Some algebraic properties of soft quasigroups

Abstract

Soft set theory, instituted by Molodsov is a robust mathematical tool for dealing with uncertainties and problems that are questionably defined. Our aim in this paper is to broaden soft theory by studying some new algebraic operations (product and product divisions) on soft quasigroups. We dene soft quasigroups and introduce different algebraic properties connected with them. It was shown that for soft quasigroups over medial quasigroups, the resulting soft sets based on product and product divisions are also soft quasigroups over medial quasigroups. With the new operations defined on soft quasigroups, it was shown that these new operations are distributive over restricted/extended union and intersection operations.