Pseudo-uninorms and Atanassov’s intuitionistic pseudo-uninorms

Abstract

This paper considers the concept of pseudo-uninorm which is a natural generalization of the concept of pseudo t-norm for uninorms and presents the relationship between pseudo-uninorms on the unit interval and their natural extension according to Atanassov’s intuitionistic framework, showing how to obtain, in a canonical manner, Atanassov’s intuitionistic pseudo-uninorms from pseudo-uninorms. Moreover, we also show that the automorphisms on the unit interval and on L ^* (the intuitionistic valued lattice) are in one-to-one correspondence and how automorphisms on L ^* act on Atanassov’s intuitionistic pseudo-uninorms. It is also proved the commutation between the action of automorphisms and the canonical construction of pseudo-uninorms on L ^* commute. Moreover, we generalize the usual generation of fuzzy negations from t-norms in order to construct fuzzy negations from pseudo-uninorms and, subsequently, generalize this construction for L ^* and relate these two constructions. Finally, we use pseudo-uninorms to obtain a class of weighted average operator and applies it in multiple attribute group decisionmaking problems.