In this paper rst we dene the notions of positive implicativehyper MV -ideals of types 1,2,3 and 4 in hyper MV -algebras and we investigatethe relationship between of them . Then by some examples we show that thesenotions are not equivalent. Finally we give some relations between these notionsand the notions of (weak) hyper MV -ideals and (weak) hyper MV -deductivesystems of hyper MV -algebras.

In this paper we investgate some properties of fuzzy ideal extension of fuzzy ideal, fuzzy prime ideal, fuzzy semiprime ideal of a Γ−semiring. Among other results we have obtained a characterization of a prime ideal I of a Γ−semiring in terms of fuzzy ideal extension of its characteristic function λI . Mathematics Subject Classification[2000]:16Y60, 16Y99, 03E72

In this paper, T. K. Dutta`s and S. K. Sardar`s semiprime ideal of -rings as a fuzzy semiprime ideal of a -rings via its operator rings was defined. Some characterizations of fuzzy semiprime ideal of -rings was obtained. That is; a characterization prove of a fuzzy semiprime ideal, the relationship between fuzzy semiprime ideal and fuzzy prime ideal was obtained. If is fuzzy semiprime ideal of ...

The aim of this article is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of union-soft sets is introduced, and its application to BCK/BCI-algebras is considered. The notions of union-soft algebras, union-soft (commutative) ideals and closed union-soft ideals are int...

We introduce the notion of reset left regular decomposition of an ideal regular language and we prove that there is a one-to-one correspondence between these decompositions and strongly connected synchronizing automata. We show that each ideal regular language has at least a reset left regular decomposition. As a consequence each ideal regular language is the set of synchronizing words of some ...

In this paper, for a complete lattice L, we introduce interval-valued L-fuzzy ideal (prime ideal) of a near-ring which is an extended notion of fuzzy ideal (prime ideal) of a near-ring. Some characterization and properties are discussed.