模糊蕴涵关于合取2-一致模满足输入律的刻画
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摘要
首先引入了模糊否定关于2-一致模满足(COMP_(U~2))的概念,并讨论了连续的模糊否定分别关于4类合取2-一致模满足(COMP_(U~2))的情形;其次,引入了模糊蕴涵关于合取2-一致模满足输入律的概念,并给出了其相关性质;最后,利用(COMP_(U~2))给出了模糊蕴涵分别关于4类合取2-一致模满足输入律的刻画。
The notion of fuzzy negations satisfying(COMP_(U~2)) with respect to 2-uninorms is introduced, and the situations that continuous fuzzy negations satisfying(COMP_(U~2)) with respect to four types of conjunctive 2-uninorms are discussed respectively. The definition and related properties of fuzzy implications satisfying the law of importation with conjunctive 2-uninorms are given. Finally, using(COMP_(U~2)), a characterization that fuzzy implications satisfy respectively the law of importation with respect to four types of conjunctive 2-uninorms is provided.
The notion of fuzzy negations satisfying(COMP_(U~2)) with respect to 2-uninorms is introduced, and the situations that continuous fuzzy negations satisfying(COMP_(U~2)) with respect to four types of conjunctive 2-uninorms are discussed respectively. The definition and related properties of fuzzy implications satisfying the law of importation with conjunctive 2-uninorms are given. Finally, using(COMP_(U~2)), a characterization that fuzzy implications satisfy respectively the law of importation with respect to four types of conjunctive 2-uninorms is provided.
引文
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[14]MAS M,MONSERRAT M,TORRENS J.A characterization of(U,N),RU,QL and D-implications derived from uninorms satisfying the law of importation[J].Fuzzy Sets and Systems,2010,161(10):1369-1387.
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[16]MASSANET S,TORRENS J.Characterization of fuzzy implication functions with a continuous natural negation satisfying the law of importation with a fixed t-norm[J].IEEE Transactions on Fuzzy Systems,2017,25(1):100-113.
[17]MASSANET S,RUIZ-AGUILERA D,TORRENS J.Characterization of a class of fuzzy implication functions satisfying the law of importation with respect to a fixed uninorm(Part I)[J].IEEE Transactions on Fuzzy Systems,2018,26(4):1983-1994.
[18]AKELLA P.Structure of n-uninorms[J].Fuzzy Sets and Systems,2007,158(15):1631-1651.
[2]GOTTWALD S.A treatise on many-valued logics[M].Baldock:Research Studies Press,2001.
[3]KERRE E,HUANG C,RUAN D.Fuzzy set theory and approximate reasoning[M].Wuhan:Wuhan University Press,2004.
[4]MAS M,MONSERRAT M,TORRENS J,et al.A survey on fuzzy implication functions[J].IEEE Transactions on Fuzzy Systems,2007,15(6):1107-1121.
[5]BUSTINCE H,MOHEDANOA V,BARRENECHEA E,et al.Definition and construction of fuzzy DI-subsethood measures[J].Information Sciences,2006,176(21):3190-3231.
[6]BUSTINCE H,PAGOLA M,BARRENECHEA E.Construction of fuzzy indices from fuzzy DI-subsethood measures:application to the global comparison of images[J].Information Sciences,2007,177(3):906-929.
[7]KERRE E,NACHTEGAEL M.Fuzzy techniques in image processing(studies in fuzziness and soft computing)[M].New York:Springer,2000.
[8]YAN P,CHEN G.Discovering a cover set of ARsi with hierarchy from quantitative databases[J].Information Sciences,2005,173(4):319-336.
[9]RADZIKOWSKA A M,KERRE E.A comparative study of fuzzy rough sets[J].Fuzzy Sets and Systems,2002,126(2):137-155.
[10]BACZYN'SKI M,JAYARAM B.Fuzzy implication[M].Berlin:Springer,2008.
[11]ZADEH L A.Outline of a new approach to the analysis of complex systems and decision processes[J].IEEE Transactions on Systems,Man,and Cybernetics,1973,3(1):28-44.
[12]GONZLEZ M,RUIZ-AGUILERA D,TORRENS J.Algebraic properties of fuzzy morphological operators based on uninorms[J].Artificial Intelligence Research and Development,2003,100:27-38.
[13]MASSANET S,TORRENS J.On the characterization of Yagers implications[J].Information Sciences,2012,201:1-18.
[14]MAS M,MONSERRAT M,TORRENS J.A characterization of(U,N),RU,QL and D-implications derived from uninorms satisfying the law of importation[J].Fuzzy Sets and Systems,2010,161(10):1369-1387.
[15]MASSANET S,TORRENS J.The law of importation versus the exchange principle on fuzzy implications[J].Fuzzy Sets and Systems,2011,168(1):47-69.
[16]MASSANET S,TORRENS J.Characterization of fuzzy implication functions with a continuous natural negation satisfying the law of importation with a fixed t-norm[J].IEEE Transactions on Fuzzy Systems,2017,25(1):100-113.
[17]MASSANET S,RUIZ-AGUILERA D,TORRENS J.Characterization of a class of fuzzy implication functions satisfying the law of importation with respect to a fixed uninorm(Part I)[J].IEEE Transactions on Fuzzy Systems,2018,26(4):1983-1994.
[18]AKELLA P.Structure of n-uninorms[J].Fuzzy Sets and Systems,2007,158(15):1631-1651.