Abstract: 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 selfcontradiction 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.

Keywords: fuzzy sets, t-norm, t-conorm, strong fuzzy negations, contradiction, measures of contradiction, fuzzy relation, compositional rule of inference.

ACM Classification Keywords: F.4.1 Mathematical Logic and Formal Languages: Mathematical Logic (Model theory, Set theory); I.2.3 Artificial Intelligence: Deduction and Theorem Proving (Uncertainty, “fuzzy” and probabilistic reasoning); I.2.4 Artificial Intelligence: Knowledge Representation Formalisms and Methods (Predicate logic, Representation languages).

Link:

CONTRADICTION VERSUS SELFCONTRADICTION IN FUZZY LOGIC*

Carmen Torres, Susana Cubillo, Elena Castineira

http://www.foibg.com/ijita/vol14/ijita14-4-p05.pdf