Aggregating fuzzy implications
The aim of this work is to study the IA I A fuzzy implication obtained by composition of an aggregation function A  and a family I I of fuzzy implications. Thus, it discusses under which conditions such functions preserve the main properties of fuzzy implications. In addition, by aggregating conjugate fuzzy implications it is shown that an IA I A fuzzy implication can be preserved by action of an order automorphism. Finally, we introduce the family of IA I A fuzzy implications obtained by taking the extended classes of (S,N)-implications which are given by t-subconorms and of R-implications underlying left continuous t-subnorms. Their dual construction is also considered.
fuzzy implication aggregation function (s n)-implication r-implication fuzzy connectives