Measuring contradiction on A-IFS defined in finite universes
The work outlined here aims to build and examine contradiction measures on Atanassov intuitionistic fuzzy sets (A-IFS) that are defined in this particular case in finite universes. The axiomatic definition of contradiction measure in the A-IFS framework was given in [7]. A number of axioms formalizing the concept of continuity for the above measures were also given. In this paper, Section 1, which briefly discusses the preliminaries required to develop the work, is followed by a section analysing how the restriction of the universe of discourse to a finite set influences the continuity axioms. The following three sections look at three types of specific contradiction measures. In Section 3, continuous t-norms and fuzzy negations are used to construct a large family of measures. These measures satisfy different types of continuity, which are examined at length. Then, Sections 4 and 5 take up other families introduced in [8,10,9], proving that their behaviour with respect to continuity is better than it was in the earlier articles because the universes considered here are finite. (C) 2011 Elsevier B.V. All rights reserved.
contradiction measures t-norms fuzzy negations intuitionistic fuzzy negations contradictory sets contradictory intuitionistic fuzzy sets semicontinuous measures continuous measures