Measuring contradiction regarding a negation on AIFS

Abstract

In, an axiomatic model for contradiction measures on Atanassov Intuitionistic fuzzy sets was presented; there, different kinds of those measures, depending on the continuity conditions required, were established. But in previous papers, not only the contradiction in general, but also the contradictions with respect to a given strong intuitionistic fuzzy negation were studied. This is due to the fact that in some applications, in order to fix a suitable model, not any negation is valid, but it is necessary to use a particular one. Thus, the problem of the axiomatization of the different types of contradiction measures regarding a given strong negation remained open. This is the main aim of the present work.