Measuring Contradiction between two AIFS

This paper is devoted to introduce an axiomatic model to distinguish what functions are suitable for measuring the degree of contradiction between two Atanassov's intuitionistic fuzzy sets. After stating the needed background, in section 2, we justify and present the axioms that a contradiction measure must satisfy, and the first examples are set out. After motivating the necessity of achieving some definition for modelling the continuity, in the next section we introduce the concepts of semicontinuity from below and semicontinuity from above for contradiction measures. Finally, in section 4, some families of contradiction measures are constructed

On the incompatibility between two AIFS

The purpose of this paper is to commence studying the incompatibility in the Atanassov's intuitionistic fuzzy sets framework. In order to do this, firstly we deal with the concept of T -incompatible sets, where T is an intuitionistic t- norm, relating it with the N-contradictory sets, where N is a intuitionistic fuzzy negation. Next, an axiomatic model for measuring T -incompatibility is introduced, and finally some methods for obtaining families of such measures are provided

Some geometrical methods for constructing contradiction measures on Atanassov's intuitionistic fuzzy sets

Trillas et al. (1999, Soft computing, 3 (4), 197–199) and Trillas and Cubillo (1999, On non-contradictory input/output couples in Zadeh's CRI proceeding, 28–32) introduced the study of contradiction in the framework of fuzzy logic because of the significance of avoiding contradictory outputs in inference processes. Later, the study of contradiction in the framework of Atanassov's intuitionistic fuzzy sets (A-IFSs) was initiated by Cubillo and Castiñeira (2004, Contradiction in intuitionistic fuzzy sets proceeding, 2180–2186). The axiomatic definition of contradiction measure was stated in Castiñeira and Cubillo (2009, International journal of intelligent systems, 24, 863–888). Likewise, the concept of continuity of these measures was formalized through several axioms. To be precise, they defined continuity when the sets ‘are increasing’, denominated continuity from below, and continuity when the sets ‘are decreasing’, or continuity from above. The aim of this paper is to provide some geometrical construction methods for obtaining contradiction measures in the framework of A-IFSs and to study what continuity properties these measures satisfy. Furthermore, we show the geometrical interpretations motivating the measures