Let $G$ be a monoid with identity $e$. In this paper, first we introduce the notions of $G$-graded hyperrings, graded hyperideals and graded hyperfields in the sense of Krasner hyperring $R$. Also, we define the notion of a greded $R$-hypermodules and some examples are presented. Then we investigate graded maximal, graded prime and graded primary hyperideals of a graded hyperring $R$. Finally, ...

The relationship between the intuitionistic fuzzy sets and the algebraic hyperstructures is described in this paper. The concept of the quasi-coincidence of an intuitionistic fuzzy interval valued with an interval-valued intuitionistic fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of an intuitionistic fuzzy point in intuitionistic fuzzy sets. By using thi...

Let R be a Γ-hyperring and M be an Γ-hypermodule over R. We introduce and study fuzzy RΓ-hypermodules. Also, we associate a Γhypermodule to every fuzzy Γ-hypermodule and investigate its basic properties.

In this paper, we define the strongly compatible relation ε on the (m,n)ary hypermodule M, so that the quotient (M/ε∗, h/ε∗) is an (m,n)-ary module over the fundamental (m,n)-ary ring (R/Γ∗, f/Γ∗, g/Γ∗). Also, we determine a family P (M) of subsets of an (m,n)-ary hypermodule M and we give a sufficient condition such that the geometric space (M,P (M)) is strongly transitive. Mathematics Subject...

Abstract The article is motivated by the recently published studies on injective and projective hypermodules. We present here a new characterization of normal First we define concept zero-divisors over hypermodule based it introduce class hypermodules, one divisible After presenting some their fundamental properties, will show that R -hypermodules M coincide whenever hyperring with no . Finally...

In this paper we define and study a new class of subfuzzy hypermodules of a fuzzy hypermodule that we call normal subfuzzy hypermodules. The connection between hypermodules and fuzzy hypermodules can be used as a tool for proving results in fuzzy hypermodules. In this manner we analyse three isomorphism theorems for fuzzy hypermodules.

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The goal of this paper is to introduce a novel soft hyperstructure called multi-fuzzy hyperstructure. We investigate the notion hypermodules and some their structural properties are discussed. discuss behavior image inverse set under function. According Zadeh’s extension principle, we prove that further hypermodule.

The main purpose of this paper is to introduce the concept of general Γ-hypermodules as a generalization of Γ-hypermodules, as a generalization of Γ-modules and as a generalization of modules. Then we extended the isomorphism theorems to general Γhypermodules. Also, it is observer that if N is a normal Γ-subhypermodule of Γ-hypermodule M, then, [M : N∗] is an abelian group. Finally, we show tha...