New approaches on some fuzzy algebraic structures

Abstract

Starting from the study of the papers [1, 14], we have seen that we can change some concepts and give some new definitions on fuzzy algebraic structures. Our goal by introducing these definitions is to get the classical and well known ones when the fuzzy set is just the characteristic function. As a second purpose we were tempted to generalize as long as it is possible some results known in the classical set theory. We get many interesting results which concern fuzzy relations, fuzzy subgroups of a given group, fuzzy ideals of a ring. We also define ideal generated by an element in the commutative case, prime and maximal ideals. Some relationships have been made and many other still open and which will be of our interest in next studies.