Neutrosophic Sets and Systems
Abstract
The novel concept called neutrosophic set w a s 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 ˆ (Q−NSG) and investigate its different algebraic properties of the quasigroups. W e shown the conditions for the sets of α−level cut of Q−NSG to be subquasigroups, the condition for each set of subquasigroups of a ˆ quasigroup to beQ−level cut neutrosophic soft subquasigroup were established. It w a s shown that Q−NSG ˆ obeys alternative property and flexible law. In addition, W e defined Q−neutrosophic soft loop and investigate some of its characteristics. In particular, it w a s shown that Q−neutrosophic soft loop obeys inverse, weak inverse and cross inverse properties. W e established the condition for a Q−neutrosophic soft loop to obey anti automorphic inverse, semi-automorphic inverse and super anti-automorphic inverse properties. The necessary ˆ and sufficient condition for Q−neutrosophic soft set under a loop (G,◦,/,\) to bea Q−neutrosophic soft loop w a s also established.
Recommended Citation
Osoba, Benard; Oyebo Tunde Yakub; and Abdulkareem Abdulafeez Olalekan. "Algebraic Properties of Quasigroup Under Q−neutrosophic Soft Set." Neutrosophic Sets and Systems 64, 1 (2024). https://digitalrepository.unm.edu/nss_journal/vol64/iss1/1
