Representable Implications via Overlap and Grouping Functions

• Cecilia Botelho Federal University of Pelotas (UFPel) http://orcid.org/0000-0002-2167-7139
• Alessandra Galvão Federal University of Pelotas (UFPel)
• Adenauer Yamin Federal University of Pelotas (UFPel) http://orcid.org/0000-0002-7333-244X
• Helida Santos Federal University of Rio Grande (FURG) http://orcid.org/0000-0003-2994-2862
• Renata Reiser Federal University of Pelotas (UFPel) http://orcid.org/0000-0001-9934-3115

DOI: https://doi.org/10.5753/weit.2021.18927

Abstract

QL- and D-implications are usually generated by strong negations together with t-norms and t-conorms, which are restrictive, as they demand properties such as associativity and the neutral element. In order to simplify and provide more flexibility in the conditions defining constructive methods to generate such implications, we consider dual aggregations as overlap and grouping functions. Some examples illustrate the proposal methods.

Keywords: Aggregate function, Overlap functions, Grouping functions, Fuzzy implications, QL-implications, D-implications

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