The Relationship between Ordinary and Soft Algebras with an Application

Abstract

This work makes a contribution to the theory of soft sets. It studies the concepts of soft semi-algebras and soft algebras, along with some operations. Then, it examines the relations of soft algebras set to their ordinary (crisp) counterparts. Among other things, we show that every algebra of soft sets induces a collection of ordinary algebras of sets. By using the formulas (in Theorem 7 and Corollary 1), we present a novel construction, allowing us to construct a soft algebra from a system of ordinary algebras of sets. Two examples are presented to show how these formulas can be used in practice. This approach is general enough to be applied to many other (soft) algebraic properties and shows that ordinary algebras contain instruments enabling us to construct soft algebras and to study their properties. As an application, we demonstrate how elements of the generated soft algebra can be used to describe the weather conditions of a region.