Pseudo-uninorms and Atanassov’s intuitionistic pseudo-uninorms

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Abstract

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.

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