(I,A)-蕴涵及其基本性质
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摘要
模糊蕴涵在模糊逻辑和近似推理领域中发挥着十分重要的作用,模糊蕴涵的构造是相关领域中的重要研究课题。基于模糊蕴涵I和聚合算子A构造出(I,A)-算子,研究(I,A)-算子成为模糊蕴涵的条件,其次研究(I,A)-蕴涵包括分配性和输入性在内的一些基本性质。
Fuzzy implications play a fundamental role in fuzzy logic and approximate reasoning, and the construction of fuzzy implications is an important research topic in related fields.(I,A)-operators are constructed based on fuzzy implications I and aggregation operators A. The conditions under which(I,A)-operators are fuzzy implications are inverstigated,and the basic properties of(I,A)-implications are discussed, including distributivity over overlap functions and grouping functions and law of importation.
Fuzzy implications play a fundamental role in fuzzy logic and approximate reasoning, and the construction of fuzzy implications is an important research topic in related fields.(I,A)-operators are constructed based on fuzzy implications I and aggregation operators A. The conditions under which(I,A)-operators are fuzzy implications are inverstigated,and the basic properties of(I,A)-implications are discussed, including distributivity over overlap functions and grouping functions and law of importation.
引文
[1]Foder J,Roubens M.Fuzzy preference modelling and multicriteria decision support[M].Dordrecht:Kluwer Academic Publishers,1993.
[2]李永明.模糊系统分析[M].北京:科学出版社,2005.
[3]Butnariu D,Klement E.Triangular norm-based measures and games with fuzzy coalitions[M].London:Kluwer Academic Publishers,1993.
[4]Baczynski M,Jayaram B.(S,N)-and R-implications:a state-of-the-art survey[J].Fuzzy Sets and Systems,2008,159:1836-1859.
[5]Baczynski M,Jayaram B.Fuzzy implications[M].Berlin:Spring,2008.
[6]Dimuro G,Bedregal B.On residual implications derived from overlap functions[J].Information Sciences,2015,312:78-88.
[7]Liu Huawen.Semi-uninorms and implications on a complete lattice[J].Fuzzy Sets and Systems,2012,191:72-82.
[8]Liu Huawen.Two classes of pseudo-triangular norms and fuzzy implications[J].Computers and Mathematics with Applications,2011,61:783-789.
[9]Baczynski M,Jayaram B.(U,N)-implications and their characterizations[J].Fuzzy Sets and Systems,2009,160:2049-2062.
[10]Dimuro G,Bedregal B,Santiago R.On(G,N)-implications derived from grouping functions[J].Information Sciences,2014,279:1-17.
[11]Mas M,Monserrat M,Torrens J.QL-implications versus D-implications[J].Kybernetika,2006,42:351-366.
[12]Yager R.On some new class of fuzzy operators and their role in approximate reasoning[J].Information Sciences,2004,167:193-216.
[13]Massanet S,Torrent J.On a new of fuzzy implication:h-implications and generalizations[J].Information Sciences,2001,181:2111-2127.
[14]Zhang Fengxia,Liu Huawen.On a new class of implications:(g,u)-implications and the distributive equations[J].International Journal of Approximate Reasoning,2013,54:1049-1065.
[15]Aguilo I,Suner J,Torrens J.A new look on fuzzy implication functions:FNI-implications[C]//International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems,2016:375-386.
[16]Baczynski M,Grzegorzewski D,Mesiar R,et al.Fuzzy implications based on semicopulas[J].Fuzzy Sets and Systems,2017,323:138-151.
[17]Pradera A,Beliakov G,Bustince H,et al.A review of the relationships between implication,negation and aggregation functions from the point of view of material implication[J].Information Sciences,2016,329:357-380.
[18]Bustince H,Burillo P,Soria F.Automorphisms,negations and implication operators[J].Fuzzy Sets and Systems,2003,134(2):209-229.
[19]Klement E,Mesiar R,Pop E.Triangular norms[M].Dordrecht:Kluwer Academic Publishers,2000.
[20]Bustince H,Fermandez J,Mesiar R,et al.Overlap functions[J].Nonlinear Analysis,2010,72(3/4):1488-1499.
[21]Bustince H,Pagola M,Mesiar R,et al.Grouping,overlaps,and generalized bientropic functions for fuzzy modeling of pairwise comparisons[J].IEEE Transactions on Fuzzy Systems,2012,20(3):405-415.
