Regular and strongly soft $Gamma$- relations on fuzzy soft $Gamma$-hyperrings

Abstract

The concept of fuzzy soft $Gamma$-hyperrings introduced by J. Zhan et al. as a generalization of the soft rings. In this paper, we prove the equivalence relation $mu^{ast}$ defined by J. Zhan et al. is a strongly soft $Gamma$-regular relation and hyperoperations defined on quotient fuzzy soft $Gamma$-hyperrings are just operations. Also, we define the equivalence relation $mu^{ast}_I$ as a generalization the relation $mu^{ast}$ and consider quotient fuzzy soft $Gamma$-hyperrings and isomorphism theorems by this<br />regular relation.