New structures for uninorms on bounded lattices

Abstract

In this article, we study new methods for constructing uninorms on bounded lattices. First, we present new methods for constructing uninorms on bounded lattices under the additional constraints and prove that some of these constraints are sufficient and necessary for the uninorms. Second, we show that the additional constraints on $t$-norms ($t$-conorms) and $t$-subnorms ($t$-subconorms) of some uninorms are exactly sufficient and necessary. At last, we give new constructions of uninorms on arbitrary bounded lattices by interation based on $t$-conorms and $t$-conorms.