直觉模糊逻辑的(α,β)-准锁语义归结方法
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摘要
为了提高直觉模糊命题逻辑的(α,β)-归结效率,将准锁语义归结策略应用于(α,β)-归结原理,得到直觉模糊命题逻辑的(α,β)-准锁语义归结方法,证明方法的可靠性与完备性.给出直觉模糊命题逻辑系统的(α,β)-准锁语义归结和(α,β)-准锁语义归结演绎的概念.讨论直觉模糊命题逻辑系统中的(α,β)-准锁语义归结式和锁子句的合并规则.最后,给出直觉模糊命题逻辑系统的基于(α,β)-准锁语义归结的自动推理算法步骤,并通过实例说明算法的有效性.
To improve the(α,β)-resolution efficiency of intuitionistic fuzzy propositional logic,quasi lock semantic resolution is applied to(α,β)-resolution.The(α,β)-quasi lock semantic resolution method is introduced into intuitionistic fuzzy logic system,and its soundness and completeness are proved.The concepts of(α,β)-quasi lock semantic resolution and(α,β)-quasi lock semantic resolution reasoning of intuitionistic fuzzy propositional logic are proposed.The formula of(α,β)-quasi lock semantic resolution and merger rule of generalized lock clauses are discussed.Finally,the steps of automated reasoning algorithm based on(α,β)-quasi lock semantic resolution for intuitionistic fuzzy propositional logic are presented and an example is given to illustrate the effectiveness of the proposed method.
To improve the(α,β)-resolution efficiency of intuitionistic fuzzy propositional logic,quasi lock semantic resolution is applied to(α,β)-resolution.The(α,β)-quasi lock semantic resolution method is introduced into intuitionistic fuzzy logic system,and its soundness and completeness are proved.The concepts of(α,β)-quasi lock semantic resolution and(α,β)-quasi lock semantic resolution reasoning of intuitionistic fuzzy propositional logic are proposed.The formula of(α,β)-quasi lock semantic resolution and merger rule of generalized lock clauses are discussed.Finally,the steps of automated reasoning algorithm based on(α,β)-quasi lock semantic resolution for intuitionistic fuzzy propositional logic are presented and an example is given to illustrate the effectiveness of the proposed method.
引文
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[10]刘叙华.基于归结方法的自动推理.北京:科学出版社,1994.(LIU X H.Automatic Reasoning Based on Resolution Method.Beijing,China:Science Press,1994.)
[11]XU Y,XU W T,ZHONG X M,et al.α-Generalized Resolution Principle Based on Lattice-Valued Propositional Logic LP(X)//Proc of the 9th International FLINS Conference on Foundations and Applications of Computational Intelligence.Chengdu,China,2010:66-71.
[12]XU Y,RUAN D,KERRE E E,et al.α-Resolution Principle Based on Lattice-Valued Propositional Logic LP(X).Information Sciences,2000,130(1/2/3/4):195-223.
[13]XU Y,RUAN D,KERRE E E,et al.α-Resolution Principle Based on First-Order Lattice-Valued Logic LF(X).Information Sciences,2001,132(1/2/3/4):221-239.
[14]HE X X,XU Y,LIU J,et al.α-Lock Resolution Method for a Lattice-Valued First-Order Logic.Engineering Applications of Artificial Intelligence,2011,24(7):1274-1280.
[15]ZHONG X M,XU Y,LIU J,et al.General Form ofα-Resolution Principle for Linguistic Truth-Valued Lattice-Valued Logic.Soft Computing,2012,16(10):1767-1781.
[16]张家锋,徐扬,何星星.格值语义归结推理方法.计算机科学,2011,38(9):201-203,210.(ZHANG J F,XU Y,HE X X.Lattice-Valued Semantic Resolution Reasoning Method.Computer Science,2011,38(9):201-203,210.)
[17]ZHONG X M,XU Y,LIU J,et al.α-Quasi-Lock Semantic Resolution Method Based on Lattice-Valued Logic.International Journal of Computational Intelligence Systems,2014,7(3):418-431.
[18]HE X X,XU Y,LIU J,et al.α-Generalized Lock Resolution Method in Linguistic Truth-Valued Lattice-Valued Logic.International Journal of Computational Intelligence Systems,2012,5(6):1120-1134.
[19]邹丽,陈图云,郑宏亮.直觉模糊逻辑中的归结原理.辽宁师范大学学报(自然科学版),1997,20(2):98-101.(ZOU L,CHEN T Y,ZHENG H L.Resolution Principle Based on Intuitionistic Fuzzy Logic.Journal of Liaoning Normal University(Natural Science),1997,20(2):98-101.)
[20]邹丽,刘迪,郑宏亮.直觉模糊逻辑的(α,β)-广义锁归结方法.计算机科学与探索,2015,9(8):1004-1009.(ZOU L,LIU D,ZHENG H L.(α,β)-Generalized Lock Resolution of Intuitionistic Fuzzy Logic.Journal of Frontiers of Computer Science and Technology,2015,9(8):1004-1009.)
[2]雷英杰,王宝树,路艳丽.基于直觉模糊逻辑的近似推理方法.控制与决策,2006,21(3):305-310.(LEI Y J,WANG B S,LU Y L.Approximate Reasoning Method Based on Intuitionistic Fuzzy Logic.Control and Decision,2006,21(3):305-310.)
