扰动模糊文法及其语言
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摘要
引入了扰动模糊文法的概念,讨论了其相应的Chomsky分类,证明了扰动模糊弱正则文法、扰动模糊正则文法和扰动值模糊有限自动机三者等价性.给出了扰动模糊上下文无关文法、最左派生、Chomsky范式和Greibach范式文法的概念,揭示它们的语言之一致性.
The concepts of disturbing fuzzy grammars and their languages are introduced,the related Chomsky class if cation is discussed,and it is shown that disturbing fuzzy weak regular grammar,disturbing fuzzy regular grammar and disturbing-valued fuzzyfnite-state automata are equivalent.The notions of disturbing fuzzy context-free grammar,leftmost derivation,Chomsky normal form and Greibach normal form are given,and the unanimity of their languages is revealed.
The concepts of disturbing fuzzy grammars and their languages are introduced,the related Chomsky class if cation is discussed,and it is shown that disturbing fuzzy weak regular grammar,disturbing fuzzy regular grammar and disturbing-valued fuzzyfnite-state automata are equivalent.The notions of disturbing fuzzy context-free grammar,leftmost derivation,Chomsky normal form and Greibach normal form are given,and the unanimity of their languages is revealed.
引文
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[2]Atanassov K.Intuitionistic Fuzzy sets[J].Fuzzy sets and Systems,1986,20(1):87-96.
[3]Gau W L,Buehrer D J.Vague sets[J].IEEE Transactions on Systems,Man,and Cybernetics,1993,23(2):610-614.
[4]Zadeh L A.The concept of a linguistic variable and its zpplication to approximate reasoning[M]//Learning Systems and Intelligent Robots.Springer US,1974:199-249.
[5]王元元.计算机科学中的现代逻辑学[M].北京:科技出版社,2001:207.
[6]彭家寅.扰动值模糊有限自动机及其语言[J].模式识别与人工智能,2016,29(4):298-312.
[7]彭家寅.扰动模糊有限转换状态机[J].计算机工程与应用,2016,52(22):1-8.
[8]彭家寅.BL-代数的扰动模糊理想[J].山东大学学报(理学版),2016,51(10):78-94.
[9]彭家寅.拟BCK-代数的扰动模糊理想[J].模糊系统与数学,2016(5):1-10.
[10]彭虹侨.BCK代数的扰动模糊理想[J].内江师范学院学报,2016,31(6):7-15.
[11]彭虹侨.Heyting代数的扰动模糊滤子[J].内江师范学院学报,2016,31(10):7-14.
[12]Lin T L.A set theory for soft computing[C].Proceeding of 1996IEEE International Conference on Fuzzy Systems,1996:1140-1146.
[13]Ying M S.Perturbation of fuzzy reasoning[J].IEEE Transactions on Fuzzy Systems,1995,1(5):625-629.
[14]刘心,陈图云.扰动模糊逻辑及其“非算子”[J].模糊系统与数学,2002,16(2):179-182.
[15]Hopcroft J E,Ullman J D.Introduction to automata theory,languages,and computation[M].New York:Addison-Wesley,1979.
[16]Shen E.Model theoretic logic and theoretical computer science[J].Advances in Mathematics,1996,25(3):193-202.
[17]Lee E T,Zadeh L A.Note on fuzzy languages[J].Information Science,1969,1(4):421-434.
[18]Santos E S.Fuzzy automata and languages[J].Information Science,1976,10(3):193-197.
[19]Santos E S.Realization of fuzzy languages by probabilistic,Max-product and maxminautomata[J].Information Science,1975,8(1):39-53.
[20]舒兰,莫智文.Fuzzy上下文无关语言的几个辅助定理[J].系统工程理论与实践,1999,19(3):47-52.
[21]柏明强.Fuzzy上下文无关语言中的Chomsky定理[J].模糊系统与数学,2004,18(Z1):271-274.
[22]彭家寅.Fuzzy上下文无关语言的运算封闭性[J].四川师范大学学报(自然科学版),1999,22(4):391-395.
[23]舒兰.关于Fuzzy 3型属性文法与Fuzzy属性自动机[J].电子科技大学学报,1991,18(1):84-87.
