New structures for uninorms on bounded lattices

TL;DR

This paper introduces new methods for constructing uninorms on bounded lattices, establishing necessary and sufficient conditions, and providing iterative constructions based on t-norms and t-conorms.

Contribution

It presents novel construction techniques for uninorms on bounded lattices, including necessary and sufficient constraints, and iterative methods based on t-norms and t-conorms.

Findings

New construction methods for uninorms on bounded lattices.

Necessary and sufficient conditions for constraints on uninorms.

Iterative constructions based on t-norms and t-conorms.

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.