serial connection are considered, after that, the behavior of them are discussed. Moreover, for a given BL-general fuzzy automaton on the basis of lattice valued, a complete BL-general fuzzy automaton on the basis of lattice valued is presented. Afterward, we may test the Pumping Lemma for the BL-general fuzzy automaton based on lattice valued. In particular, a connection between the behavior of BL-general fuzzy automaton based on lattice valued and its language is presented. Also, it is proven that L is a recognizable set if and only if L is rational. Also, it is driven that Kleen’s Theorem is valid for the BL-general fuzzy automaton on the basis of lattice valued. Finally, we give some examples to clarify these notions. | ||
| کلیدواژهها | ||
| BL-general fuzzy automata؛ Closure properties؛ Behavior of fuzzy automata؛ Pumping Lemma؛ Kleen’s Theorem | ||
| مراجع | ||
|
[1] K. Abolpour, M.M. Zahedi, Isomorphism between two BL-general fuzzy automata, Soft Computing, 16 (2012), 729-736. [2] M. Doostfatemeh, S.C. Kremer, New directions in fuzzy automata, International Journal of Approximate Reasoning, 38 (2005), 175-214. [3] C.L. Giles, C.W. Omlin, K.K. Thornber, Equivalence in knowledge representation: automata, recurrent neural networks, and dynamical fuzzy systems, Proceedings of IEEE, 87 (1999), 1623-1640. [4] M.M. Gupta, G.N. Saridis, B.R. Gaines, Fuzzy Automata and Decision Processes, North Holland, New York, 1977, 111-175. [5] P. Hajek, Metamathematics of fuzzy logic, Kluwer, Dordrecht, (1988). [6] J. E. Hopcroft, R. Motwani, J. D. Ullman, Introduction to Automata Theory, Languages and Computation, seconded., Addison-Wesley, Reading, MA, 2001. [7] E. T. Lee, L. A. Zadeh, Note on fuzzy languages, Information Sciences 1 (1969) 421-434. [8] Y. M. Li, W. Pedryez, Fuzzy nite automata and fuzzy regular expressions with membership values in lattice-ordered monoid, Fuzzy Sets and Systems, 156 (2005), 68-92. [9] D. S. Malik, J. N. Mordeson, Fuzzy Automata and Languages: Theory and Applications, Chapman Hall, CRC Boca Raton, London, New York, Washington DC, 2002. [10] D. S. Malik, J. N. Mordeson, Fuzzy Discrete Structures, Physica-Verlag, New York, 2000. [11] C. W. Omlin, K. K. Thornber, C. L. Giles, Fuzzy nite-state automata can be determnistically encoded in recurrent neural networks, IEEE Transactions on Fuzzy Systems, 5(1998), 76-89. [12] W. Pedrycz, A. Gacek, Learning of fuzzy automata, International Journal of Computational Intelligence and Applications, 1 (2001), 19-33. [13] K. Peeva, Equivalence, reduction and minimization of nite automata over semirings,Theoretical Computer Science 88 (1991) 269-285. [14] D. Qiu, Automata theory based on complete residuated lattice-valued logic, Science in China Series: Information Sciences, 44 (2001), 419-429. [15] D. Qiu, Automata theory based on complete residuated lattice-valued logic (II), Science in China Series F: Information Sciences, 45 (2002), 442-452. [16] D. Qiu, Characterizations of fuzzy nite automata, Fuzzy Sets and Systems, 141 (2004), 391-414. [17] D. Qiu, Pumping lemma in automata theory based on complete residuated lattice-valued logic: A not, Fuzzy Sets and Systems, 157 (2006), 2128-2138. [18] D. Qiu, Supervisory control of fuzzy discrete event systems: a formal approach, IEEE Transactions on Systems, Man and CyberneticsPart B, 35 (2005), 72-88. [19] A. Salomaa, Theory of Automata, Pergamon Press, Oxford, 1969. [20] E. S. Santos, Maximin automata, Information and Control 13 (1968) 363-377. [21] M. Shamsizadeh, M. M. Zahedi. A note on Quotient structures of intuitionistic fuzzy nite state machines, Journal of Applied Mathematics and Computing, 51(2016), 413-423. [22] M. Shamsizadeh, M. M. Zahedi, Bisimulation of type 2 for BL-general fuzzy automata, Soft Computing, 23 (2019), 9843-9852. [23] M. Shamsizadeh, M. M. Zahedi, Intuitionistic general fuzzy automata, Soft Computing, 20 (2015), 3505-3519. [24] M. Shamsizadeh, M. M. Zahedi, Minimal intutionistic general L-fuzzy automata, Italian Journal of Pure and Applied Mathematics, 35 (2015), 155-186. [25] M. Shamsizadeh, M. M. Zahedi, Kh. Abolpour, Bisimulation for BL-general fuzzy automata, Iranian Journal of Fuzzy Systems, 13 (2016), 35-50. [26] V. Topencharov, K. Peeva, Equivalence, reduction and minimization of nite fuzzy automata, Journal of Mathematical Analysis and Applications 84 (1981) 270-281. [27] W. Wechler, The Concept of Fuzziness in Automata and Language Theory, Akademie-Verlag, Berlin, 1978. [28] W. G. Wee, On generalizations of a daptive algorithm and application of the fuzzy sets concept to pattern classi cation, Ph.D. Thesis, Purdue University, June, 1967. [29] L. Wu and D. Qiu, Automata theory based on complete residuated lattice-valued logic: Reduction and minimization, Fuzzy Sets and Systems, 161 (2010), 1635-1656. [30] H. Xing and D. W. Qiu, Automata theory based on complete residuated lattice-valued logic: A categorical approach, Fuzzy Sets and Systems, 160 (2009), 2416-2428. [31] H. Xing and D. W. Qiu, Pumping lemma in context-free grammar theory based on complete residuated lattice-valued logic, Fuzzy Sets and Systems, 160 (2009), 1141 -1151. [32] H. Xing, D. W. Qiu and F. C. Liu, Automata theory based on complete residuated lattice-valued logic: Pushdown automata, Fuzzy Sets and Systems, 160 (2009), 1125-1140. [33] H. Xing, D. W. Qiu, F. C. Liu and Z. J. Fan, Equivalence in automata theory based on complete residuated lattice-valued logic, Fuzzy Sets and Systems, 158 (2007), 1407-1422. [34] M. S. Ying, A formal model of computing with words, IEEE Transactions on Fuzzy Systems, 10 (2002), 640-652. [35] L.A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353. | ||
|
آمار تعداد مشاهده مقاله: 291 تعداد دریافت فایل اصل مقاله: 206 |
||