(2104-6613) Construction of 2-uninorms on bounded lattices

Abstract

Uninorms and nullnorms are special 2-uninorms. In this work, we construct 2-uninorms on bounded lattices. Let L be a bounded lattice with a nontrivial element d. Given two uninorms U1 and U2, defined on sublattices [0, d] and [d, 1], respectively, this paper presents two methods for constructing binary operators on L which extend both U1 and U2. We show that our  first construction is a 2-uninorm on L if and only if U2 is conjunctive and our second construction is a 2-uninorm on L if and only if U1 is disjunctive. Moreover, we prove that the two 2-uninorms are, respectively, the weakest and the strongest 2-uninorm among all 2-uninorms, the restrictions of which on [0, d]2 and [d, 1]2 are respectively U1 and U2.