[22]Bedregal B,Dimuro G,Reiser R.New results on overlap and grouping functions[J].Information Sciences,2013,249:148-170.
[23]Balasubram J,Rao C.On the distributivity of implication operators over T-and S-norms[J].IEEE Transactions on Fuzzy Systems,2004,12(2):194-198.
[24]Qiao Junsheng,Hu Baoqing.The distributive laws of fuzzy implications over overlap and grouping functions[J].Information Sciences,2018,438:107-126.
[25]Zadeh L.Outline of a new approach to the analysis of complex system and decision processes[J].IEEE Transactions on Fuzzy Systems,1973,3:28-44.
[2]李永明.模糊系统分析[M].北京:科学出版社,2005.
[3]Butnariu D,Klement E.Triangular norm-based measures and games with fuzzy coalitions[M].London:Kluwer Academic Publishers,1993.
[4]Baczynski M,Jayaram B.(S,N)-and R-implications:a state-of-the-art survey[J].Fuzzy Sets and Systems,2008,159:1836-1859.
[5]Baczynski M,Jayaram B.Fuzzy implications[M].Berlin:Spring,2008.
[6]Dimuro G,Bedregal B.On residual implications derived from overlap functions[J].Information Sciences,2015,312:78-88.
[7]Liu Huawen.Semi-uninorms and implications on a complete lattice[J].Fuzzy Sets and Systems,2012,191:72-82.
[8]Liu Huawen.Two classes of pseudo-triangular norms and fuzzy implications[J].Computers and Mathematics with Applications,2011,61:783-789.
[9]Baczynski M,Jayaram B.(U,N)-implications and their characterizations[J].Fuzzy Sets and Systems,2009,160:2049-2062.
[10]Dimuro G,Bedregal B,Santiago R.On(G,N)-implications derived from grouping functions[J].Information Sciences,2014,279:1-17.
[11]Mas M,Monserrat M,Torrens J.QL-implications versus D-implications[J].Kybernetika,2006,42:351-366.
[12]Yager R.On some new class of fuzzy operators and their role in approximate reasoning[J].Information Sciences,2004,167:193-216.
[13]Massanet S,Torrent J.On a new of fuzzy implication:h-implications and generalizations[J].Information Sciences,2001,181:2111-2127.
[14]Zhang Fengxia,Liu Huawen.On a new class of implications:(g,u)-implications and the distributive equations[J].International Journal of Approximate Reasoning,2013,54:1049-1065.
[15]Aguilo I,Suner J,Torrens J.A new look on fuzzy implication functions:FNI-implications[C]//International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems,2016:375-386.
[16]Baczynski M,Grzegorzewski D,Mesiar R,et al.Fuzzy implications based on semicopulas[J].Fuzzy Sets and Systems,2017,323:138-151.
[17]Pradera A,Beliakov G,Bustince H,et al.A review of the relationships between implication,negation and aggregation functions from the point of view of material implication[J].Information Sciences,2016,329:357-380.
[18]Bustince H,Burillo P,Soria F.Automorphisms,negations and implication operators[J].Fuzzy Sets and Systems,2003,134(2):209-229.
[19]Klement E,Mesiar R,Pop E.Triangular norms[M].Dordrecht:Kluwer Academic Publishers,2000.
[20]Bustince H,Fermandez J,Mesiar R,et al.Overlap functions[J].Nonlinear Analysis,2010,72(3/4):1488-1499.
[21]Bustince H,Pagola M,Mesiar R,et al.Grouping,overlaps,and generalized bientropic functions for fuzzy modeling of pairwise comparisons[J].IEEE Transactions on Fuzzy Systems,2012,20(3):405-415.
[22]Bedregal B,Dimuro G,Reiser R.New results on overlap and grouping functions[J].Information Sciences,2013,249:148-170.
[23]Balasubram J,Rao C.On the distributivity of implication operators over T-and S-norms[J].IEEE Transactions on Fuzzy Systems,2004,12(2):194-198.
[24]Qiao Junsheng,Hu Baoqing.The distributive laws of fuzzy implications over overlap and grouping functions[J].Information Sciences,2018,438:107-126.
[25]Zadeh L.Outline of a new approach to the analysis of complex system and decision processes[J].IEEE Transactions on Fuzzy Systems,1973,3:28-44.