Characterizations of Semihyperrings by Their (∈γ,∈γ∨qδ)-Fuzzy Hyperideals

Abstract

The concepts of (${\in }_{\gamma },{\in }_{\gamma }\vee q_{\delta }$)-fuzzy bi-hyperideals and (${\in }_{\gamma },{\in }_{\gamma }\vee q_{\delta }$)-fuzzy quasi-hyperideals of a semihyperring are introduced, and some related properties of such (${\in }_{\gamma },{\in }_{\gamma }\vee q_{\delta }$)-fuzzy hyperideals are investigated. In particular, the notions of hyperregular semihyperrings and left duo semihyperrings are given, and their characterizations in terms of hyperideals and (${\in }_{\gamma },{\in }_{\gamma }\vee q_{\delta }$)-fuzzy hyperideals are studied.