On k-Regularities in Fuzzy Semihyperrings

Abstract

We introduce the notion of interval-valued (i.v.) fuzzy k-quasi ideals and i.v. fuzzy k-bi-ideals of a semihyperring and deduce certain characterizations for k-regularities in semihyperring by using these i.v. fuzzy k-hyperideals. Finally, our goal is to establish a relation between different types of k-hyperideals of a semihyperring and i.v. fuzzy k-hyperideals of the associated i.v. fuzzy semihyperring and also to find out the relation between k-regularity, k-intra-regularity of semihyperring and the associated i.v. fuzzy semihyperring.