Aggregating fuzzy implications

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

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