Fuzzy Sets T-Norm T-Conorm Strong Fuzzy Negations Contradiction Measures of Contradiction Fuzzy Relation Compositional Rule of Inference
Institute of Information Theories and Applications FOI ITHEA
Trillas et al. introduced in  and  the concepts of both self-contradictory fuzzy set and contradiction
between two fuzzy sets. Later, in  and  the necessity of determine not only the contradiction, but also the
degree in that this property occurs, was considered. This paper takes up again these subjects, and firstly we
study if there exists some connection between the two first notions. After that, taking into account that self-
contradiction of a fuzzy set could be understood as the contradiction with itself, and starting from the degrees of
contradiction between two fuzzy sets proposed in , we obtain degrees of self-contradiction. Finally,
preservation of some intuitive properties both in the use of connectives and in the obtaining of new knowledge
throughout compositional rule of inference, are tested.
* This work is partially supported by CICYT (Spain) under project TIN 2005-08943-C02-001 and by UPM-CAM (Spain) under project R05/11240.