A new look on the ordinal sum of fuzzy implication functions

Abstract

Fuzzy implication functions are logical connectives commonly used to model fuzzy conditional and consequently they are essential in fuzzy logic and approximate reasoning. From the theoretical point of view, the study of how to construct new implication functions from old ones is one of the most important topics in this field. In this paper new ordinal sum construction methods of implication functions based on fuzzy negations N are presented. Some general properties are analysed and particular cases when the considered fuzzy negation is the classical one or any strong negation are highlighted.