Regular and strongly regular relations on soft hyperrings

Abstract

Soft set theory, introduced by Molodtsov, has been considered as an effective mathematical tool for modeling uncertainties, and soft hyperrings can be regarded as a generalization of soft rings. The motivation for such an investigation is to generalize the concept of quotient soft hyperrings and isomorphism theorems. Also, we consider when the fuzzy hyperideals of a soft hyperring are normal, then the equivalence relations defined by J. Wang et. al. on soft hyperrings are strongly regular. Moreover, the quotient soft hyperrings determined by this equivalence relation are soft rings.