Aggregating Fuzzy QL-Implications

This paper presents the fuzzy (S, N- and QL- subimplication classes, which is obtained by a distributive n-ary aggregation operation performed over the families T of t-subnorms and S t-subconorms along with a fuzzy negation. Since these classes of sub implications are explicitly represented by t-subconorms and t-subnorms which are characterized by generalized associativity, the corresponding (S, N)-and QL-sub implications referred as IS, N and IS, T, N, are characterized by distributive n-ary aggregation together with related generalizations as the exchange and neutrality principles. Additionally, we discuss two subclasses of (S, N)-and QL-sub implication classes, which are obtained by the median aggregation operation performed over the standard negation Ns together with the families of TP and SP of t-subnorms and t-subconorms, respectively. In particular, the subclass TP extends the product t-norm TP as well as SP extends the algebraic sum SP. As the main results, the family of sub implications ISP, N and ISP, TP, N extends the implication by preserving the corresponding properties.