[24]莫智文,舒兰.Fuzzy属性文法及在心电图识别中的应用[J].四川师范大学学报(自然科学版),1995,18(4):12-16.
[25]彭家寅.Fuzzy 2型属性文法与Fuzzy属性下推自动机[J].四川师范大学学报(自然科学版),1999,22(3):260-264.
[26]邱道文.基于完备剩余格值逻辑的自动机理论:拓扑刻画[J].中国科学(E辑),2003,33(2):137-146.
[27]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[J].中国科学(E),2003,33(4):340-349.
[28]彭家寅.基于完备剩余格值逻辑的自动机理论与文法理论[J].模式识别与人工智能,2011,24(5):610-617.
[29]李永明.格值自动机与语言[J].陕西师范大学学报,2003,31(4):1-6.
[30]彭家寅.格值下推自动机与格值上下文无关文法[J].计算机工程与应用,2011,47(25):34-38.
[31]Ying M S.Automata Theory Based on Quantum Logic I,II[J].Intemational Journal of Theoretical Physics.,2000,39(4):981-991;2000,39(4):2545-2557.
[32]李永明.基于量子逻辑的有穷自动机与单体二阶量子逻辑[J].中国科学(F辑:信息科学),2009,39(11):1135-1145.
[33]Qiu D W.Automata theory based on quantum logic:Some characterizations[J].Information and Comput ation,2004,190:179-195.
[34]彭家寅.基于unsharp量子逻辑的自动机和文法理论[J].计算机工程与应用,2012,48(28):57-60.
[35]Jun Y B,Kevikumar J.Bipolar Fuzzy Finite State Machines[J].Bulletin of the Malaysian Mathematical Sciences Society,2011,34(1):181-188.
[36]Choubey A,Ravi K M.Vague regular language[J].Advances in Fuzzy Mathematics,2009,4(2):147-165.
[37]Jun Y B.Intuitionistic fuzzy finite state machines[J].Journal of Applied Mathematics and Computing,2005,17(1/3):109-120.
[38]Choubey A,Ravi K M.Minimization of deterministic finite automata with vague(Final)states and Intuitionistic fuzzy(final)states[J].Iranian Journal of Fuzzy Systems,2013,10(1):75-88.
[39]Ravi K M,Choubey A.interval-valued Fuzzy regular language[J].Jouraal of Applied.Mathematical&Informatics,2010,28(3/4):639-649.
[40]韩莹.扰动模糊理论及其在推理决策中的应用[D].南京:东南大学,2009:6-14.
[41]韩莹,陈森发,陈胜.TD型扰动值模糊正规子群[J].模糊系统与数学,2006,20(5):25-29.
[2]Atanassov K.Intuitionistic Fuzzy sets[J].Fuzzy sets and Systems,1986,20(1):87-96.
[3]Gau W L,Buehrer D J.Vague sets[J].IEEE Transactions on Systems,Man,and Cybernetics,1993,23(2):610-614.
[4]Zadeh L A.The concept of a linguistic variable and its zpplication to approximate reasoning[M]//Learning Systems and Intelligent Robots.Springer US,1974:199-249.
[5]王元元.计算机科学中的现代逻辑学[M].北京:科技出版社,2001:207.
[6]彭家寅.扰动值模糊有限自动机及其语言[J].模式识别与人工智能,2016,29(4):298-312.
[7]彭家寅.扰动模糊有限转换状态机[J].计算机工程与应用,2016,52(22):1-8.
[8]彭家寅.BL-代数的扰动模糊理想[J].山东大学学报(理学版),2016,51(10):78-94.
[9]彭家寅.拟BCK-代数的扰动模糊理想[J].模糊系统与数学,2016(5):1-10.
[10]彭虹侨.BCK代数的扰动模糊理想[J].内江师范学院学报,2016,31(6):7-15.
[11]彭虹侨.Heyting代数的扰动模糊滤子[J].内江师范学院学报,2016,31(10):7-14.
[12]Lin T L.A set theory for soft computing[C].Proceeding of 1996IEEE International Conference on Fuzzy Systems,1996:1140-1146.
