Aggregating fuzzy implications

The aim of this work is to study the IAIA fuzzy implication obtained by composition of an aggregation function A   and a family II 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 IAIA fuzzy implication can be preserved by action of an order automorphism. Finally, we introduce the family of IAIA 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.