Self-dual pseudo-uninorms

Uninorms are a common generalization of t-norms and t-conorms, which are mutually dual aggregation functions. However, no uninorm is self-dual. In this paper, we show that dropping the axiom of commutativity allows a construction for self-dual pseudo-uninorms. We characterize three important classes of self-dual pseudo-uninorms, namely the representable pseudo-uninorms, pseudo-uninorms with all elements idempotent and those pseudo-uninorms that have both underlying functions continuous. Finally, it is proven that each self-dual pseudo-uninorm has continuous underlying functions. Note such a slight change has only a little effect on the continuity and commutativity of the pseudo-uninorm.

کلیدواژه ها:

Pseudo-uninorm ، uninorm ، Self-duality ، Semigroup ، Strong negation