Analysis of the law of non-contradiction using additive generators

摘要

Reflexivity of some fuzzy similarity indexes drives the search for conditions that will ensure a t-norm satisfying the law of non-contradiction. These conditions are established by relating the additive generator of the t-norm to the additive generator of the Lukasiewicz t-norm. Theoretical results are checked against a long list of known t-norms. From an analytical argument, we are able to generate a new t-norm, which can be generalized in a natural way, fulfilling the law of non-contradiction. Finally, we apply this procedure to calculate fuzzy similarity matrices in the context of the Fuzzy Feature Contrast Model.