On Intuitionistic Fuzzy Hyper GR-ideals in Hyper GR-algebras

Abstract

Let $P(H)$ be the power set of $H$. Consider $\text{ds}{P}^{\ast }(H)=P(H)\setminus \{\varphi \}$. A hyperoperation on a nonempty set $H$ is a function $\text{ds}⊛:H\times H\to P^{\ast }(H).$ A set $H$ endowed with a family $\mathrm{\Gamma }$ of hyperoperations is called a
hyperstructure. Hyperstructures have many applications to several sectors of both pure and applied sciences. One of the well developed hyperstructures is the hyper BCI-algebra. Recently, by following this hyperstructure, a new hyperstructure was created by Indangan et al., named as hyper GR-algebras. In this paper, fuzzy set and intuitionistic fuzzy set are applied to hyper GR-algebra. Particularly, the fuzzy hyper GR-ideal of type 1 and the intuitionistic fuzzy hyper GR-ideal are introduced, and a relationship between them are obtained. Moreover, some of their characterizations are established by the use of their level subsets.