Distributivity between extended nullnorms and uninorms on fuzzy truth values

TL;DR

This paper explores the distributive properties between extended nullnorms and uninorms on fuzzy truth values, focusing on conditions where nullnorms are conditionally distributive over uninorms, and presents related distributive laws.

Contribution

It introduces new distributive laws between extended nullnorms and uninorms, including generalizations, under specific conditions, advancing the theoretical understanding of fuzzy logic operators.

Findings

Distributive laws between extended nullnorms and t-conorms established.

Left and right distributive laws for generalized nullnorms and uninorms derived.

Conditions for conditional distributivity of nullnorms over uninorms identified.

Abstract

This paper mainly investigates the distributive laws between extended nullnorms and uninorms on fuzzy truth values under the condition that the nullnorm is conditionally distributive over the uninorm. It presents the distributive laws between the extended nullnorm and t-conorm, and the left and right distributive laws between the extended generalization nullnorm and uninorm, where a generalization nullnorm is an operator from the class of aggregation operators with absorbing element that generalizes a nullnorm.