A weakening of Schur-concavity for copulas
Fuzzy Sets and Systems
Aggregation of ordinal information
Fuzzy Optimization and Decision Making
(U,N)-implications and their characterizations
Fuzzy Sets and Systems
A non-associative generalization of Hájek's BL-algebras
Fuzzy Sets and Systems
Joint cumulative distribution functions for Dempster---Shafer belief structures using copulas
Fuzzy Optimization and Decision Making
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Two related aggregation operators called copulas and co-copulas are introduced and various properties are described. The relationship, of these operators to t-norms and t-conorms is noted. Generalizations of these, respectively, called conjunctors and disjunctors, are introduced. We suggest the use of disjunctor operators for modeling the multi-valued implication operator in fuzzy logic. We point out that the selection of operators used in fuzzy logic, in addition to having appropriate pointwise properties, should be holistic, this requires consideration of the nature of the resulting fuzzy set as a whole. Focusing on the protoform of fuzzy modus ponens and looking at the information contained in the inferred fuzzy set we show that the use of co-copulas has some desirable properties. Taking advantage of the fact that the weighted sum of co-copulas is a co-copula we consider the problem of constructing customized implication operators.