基于相似度的一般全蕴涵推理方法
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摘要
自我国著名数学家王国俊提出全蕴涵推理方法以来,对该推理方法的改进或完善已成为模糊推理研究的热点之一。为了使得全蕴涵推理方法有更广泛的适用性,结合相似度推理方法,在全蕴涵推理方法的基础上,提出了一种新的模糊推理方法,即基于相似度的一般全蕴涵推理方法。给出针对两个基本推理模型FMP和FMT的统一算法,并且分别讨论该方法在两个模型下算法的还原性,从而为模糊推理提供了更多的方法。
Since the Chinese famous mathematician Wang Guojun proposed the full implication reasoning method,improving the reasoning method has become one of the hot topics in the study of fuzzy reasoning.In order to make full implication reasoning method more widely applicable,a new fuzzy reasoning method based on full implication reasoning method is proposed by combining similarity reasoning method,i.e.similarity-based general full implication reasoning method.A unified algorithm for two basic reasoning models FMP and FMT is given,and the reductiveness of the algorithm under the two models is discussed respectively,which provides more methods for fuzzy reasoning.
Since the Chinese famous mathematician Wang Guojun proposed the full implication reasoning method,improving the reasoning method has become one of the hot topics in the study of fuzzy reasoning.In order to make full implication reasoning method more widely applicable,a new fuzzy reasoning method based on full implication reasoning method is proposed by combining similarity reasoning method,i.e.similarity-based general full implication reasoning method.A unified algorithm for two basic reasoning models FMP and FMT is given,and the reductiveness of the algorithm under the two models is discussed respectively,which provides more methods for fuzzy reasoning.
引文
[1]刘华文.基于三角模的模糊逻辑理论及其应用[M].北京:科学出版社,2013:1-167.
[2]王国俊.非经典数理逻辑与近似推理[M].北京:科学出版社,2008:69-116.
[3]刘华文.关于模糊逻辑与模糊推理逻辑基础问题的十年研究综述[J].工程数学学报,2004,21(2):249-258.
[4]Wang G J.On the logic foundation of fuzzy reasoning[J].Information Sciences,1999,177(1):47-88.
[5]Pei D W.Unified full implication algorithms of fuzzy reasoning[J].Information Sciences,2008,178(2):520-530.
[6]Tang Y M,Yang X Z.Symmetric implicational method offuzzyreasoning[J]. InternationalJournalof Approximate Reasoning,2013,54(8):1034-1048.
[7]Zhou B K,Xu G,Li S.The quintuple implication principle of fuzzy reasoning[J].Information Sciences,2015,297(10):202-215.
[8]王国俊,刘华文,宋建社.三I方法综述[J].模糊系统与数学,2006,20(6):1-14.
[9]Tursken I B, Zhao Z.An approximate analogical reasoning approach based on similarity measures[J].IEEE Transactions Systems Man and Cybernetics,1988,18(6):1049-1056.
[10]Wang D G,Meng Y P.A fuzzy similarity inference method for fuzzy reasoning[J]. Computers and Mathematics with Applications,2008,56(10):2445-2454.
[11]汪培庄.模糊集合论及其应用[M].上海:上海科技出版社,1983:22-158.
[12]Zadeh L A.Fuzzy Sets.Information and Control,1965,8(3):338-335.
[2]王国俊.非经典数理逻辑与近似推理[M].北京:科学出版社,2008:69-116.
[3]刘华文.关于模糊逻辑与模糊推理逻辑基础问题的十年研究综述[J].工程数学学报,2004,21(2):249-258.
[4]Wang G J.On the logic foundation of fuzzy reasoning[J].Information Sciences,1999,177(1):47-88.
[5]Pei D W.Unified full implication algorithms of fuzzy reasoning[J].Information Sciences,2008,178(2):520-530.
[6]Tang Y M,Yang X Z.Symmetric implicational method offuzzyreasoning[J]. InternationalJournalof Approximate Reasoning,2013,54(8):1034-1048.
[7]Zhou B K,Xu G,Li S.The quintuple implication principle of fuzzy reasoning[J].Information Sciences,2015,297(10):202-215.
[8]王国俊,刘华文,宋建社.三I方法综述[J].模糊系统与数学,2006,20(6):1-14.
[9]Tursken I B, Zhao Z.An approximate analogical reasoning approach based on similarity measures[J].IEEE Transactions Systems Man and Cybernetics,1988,18(6):1049-1056.
[10]Wang D G,Meng Y P.A fuzzy similarity inference method for fuzzy reasoning[J]. Computers and Mathematics with Applications,2008,56(10):2445-2454.
[11]汪培庄.模糊集合论及其应用[M].上海:上海科技出版社,1983:22-158.
[12]Zadeh L A.Fuzzy Sets.Information and Control,1965,8(3):338-335.