ON GRADED FUZZY 1-ABSORBING PRIMARY HYPERIDEALS

Abstract

Let G be a group with identity e and R be a graded commutative multiplicative hyperring. In this article, we aim to introduce the concepts of graded fuzzy radical of a graded fuzzy hyperideal and graded fuzzy primary hyperideals of a graded hyperring. Also, we introduce and study the notion of graded fuzzy 1-absorbing primary hyperideals of R as a generalization of graded fuzzy primary hyperideals. Many properties and characterizations of graded fuzzy 1-absorbing primary hyperideals of R are stated. Moreover, we investigate the notions of graded fuzzy strongly 1-absorbing primary hyperideals, graded fuzzy weakly completely primary hyperideals and graded fuzzy weakly completely 1-absorbing primary hyperideals. We obtain some basic properties and new results of these cases of structures.