[3]裴峥,秦克云.粗糙集的直觉模糊特殊集表示及其在属性约简中的应用.模式识别与人工智能,2004,17(3):262-266.(PEI Z,QIN K Y.Intuitionistic Fuzzy Special Set Expression of Rough Set and Its Application in Reduction of Attributes.Pattern Recognition and Artificial Intelligence,2004,17(3):262-266.)
[4]徐泽水.区间直觉模糊信息的集成方法及其在决策中的应用.控制与决策,2007,22(2):215-219.(XU Z S.Methods for Aggregating Interval-Valued Intuitionistic Fuzzy Information and Their Application to Decision Making.Control and Decision,2007,22(2):215-219.)
[5]徐泽水.直觉模糊信息集成理论及应用.北京:科学出版社,2008.(XU Z S.Intuitionistic Fuzzy Information Aggregation:Theory and Applications.Beijing,China:Science Press,2008.)
[6]徐泽水.直觉模糊偏好信息下的多属性决策途径.系统工程理论与实践,2007,27(11):62-71.(XU Z S.Approaches to Multiple Attribute Decision Making with Intuitionistic Fuzzy Preference Information.Systems EngineeringTheory&Practice,2007,27(11):62-71.)
[7]谭春桥.基于区间值直觉模糊集的TOPSIS多属性决策.模糊系统与数学,2010,24(1):92-97.(TAN C Q.TOPSIS Multiple Attribute Decision Making Based on Interval-Valued Intuitionistic Fuzzy Sets.Fuzzy Systems and Mathematics,2010,24(1):92-97.)
[8]雷阳,雷英杰,冯有前,等.基于直觉模糊推理的目标识别方法.控制与决策,2011,26(8):1163-1168.(LEI Y,LEI Y J,FENG Y Q,et al.Techniques for Target Recognition Based on Intuitionistic Fuzzy Reasoning.Control and Decision,2011,26(8):1163-1168.)
[9]巩增泰,冯雪.基于Orlicz函数及强缺项收敛的模糊数列空间.陕西师范大学学报(自然科学版),2015,43(1):1-7.(GONG Z T,FENG X.On Sequence Spaces of Fuzzy Numbers Based on Orlicz Functions and Strongly Lacunary Convergence.Journal of Shaanxi Normal University(Natural Science Edition),2015,43(1):1-7.)
[10]刘叙华.基于归结方法的自动推理.北京:科学出版社,1994.(LIU X H.Automatic Reasoning Based on Resolution Method.Beijing,China:Science Press,1994.)
[11]XU Y,XU W T,ZHONG X M,et al.α-Generalized Resolution Principle Based on Lattice-Valued Propositional Logic LP(X)//Proc of the 9th International FLINS Conference on Foundations and Applications of Computational Intelligence.Chengdu,China,2010:66-71.
[12]XU Y,RUAN D,KERRE E E,et al.α-Resolution Principle Based on Lattice-Valued Propositional Logic LP(X).Information Sciences,2000,130(1/2/3/4):195-223.
[13]XU Y,RUAN D,KERRE E E,et al.α-Resolution Principle Based on First-Order Lattice-Valued Logic LF(X).Information Sciences,2001,132(1/2/3/4):221-239.
[14]HE X X,XU Y,LIU J,et al.α-Lock Resolution Method for a Lattice-Valued First-Order Logic.Engineering Applications of Artificial Intelligence,2011,24(7):1274-1280.
[15]ZHONG X M,XU Y,LIU J,et al.General Form ofα-Resolution Principle for Linguistic Truth-Valued Lattice-Valued Logic.Soft Computing,2012,16(10):1767-1781.
[16]张家锋,徐扬,何星星.格值语义归结推理方法.计算机科学,2011,38(9):201-203,210.(ZHANG J F,XU Y,HE X X.Lattice-Valued Semantic Resolution Reasoning Method.Computer Science,2011,38(9):201-203,210.)
[17]ZHONG X M,XU Y,LIU J,et al.α-Quasi-Lock Semantic Resolution Method Based on Lattice-Valued Logic.International Journal of Computational Intelligence Systems,2014,7(3):418-431.
[18]HE X X,XU Y,LIU J,et al.α-Generalized Lock Resolution Method in Linguistic Truth-Valued Lattice-Valued Logic.International Journal of Computational Intelligence Systems,2012,5(6):1120-1134.
[19]邹丽,陈图云,郑宏亮.直觉模糊逻辑中的归结原理.辽宁师范大学学报(自然科学版),1997,20(2):98-101.(ZOU L,CHEN T Y,ZHENG H L.Resolution Principle Based on Intuitionistic Fuzzy Logic.Journal of Liaoning Normal University(Natural Science),1997,20(2):98-101.)
[20]邹丽,刘迪,郑宏亮.直觉模糊逻辑的(α,β)-广义锁归结方法.计算机科学与探索,2015,9(8):1004-1009.(ZOU L,LIU D,ZHENG H L.(α,β)-Generalized Lock Resolution of Intuitionistic Fuzzy Logic.Journal of Frontiers of Computer Science and Technology,2015,9(8):1004-1009.)