Distributivity equation in the class of 2-uninorms

Abstract

This paper is mainly devoted to solving the functional equation of distributivity between aggregation operators with 2-neutral element. Our investigations are motivated by the couple of distributive logical connectives and their generalizations used in fuzzy set theory e.g., triangular norms, conorms, uninorms, nullnorms and implications. One of the recent generalizations covering both uninorms and nullnorms are 2-uninorms, which form a class of commutative, associative and increasing operators on the unit interval with an absorbing element separating two subintervals having their own neutral elements. In this work the distributivity of two binary operators from the class of 2-uninorms is considered. In particular, all possible solutions of the distributivity equation for the three defined subclasses of these operators depending on the position of its zero and neutral elements are characterized.