A generalization of a copula-based construction of fuzzy implications

In this paper we complement and generalize some constructions of fuzzy implications based on two arbitrary copulas, obtaining new fuzzy implications. By means of (restricted) aggregation functions acting on [0, 1]S, where S is a fixed finite or infinite set, and related S-systems of fuzzy implications and transforming functions, we introduce and discuss a rather general method for constructing fuzzy implications. Several examples illustrating our results are also included.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

In this paper, we propose new fuzzy implications by complementing and generalizing existing constructions based on two arbitrary copulas. We introduce a general method for constructing fuzzy implications using (restricted) aggregation functions on a fixed finite or infinite set S within the range of [0, 1], along with related S-systems of fuzzy implications and transforming functions. Several examples demonstrating our results are provided.