In the present article we study the generalized laws of importation and crossmigrativity based on(D,N)-implications.On the one hand,we consider the generalized law of importation I(T(x,α),y)=I(x,J(α,y)),when T is co...In the present article we study the generalized laws of importation and crossmigrativity based on(D,N)-implications.On the one hand,we consider the generalized law of importation I(T(x,α),y)=I(x,J(α,y)),when T is concretized as a fuzzy conjunction C,I and J are concretized as(D,N)-implications generated by a fuzzy disjunction D and a fuzzy negation N.On the other hand,we discuss the cross-migrativity of fuzzy disjunctions over fuzzy implications,that is,I(x,D(y,z))=D(y,I(x,z)),where I is a fuzzy implication,D is a fuzzy disjunction.In addition,we study the relationship between the(α-)cross-migrative of(I,D)and the(α-)cross-law of importation(I,ID,N,C).展开更多
The cross-migrativity can be regarded as the weaker form of the commuting equation, which plays a crucial part in the framework of fuzzy connectives. This paper studies the cross-migrativity of continuous t-conorms ov...The cross-migrativity can be regarded as the weaker form of the commuting equation, which plays a crucial part in the framework of fuzzy connectives. This paper studies the cross-migrativity of continuous t-conorms over Ihimplications. We obtain full characterizations for the cross-migrativity of continuous t-conorms over Ihimplications.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.12471438,12001413)the Natural Science Basic Research Plan Project of Shaanxi Province(Grant No.2022JM-048)the Shaanxi Fundamental Science Research Project for Mathematics and Physics(Grant No.23JSQ043)。
文摘In the present article we study the generalized laws of importation and crossmigrativity based on(D,N)-implications.On the one hand,we consider the generalized law of importation I(T(x,α),y)=I(x,J(α,y)),when T is concretized as a fuzzy conjunction C,I and J are concretized as(D,N)-implications generated by a fuzzy disjunction D and a fuzzy negation N.On the other hand,we discuss the cross-migrativity of fuzzy disjunctions over fuzzy implications,that is,I(x,D(y,z))=D(y,I(x,z)),where I is a fuzzy implication,D is a fuzzy disjunction.In addition,we study the relationship between the(α-)cross-migrative of(I,D)and the(α-)cross-law of importation(I,ID,N,C).
文摘The cross-migrativity can be regarded as the weaker form of the commuting equation, which plays a crucial part in the framework of fuzzy connectives. This paper studies the cross-migrativity of continuous t-conorms over Ihimplications. We obtain full characterizations for the cross-migrativity of continuous t-conorms over Ihimplications.
