Contradiction versus Selfcontradiction in Fuzzy Logic

* This work is partially supported by CICYT (Spain) under project TIN 2005-08943-C02-001 and by UPM-CAM (Spain) under project R05/11240.

Trillas et al. introduced in [7] and [8] the concepts of both self-contradictory fuzzy set and contradiction between two fuzzy sets. Later, in [1] and [2] 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 [5], 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.