The Relationship between Ordinary and Soft Algebras with an Application

Zanyar A. Ameen, Tareq M. Al-shami, Radwan Abu-Gdairi and Abdelwaheb Mhemdi ()
Additional contact information
Zanyar A. Ameen: Department of Mathematics, College of Science, University of Duhok, Duhok 42001, Iraq
Tareq M. Al-shami: Department of Mathematics, Sana’a University, Sana’a P.O. Box 1247, Yemen
Radwan Abu-Gdairi: Department of Mathematics, Faculty of Science, Zarqa University, Zarqa P.O. Box 13110, Jordan
Abdelwaheb Mhemdi: Department of Mathematics, College of Sciences and Humanities in Aflaj, Prince Sattam bin Abdulaziz University, Riyadh 16273, Saudi Arabia

Mathematics, 2023, vol. 11, issue 9, 1-12

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.

Keywords: soft set; soft algebra; soft mapping; probability; soft measure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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