Intuitionistic fuzzy generators: application to intuitionistic fuzzy complementation
Fuzzy Sets and Systems
On the relationship between some extensions of fuzzy set theory
Fuzzy Sets and Systems - Theme: Basic notions
Case Generation Using Rough Sets with Fuzzy Representation
IEEE Transactions on Knowledge and Data Engineering
Soft data mining, computational theory of perceptions, and rough-fuzzy approach
Information Sciences: an International Journal - Special issue: Soft computing data mining
Information Sciences: an International Journal
Fuzzy rough set theory for the interval-valued fuzzy information systems
Information Sciences: an International Journal
Clustering algorithm for intuitionistic fuzzy sets
Information Sciences: an International Journal
On characterization of intuitionistic fuzzy rough sets based on intuitionistic fuzzy implicators
Information Sciences: an International Journal
Measures of self-contradiction on Atanassov's intuitionistic fuzzy sets: An axiomatic model
International Journal of Intelligent Systems
Information Sciences: an International Journal
General IF-sets with triangular norms and their applications to group decision making
Information Sciences: an International Journal
Type-2 Fuzzy Logic: A Historical View
IEEE Computational Intelligence Magazine
On the representation of intuitionistic fuzzy t-norms and t-conorms
IEEE Transactions on Fuzzy Systems
Editorial: Modelling uncertainty
Information Sciences: an International Journal
Hi-index | 0.07 |
The importance of dealing with contradictory information or of deriving contradictory consequences in inference processes justifies undertaking a theoretical study on the subject of contradiction. In [S. Cubillo, E. Castineira, Contradiction in intuitionistic fuzzy sets, in: Proceedings of the Conference IPMU'2004, Perugia, Italy, 2004, pp. 2180-2186] we defined contradictory and N-contradictory Atanassov intuitionistic sets, where we established that two sets A and B are N-contradictory, with respect to a given intuitionistic negation N, if A implies N(B), and are contradictory if they are N-contradictory for some negation N. The purpose of this article is to thoroughly examine the model for measuring contradiction between two Atanassov intuitionistic fuzzy sets irrespective of a fixed negation, proposed in [C. Torres-Blanc, E.E. Castineira, S. Cubillo, Measuring contradiction between two AIFS, in: Proceedings of the Eighth International FLINS Conference, Madrid, Spain, 2008, pp. 253-258], and also to introduce a mathematical model to measure N-contradiction between sets, where N is an intuitionistic negation. First, we justify and determine the minimum axioms that a function must satisfy to be able to be used as a measure of contradiction or a measure of N-contradiction. Also, we introduce some early examples of valid functions that conform to the model. Then, we establish the conditions for these measures to be continuous from below or continuous from above. Finally, we build families of contradiction and N-contradiction measures, establishing how they are relate to each other, and we look at how they behave with respect to continuity.