A new approach to soft relations and topology

Hamouda, Essam

doi:10.47974/JIM-2330

Open Access Research Article

A new approach to soft relations and topology

^*Essam HamoudaCorresponding authorehamouda70@gmail.comDepartment of Basic SciencesFaculty of Technology and EducationUniversity of Beni-SuefBeni-Suef, 62511, Egypt0000-0001-9506-2172View full profile →

* Corresponding author · click or hover a name for details

pp. 447–458Vol. 29Issue 2February 2026DOI: 10.47974/JIM-2330XML

Received:: 08 Jan 2025
Published Online:: 19 Dec 2025
Article type:: Research Article
Language:: EN
Article no.:: JIM-2330
Pages:: 447–458

Abstract

Let R = (q, A) be a soft relation over a set X, where q : A → P(X × X). In this paper, we first associate a mapping aq : X × X → P(A) with every soft relation R over X. This mapping is then utilized to redefine the concept of soft equivalence relation as developed in [8]. Next, we introduce soft topologies generated by R and explore several related results within this framework. Specifically, we have characterised soft topologies that are produced by a soft relation and a soft selection. Finally, we applied these concepts to fuzzy frameworks. This revised approach to soft structures brings working with soft set theory into closer alignment with fuzzy set theory.

Keywords

Soft sets Soft relations Soft topology Fuzzy topology

Subject Classifications

45D1445D18

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