Uninorms and Nullnorms and their Idempotent Versions on Bounded Posets

Abstract

The paper deals with uninorms and nullnorms as basic operations which are associative, commutative and monotone (increasing). These operations were first introduced on the unit interval and later generalized to bounded lattices. In this contribution we show how it is possible to generalize them to bounded posets. We will study their existence, property and conditions under which it is possible to construct their idempotent versions, since these are the most important operations from the point of view of possible applications.