Algebraic Properties of Quasigroup Under Q-neutrosophic Soft Set.

The novel concept called neutrosophic set was launched to take care of indeterminate factors in real-life data. The hybrid model of neutrosophic set and soft set has been widely studied in different areas of algebra, especially in associative structures such as fields, groups, rings, and modules. In this current paper, the novel concept is further introduce to a non-associative structure termed Q-neutrosophic soft quasigroup (Q-NSG) and investigate its different algebraic properties of the quasigroups. We shown the conditions for the sets of a-level cut of Q-NSG to be subquasigroups, the condition for each set of subquasigroups of a quasigroup to be Q-level cut neutrosophic soft subquasigroup were established. It was shown that Q-NSG obeys alternative property and flexible law. In addition, We defined Q-neutrosophic soft loop and investigate some of its characteristics. In particular, it was shown that Q-neutrosophic soft loop obeys inverse, weak inverse and cross inverse properties. We established the condition for a Q-neutrosophic soft loop to obey antiautomorphic inverse, semi-automorphic inverse and super anti-automorphic inverse properties. The necessary and sufficient condition for Q-neutrosophic soft set under a loop (G, ◦,/, \) to be a Q-neutrosophic soft loop was also established. [ABSTRACT FROM AUTHOR]