On constructing the largest and smallest uninorms on bounded lattices

Abstract Uninorms on the unit interval are a common extension of triangular norms (t-norms) and triangular conorms (t-conorms). As important aggregation operators, uninorms play a very important role in fuzzy logic and expert systems. Recently, several researchers have studied constructions of uninorms on more general bounded lattices. In particular, Cayli (2019) gave two methods for constructing uninorms on a bounded lattice L with e ∈ L ∖ { 0 , 1 } , which is based on a t-norm T e on [ 0 , e ] and a t-conorms S e on [ e , 1 ] that satisfy strict boundary conditions. In this paper, we propose two new methods for constructing uninorms on bounded lattices. Our constructed uninorms are indeed the largest and the smallest among all uninorms on L that have the same restrictions T e and S e on [ 0 , e ] and, respectively, [ e , 1 ] . Moreover, our constructions does not require the boundary condition, and thus completely solved an open problem raised by Cayli.