Solutions of equation I(x, y) = I(x, I(x, y)) for implications derived from uninorms

Authors:
Sebastia Massanet;Joan Torrens
Affiliations:
Department of Mathematics and Computer Science, University of the Balearic Islands, Palma de Mallorca, Spain;Department of Mathematics and Computer Science, University of the Balearic Islands, Palma de Mallorca, Spain
Venue:
WILF'11 Proceedings of the 9th international conference on Fuzzy logic and applications
Year:
2011

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Abstract

Uninorms are one of the most studied classes of aggregation functions and with more applications in the field of the aggregation of information. Their conjunctive or disjunctive behaviour is essential for their use as logical connectives and for obtaining fuzzy implications derived from uninorms. In this communication, we want to analyse which fuzzy implications derived from uninorms satisfy the iterative equation I(x, y) = I(x, I(x, y)). This equation comes from p → q ≡ p → (p → q), a tautology in classical logic, and it is related with the law of importation respect to the minimum I(min{x, y}, z) = I(x, I(y, z)).