Abstract：The concepts of disturbing-valued fuzzy finite-state automata and their languages are introduced. The extension of state transition function for disturbing-valued fuzzy finite-state automata is discussed. The non-deterministic disturbing-valued fuzzy finite-state automata and three kinds of deterministic disturbing-valued fuzzy finite-state automata are equivalent to each other. The closeness of the languages families of disturbing-valued fuzzy finite-state automata under regular operations are studied.
[1] ZADEH L A. Fuzzy Sets. Information and Control, 1965, 8(3):338-353. [2] ATANASSOV K T. Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 1986, 20(1): 87-96. [3] GAU W L, BUEHRER D J. Vague Sets. IEEE Trans on Systems, Man, and Cybernetics, 1993, 23(2): 610-614. [4] ZADEH L A. The Concept of a Linguistic Variable and Its Application to Approximate Reasoning. Information Sciences, 1975, 8(3):199-249. [5] 王元元.计算机科学中的现代逻辑学.北京:科学出版社, 2001. (WANG Y Y. Modern Logic in Computer Science. Beijing, China:Science Press, 2001.) [6] LIN T L. A Set Theory for Soft Computing: A Unified View of Fuzzy Sets via Neighborhoods // Proc of the 5th IEEE International Conference on Fuzzy Systems. New Orleans, USA, 1996, II: 1140-1146. [7] YING M S. Perturbation of Fuzzy Reasoning. IEEE Trans on Fuzzy Systems, 1999, 7(5): 625-629. [8] 刘 心,陈图云.扰动模糊逻辑及其“非”算子.模糊系统与数学,2002, 16(2): 179-182. (LIU X, CHEN T Y. Disturbancy Fuzzy Logic and Its Negative Operators. Fuzzy Systems and Mathematics, 2002, 16(2): 179-182.) [9] HOPCROFT J E, MOTWANI R, ULLMAN J D. Introduction to Automata Theory, Languages, and Computation. New York, USA: Addision-Wesley, 1979. [10] ALON N, DEWDNEY A K, OTT T J. Efficient Simulation of Finite Automata by Neural Nets. Journal of the ACM, 1991, 38(2): 495-514. [11] 沈恩绍.模型论逻辑与理论计算机科学.数学进展, 1996, 25(3): 193-202. (SHEN E S. Model Theoretic Logic and Theoretical Computer Science. Advance in Mathematics, 1996, 25(3): 193-202.) [12] WEE W G. On Generalizations of Adaptive Algorithms and Application of the Fuzzy Sets Concept to Pattern Classification. Ph. D Dissertation. Westlafayett, India: Purdue University, 1967. [13] MORDESON J N, MALIK D S. Fuzzy Automata and Languages: Theory and Applications. Boca Raton, UK: Chapman and Hall 2002. [14] SANTOS E S. Maximin Automata. Information and Control, 1968,13(4): 363-377. [15] THOMASON M G, MARINOS P N. Deterministic Acceptors of Regular Fuzzy Languages. IEEE Trans on Systems, Man, and Cybernetics, 1974, SMC-4(2): 228-230. [16] 彭家寅.关于属性G-(g-)量子文法与属性量子自动机.四川师范大学学报(自然科学版), 2002, 25(2): 168-170. (PENG J Y. On Attributed G-(g-) Quantum Grammars and Attributed Quantum Automata. Journal of Sichuan Normal University(Natural Science), 2002, 25(2): 168-170.) [17] 柏明强.Fuzzy树自动机的等价性.四川师范大学学报(自然科学版), 2009, 32(l): 13-16. (BAI M Q. The Equivalence on Two kinds of Fuzzy Tree Automata. Journal of Sichuan Normal University (Natural Science), 2009, 32(1): 13-16.) [18] PEEVA K. Equivalence, Reduction and Minimization of Finite Automata over Semirings. Theoretical Computer Science, 1991, 88(2): 269-285. [19] 彭家寅.Fuzzy 2型属性文法与Fuzzy属性下推自动机.四川师范大学学报(自然科学报), 1999, 22(3): 260-264. (PENG J Y. Relation between a Fuzzy 2-Type Attributed Grammar and a Fuzzy Attributed Pushdown Automata. Journal of Sichuan Normal University (Natural Science), 1999, 22(3): 260-264.) [20] LIU J, MO Z W, QIU D, et al. Products of Mealy-Type Fuzzy Finite State Machines. Fuzzy Sets and Systems, 2009,160(16):2401-2415. [21] 邱道文.