Some Generalized Forms of Fuzzy Interval Valued Hyperideals in a Hyperring

Abstract

Some generalized forms of the hyperideals of a hyperring in the paper of Zhan et al. (2008) will be given. As a generalization of the interval valued $(\alpha ,\beta )$-fuzzy hyperideals of a hyperring with $\alpha ,\beta \in \{\in ,q,\in \wedge q,\in \vee q\}$ and $\alpha \ne \in \wedge q$, the notion of generalized interval valued $(\alpha ,\beta )$-fuzzy hyperideals of a hyperring is also introduced. Special attention is concentrated on the interval valued $({\in }_{\tilde{\gamma }},{\in }_{\tilde{\gamma }}\vee q_{\tilde{\delta }}\mathrm{})$-fuzzy hyperideals. As a consequence, some characterizations theorems of interval valued $({\in }_{\tilde{\gamma }},{\in }_{\tilde{\gamma }}\vee q_{\tilde{\delta }}\mathrm{})$-fuzzy hyperideals will be provided.