Constructing non-functionally expressible fuzzy implications

Abstract

This article discusses a new method for the construction of non-functionally expressible fuzzy implications. In a recent work, we have considered non-functionally expressible fuzzy implications from an implication function acting on the inputs followed by an aggregation process. Now, we first perform an aggregation of the inputs and then an implication function between the aggregated values. The main part is devoted to analyse under which conditions the two construction processes coincide.

The ⊛-composition of fuzzy implications: Closures with respect to properties, powers and families

“…By constructive methods, we refer to those methods that somehow depend on the underlying geometry to construct a fuzzy implication from a pair of fuzzy implications, often by specifying the values over different sub-regions of [0, 1] 2 . For instance, the threshold and vertical threshold generation methods of Massanet and Torrens [32,37,39,40] fall under this category.…”