基于完备剩余格值逻辑的自动机理论——I.拓扑刻画.中国科学(E辑), 2003, 33(2): 137-146. (QIU D W. Automata Theory Based on Complete Residuated Lattice-Valued Logic I. Science in China (Series E), 2003, 33(2):137-146.) [22] 邱道文.基于完备剩余格值逻辑的自动机理论——II.可逆性及同态. 中国科学(E辑), 2003, 33(4): 340-349. (QIU D W. Automata Theory Based on Complete Residuated Lattice-Valued Logic II. Science in China (Series E), 2003, 33(4): 340-349.) [23] 彭家寅.基于完备剩余格值逻辑的自动机理论与文法理论.模式识别与人工智能, 2011, 24(5): 610-618. (PENG J Y. Automata and Grammars Theory Based on Complete Residuated Lattice-Valued Logic. Pattern Recognition and Artificial Intelligence, 2011, 24(5): 610-618.) [24] 李永明.格值自动机与语言.陕西师范大学学报(自然科学版), 2003, 31(4): l-6. (LI Y M. Lattice-Valued Automata and Their Languages. Journal of Shaanxi Normal University(Natural Science Edition), 2003, 31(4): 1-6.) [25] 彭家寅.格值下推自动机与格值上下文无关文法.计算机工程与应用, 2011, 47(25): 34-38. (PENG J Y. Lattice-Valued Pushdown Automata and Lattice-Valued Context-Free Grammars. Computer Engineering and Applications, 2011, 47(25): 34-38.) [26] YING M S. Automata Theory Based on Quantum Logic I. International Journal of Theoretical Physics, 2000, 39(4): 985-995. [27] YING M S. Automata Theory Based on Quantum Logic II. International Journal of Theoretical Physics, 2000, 39(11): 2545-2557. [28] QIU D W. Automata Theory Based on Quantum Logic: Some Characterizations. Information and Computation, 2004, 190(2): 179-195. [29] CHENG W, WANG J. Grammar Theory Based on Quantum Logic. International Journal of Theoretical Physics, 2003, 42(8): 1677-1691. [30] SHANG Y, LU X, LU R Q. Automata Theory Based on Unsharp Quantum Logic. Mathematical Structures in Computer Science, 2009, 19(4): 737-756. [31] 彭家寅.基于Unsharp量子逻辑的自动机和文法理论.计算机工程与应用, 2012, 48(28): 57-60. (PENG J Y. Automata and Grammars Theory Based on Unsharp Quantum Logic. Computer Engineering and Applications, 2012, 48(28): 57-60.) [32] JUN Y B. Intuitionistic Fuzzy Finite State Machines. Journal of Applied Mathematics and Computing, 2005, 17(1): 109-120. [33] CHOUBEY A, RAVI K M. Minimization of Deterministic Finite Automata with Vague (Final) States and Intuitionistic Fuzzy (Final) States. Iranian Journal of Fuzzy Systems, 2013, 10(l): 75-88. [34] JUN Y B, KAVIKUMAR J. Bipolar Fuzzy Finite State Machines. Bulletin of the Malaysian Mathematical Sciences Society, 2011, 34(1): 181-188. [35] RAVI K M, CHOUBEY A. Vague Regular Language. Advances in Fuzzy Mathematics, 2009, 4(2): 149-165. [36] 韩 莹.扰动模糊理论及其在推理决策中的应用.博士学位论文.南京:东南大学, 2009. (HAN Y. Disturbance Fuzzy Theory and Its Application in Reasoning and Decision Making. Ph. D Dissertation. Nanjing, China: Southeast University, 2009.) [37] 韩 莹,陈森发,陈 胜.TD型扰动值模糊正规子群.模糊系统与数学, 2006, 20(5): 25-29. (HAN Y, CHEN S F, CHEN S. The TD-Disturbing-Valued Fuzzy Normal Subgroup. Fuzzy Systems and Mathematics, 2006, 20(5):25-29.) [38] 陈图云,孟艳平.扰动模糊集相似度限定推理方法.辽宁工程技 术大学学报, 2004, 23(4): 564-566. (CHEN T Y, MENG Y P. Reasoning Method by Similarity Degree of Disturbing Fuzzy Sets. Journal of Liaoning Technical University, 2004, 23(4): 564-566.) [39] 李金宗.模式识别导论.北京:高等教育出版社, 1994. (LI J Z. An Introduction on Pattern Recognition. Beijing, China:Higher Education Press, 1994.)
2016, Vol. 29 
