Isotopic Properties of Neutrosophic Soft Quasigroup and Its  Application in Decision-making

Benard Osoba; Oyebo Tunde Yakub; Abdulkareem Abdulafeez Olalekan; Oyewole Oluwapamilerin; Adenibuyan Micheal Tokunbo; Oluwatobi Balogun; Adekola Lanrewaju Olumide

Authors

Benard Osoba Bells University of Technology, Ota
Oyebo Tunde Yakub Department of Mathematics, Lagos State University Ojo, 102101 Nigeria ;
Abdulkareem Abdulafeez Olalekan Department of Mathematics, Lagos State University Ojo, 102101 Nigeria ;
Oyewole Oluwapamilerin Bells University of Technology, Ota ;
Adenibuyan Micheal Tokunbo Bells University of Technology, Ota ;
Oluwatobi Balogun Bells University of Technology, Ota
Adekola Lanrewaju Olumide Bells University of Technology, Ota

Keywords:

Isotopism; homomorphism; Isomorphism; Soft set; Neutrosophic set; Quasigroup

Abstract

A Q-neutrosophic soft quasigroup (ϕQ,A) represents a novel mathematical framework designed
to address scenarios characterized by indeterminate occurrences. This paper seeks to extend the classical
examination of quasigroups to include Q-neutrosophic soft quasigroups. It provides a thorough investigation into
isotopism, homomorphism, isomorphism, and the direct product concerning the hybrid concept of neutrosophic
soft sets under a non-associative structure. This research expands the concept of the Q-set to a groupoid, which
facilitates the development of an algorithm for Q-neutrosophic soft quasigroups. The de nitions of isotopism
and homomorphism for Q-neutrosophic soft quasigroups are introduced, revealing that every isotope of a Q
neutrosophic soft quasigroup is indeed a Q-neutrosophic soft quasigroup. Furthermore, it is established that the
homomorphic image of a Q-neutrosophic soft quasigroup under a quasigroup is not necessarily a Q-neutrosophic
soft quasigroup. The ndings indicate that the direct product of any two Q-neutrosophic soft quasigroups is
also a Q-neutrosophic soft quasigroup. Generalized properties regarding the direct product of Q-neutrosophic
soft quasigroups of order n have been established. Additionally, the study presents the necessary and su cient
conditions under which the direct product of two Q-neutrosophic soft subquasigroups, ψQ(a)×ψQ(b), contains at
least one Q-neutrosophic soft subquasigroup, πQ(c), that is isomorphic to the Q-neutrosophic soft subquasigroup
πQ(a). Speci cally, ψQ(a) ∼
=πQ(c) ≤ ψQ(a)×ψQ(b) if and only if a homomorphism exists from ψQ(a) to ψQ(b).
To validate some of these results, examples have been constructed, and a practical application utilizing real-life
data has been demonstrated