Aggregating Fuzzy QL- and (S,N)-Subimplications: Conjugate and Dual Constructions

Abstract

ABSTRACT. (S,N)-and QL-subimplications can be obtained by a distributive n-ary aggregation performed over the families T of t-subnorms and S of t-subconorms along with a fuzzy negation. Since these classes of subimplications are explicitly represented by t-subconorms and t-subnorms verifying the generalized associativity, the corresponding (S,N)-and QL-subimplicators, referred as I S,N and I S,T,N , are characterized as distributive n-ary aggregation together with related generalizations as the exchange and neutrality principles. Moreover, the classes of (S,N)-and QL-subimplicators are obtained by the median operation performed over the standard negation N S together with the families of t-subnorms and t-subconorms by considering the product t-norm T P as well as the algebraic sum S P , respectively. As the main results, the family of subimplications I S P ,N and I S P ,T P ,N extends the corresponding classes of implicators by preserving their properties, discussing dual and conjugate constructions.