A Study of Q-Neutrosophic Soft Quasigroups and Their Application to Medical Decisions

Benard Osoba; Temıtope Gbolahan Jaıyeola; Yakub Tunde Oyebo; Oluwatobi Balogun; Oluwasayo Peter Abodunrin; Oludare Johnson Olaleye

Authors

Benard Osoba Department of Physical Sciences, Bells University of Technology, Ota, Ogun State, Nigeria;
Temıtope Gbolahan Jaıyeola Department of Mathematics Obafemi Awolowo University, Ile Ife 220005, Nigeria; Department of Mathematics University of Lagos, Akoka, Nigeria;
Yakub Tunde Oyebo Department of Mathematics, Lagos State University, Ojo, Lagos State, Nigeria ;
Oluwatobi Balogun Department of Physical Sciences, Bells University of Technology, Ota, Ogun State, Nigeria;
Oluwasayo Peter Abodunrin
Oludare Johnson Olaleye Department of Computer Science, Bells University of Technology, Ota;

Keywords:

Soft set, neutrosophic set, quasigroup

Abstract

In this paper, we investigate the algebraic structure of Q-neutrosophic soft quasigroups as an ex
tension of Q-neutrosophic soft sets to non-associative systems. We establish several fundamental properties of
these structures. In particular, we prove that the intersection of two Q-neutrosophic soft quasigroups is itself a
Q-neutrosophic soft quasigroup, whereas their union is not necessarily closed under quasigroup operations. The
conditions under which the product, left division, and right division of two Q-neutrosophic soft quasigroups
remain Q-neutrosophic soft quasigroups, particularly within entropic quasigroups, are established. We further
derive necessary and sufficient conditions for a Q-neutrosophic soft groupoid to become a Q-neutrosophic soft
quasigroup and examine structural properties such as idempotency, unipotency, 3-power associativity, and n
power associativity in relation to membership degrees. Using these results, we construct a decision-making
algorithm that models uncertainty through truth-, indeterminacy-, and falsity-membership functions. An ap
plication to medical decision processes demonstrates how quasigroup operations can systematically combine
indeterminate and interacting clinical information. The findings show that Q-neutrosophic soft quasigroups
provide a rigorous mathematical framework for analyzing indeterminate, inconsistent, and non-associative data
across two universal sets, offering enhanced modeling capabilities for complex real-world systems..

DOI 10.5281/zenodo.19075811