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

Document Type : Research Paper


1 Department of mathematics, University of Hormozgan, Hormozgan, Bandar abbas, Iran.

2 Department of Mathematics, Shahid Beheshti University, Tehran Iran



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
regular relation.


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