Element-Based Construction Methods for Uninorms on Bounded Lattices

Uninorms are aggregation operators that generalize the t-norms (t-conorms), which are extensions of the logical connectives boolean AND(boolean OR) to the fuzzy set theory. The methods of constructing uninorms on more general algebraic structures (such as bounded posets, lattices, etc.) are an important subject of study, including an extensive work concerning these operations on the unit real interval [0, 1]. The construction of uninorms on bounded lattices has been extensively studied using various aggregation functions, such as t-norms, t-conorms, and t-subnorms. In this paper, we present construction methods for uninorms, based on the elements of a lattice, without using the existence of the mentioned operators. We determine the necessary and sufficient conditions for the introduced construction methods to result in the uninorms. Then, we show the differences between our methods and several methods known from the literature, including some illustrative examples.