Investigation of the De Morgan identities in fuzzy set theory

Abstract

In this paper we formulate and prove statements about the fulfillment of the fuzzy generalization of the De Morgan identities in cases of different t -norms, t-conorms and negations. In the proofs of the statements implicitly we propose methods to give uncountable infinitely many other norms and negations for a given norm, for which the triplets fulfill: none of identities, the exactly one of them or both of them.