Soft Neutrosophic Quasigroups

Abstract

This paper introduced and studied for the first time the object of neutrosophic quasigroup Q(Q,·) over a quasigroup (Q, ·). It was shown that the direct product of any two neutrosophic quasigroups is a neutrosophic quasigroup. Also, it was established that the holomorph of any neutrosophic quasigroup is a neutrosophic quasigroup. The soft set theory which Molodtsov innovated is a potent mathematical tool used for solving mathematical problems with uncertainties and things that are not clearly defined. We broaden soft set theory by introducing soft neutrosophic quasigroup (NF , A)Q(Q,·) over a neutrosophic quasigroup Q(Q,·). We introduced and established the order of a finite soft neutrosophic quasigroup with varied mathematical inequality expressions which exist between the order of a finite neutrosophic quasigroup and that of its soft neutrosophic quasigroup.

Keywords

• soft set
• neutrosophic set
• quasigroup
• neutrosophic quasigroup
• neutrosophic subquasigroup
• soft neutrosophic quasigroup
• soft neutrosophic subquasigroup