Interval-Valued Topology on Soft Sets

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Bayramov S., Aras Ç. G., Kočinac L. D. R.

Axioms, vol.12, no.7, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 7
  • Publication Date: 2023
  • Doi Number: 10.3390/axioms12070692
  • Journal Name: Axioms
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: base, continuous mapping, direct sum, interval-valued fuzzy neighborhood, interval-valued fuzzy topology (cotopology), subbase
  • Kocaeli University Affiliated: Yes


In this paper, we study the concept of interval-valued fuzzy set on the family (Formula presented.) of all soft sets over X with the set of parameters E and examine its basic properties. Later, we define the concept of interval-valued fuzzy topology (cotopology) (Formula presented.) on (Formula presented.). We obtain that each interval-valued fuzzy topology is a descending family of soft topologies. In addition, we study some topological structures such as interval-valued fuzzy neighborhood system of a soft point, base and subbase of (Formula presented.) and investigate some relationships among them. Finally, we give some concepts such as direct sum, open mapping and continuous mapping and consider connections between them. A few examples support the presented results.