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

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 IS, N and IS, 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 Ns together with the families of t-subnorms and t-subconorms by considering the product t-norm Tp as well as the algebraic sum Sp, respectively. As the main results, the family of subimplications and extends the corresponding classes of implicators by preserving their properties, discussing dual and conjugate constructions.

Keywords:
median aggregation; t-sub(co)norms; fuzzy (sub)implications; QL-implications; (S, N)-implications