Algebraic Properties of Quasigroup Under Q−neutrosophic Soft Set

Abstract

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−NSˆ G) and investigate its different algebraic properties of the quasigroups. We shown the conditions for
the sets of α−level cut of Q−NSˆG 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−NSˆG
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 ( ˆ G, ◦, /, \) to be a Q−neutrosophic soft loop
was also established.

DOI: 10.5281/zenodo.10674590