New construction methods for uninorms on bounded lattices

Abstract

After Kara ̧cal and Mesiar showed that uninorms exist on a bounded lattice [27], construction methods of uninorms on bounded lattices have been widely studied in which the existence of t-norms and t-conorms on sublattices of the bounded lattice L was generally exploited. In this paper, we introduce two new construction methods for uninorms on a bounded lattice L by exploiting the existence of a triangular norm T and triangular conorm S on a sublattice of L, where L \ {0, 1} has the bottom and the top elements. Then, we demonstrate that our new construction methods are also different from the existing construction methods in the literature. Additionally, some illustrative examples are provided. Finally, we generalize by induction our construction methods to a more general form.