Some New Types of Fuzzy Closed Sets, SeparationAxioms, and Compactness via Double Fuzzy Topologies

Authors

  • Fahad Alsharari Jouf University
  • Osama Taha Sohag University
  • Islam Taha Sohag University

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i4.5573

Keywords:

intuitionistic fuzzy set, double fuzzy topology, (r, s)-gfsc set, (r,s)-g*fsc set, continuity, (r,s)-GFS-regular space, (r,s)-GFS-normal space, compactness

Abstract

In this article, we first defined a stronger form of (r,s)-generalized fuzzy semi-closed sets (briefly, (r,s)-gfsc sets) called (r,s)-g*fsc sets and investigated some of its features. Moreover, we showed that (r,s)-fsc set → (r,s)-g*fsc set → (r,s)-gfsc set, but the converse may not be true. In addition, we explored novel types of fuzzy generalized mappings between double fuzzy topological spaces (U, τ, τ*) and (V, η, η*), and the relationships between these classes of mappings were examined with the help of some illustrative examples. Thereafter, we introduced novel types of higher separation axioms called (r,s)-GFS-regular and (r,s)-GFS-normal spaces with the help of (r,s)-gfsc sets and discussed some topological properties of them. Finally, some novel types of compactness via (r,s)-gfso sets were defined and the relationships between them were introduced.

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Published

2024-10-31

Issue

Section

Nonlinear Analysis

How to Cite

Some New Types of Fuzzy Closed Sets, SeparationAxioms, and Compactness via Double Fuzzy Topologies. (2024). European Journal of Pure and Applied Mathematics, 17(4), 4093-4111. https://doi.org/10.29020/nybg.ejpam.v17i4.5573