[13]Ying M S.Perturbation of fuzzy reasoning[J].IEEE Transactions on Fuzzy Systems,1995,1(5):625-629.
[14]刘心,陈图云.扰动模糊逻辑及其“非算子”[J].模糊系统与数学,2002,16(2):179-182.
[15]Hopcroft J E,Ullman J D.Introduction to automata theory,languages,and computation[M].New York:Addison-Wesley,1979.
[16]Shen E.Model theoretic logic and theoretical computer science[J].Advances in Mathematics,1996,25(3):193-202.
[17]Lee E T,Zadeh L A.Note on fuzzy languages[J].Information Science,1969,1(4):421-434.
[18]Santos E S.Fuzzy automata and languages[J].Information Science,1976,10(3):193-197.
[19]Santos E S.Realization of fuzzy languages by probabilistic,Max-product and maxminautomata[J].Information Science,1975,8(1):39-53.
[20]舒兰,莫智文.Fuzzy上下文无关语言的几个辅助定理[J].系统工程理论与实践,1999,19(3):47-52.
[21]柏明强.Fuzzy上下文无关语言中的Chomsky定理[J].模糊系统与数学,2004,18(Z1):271-274.
[22]彭家寅.Fuzzy上下文无关语言的运算封闭性[J].四川师范大学学报(自然科学版),1999,22(4):391-395.
[23]舒兰.关于Fuzzy 3型属性文法与Fuzzy属性自动机[J].电子科技大学学报,1991,18(1):84-87.
[24]莫智文,舒兰.Fuzzy属性文法及在心电图识别中的应用[J].四川师范大学学报(自然科学版),1995,18(4):12-16.
[25]彭家寅.Fuzzy 2型属性文法与Fuzzy属性下推自动机[J].四川师范大学学报(自然科学版),1999,22(3):260-264.
[26]邱道文.基于完备剩余格值逻辑的自动机理论:拓扑刻画[J].中国科学(E辑),2003,33(2):137-146.
[27]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[J].中国科学(E),2003,33(4):340-349.
[28]彭家寅.基于完备剩余格值逻辑的自动机理论与文法理论[J].模式识别与人工智能,2011,24(5):610-617.
[29]李永明.格值自动机与语言[J].陕西师范大学学报,2003,31(4):1-6.
[30]彭家寅.格值下推自动机与格值上下文无关文法[J].计算机工程与应用,2011,47(25):34-38.
[31]Ying M S.Automata Theory Based on Quantum Logic I,II[J].Intemational Journal of Theoretical Physics.,2000,39(4):981-991;2000,39(4):2545-2557.
[32]李永明.基于量子逻辑的有穷自动机与单体二阶量子逻辑[J].中国科学(F辑:信息科学),2009,39(11):1135-1145.
[33]Qiu D W.Automata theory based on quantum logic:Some characterizations[J].Information and Comput ation,2004,190:179-195.
[34]彭家寅.基于unsharp量子逻辑的自动机和文法理论[J].计算机工程与应用,2012,48(28):57-60.
[35]Jun Y B,Kevikumar J.Bipolar Fuzzy Finite State Machines[J].Bulletin of the Malaysian Mathematical Sciences Society,2011,34(1):181-188.
[36]Choubey A,Ravi K M.Vague regular language[J].Advances in Fuzzy Mathematics,2009,4(2):147-165.
[37]Jun Y B.Intuitionistic fuzzy finite state machines[J].Journal of Applied Mathematics and Computing,2005,17(1/3):109-120.
[38]Choubey A,Ravi K M.Minimization of deterministic finite automata with vague(Final)states and Intuitionistic fuzzy(final)states[J].Iranian Journal of Fuzzy Systems,2013,10(1):75-88.
[39]Ravi K M,Choubey A.interval-valued Fuzzy regular language[J].Jouraal of Applied.Mathematical&Informatics,2010,28(3/4):639-649.
[40]韩莹.扰动模糊理论及其在推理决策中的应用[D].南京:东南大学,2009:6-14.
[41]韩莹,陈森发,陈胜.TD型扰动值模糊正规子群[J].模糊系统与数学,2006,20(5):25-29.