Some properties of \((r,s)\)-generalized fuzzy semi-closed sets and some applications

Volume 27, Issue 2, pp 164--175 http://dx.doi.org/10.22436/jmcs.027.02.06

Publication Date: April 13, 2022 Submission Date: November 02, 2021 Revision Date: February 09, 2022 Accteptance Date: February 15, 2022

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Authors

I. M. Taha - Department of Basic Sciences, Higher Institute of Engineering and Technology, Menoufia, Egypt. - Department of Mathematics, Faculty of Science, Sohag University, Egypt.

Abstract

In this work, the notion of \((r,s)\)-generalized fuzzy semi-closed sets is introduced and some properties are given. Also, we show that every \((r,s)\)-generalized fuzzy closed set by Abbas (2006) is \((r,s)\)-generalized fuzzy semi-closed set, but the converse need not be true. After that, the generalized forms of fuzzy continuous mappings between double fuzzy topological spaces \((X,\tau_{1}, \tau_{1}^*)\) and \((Y,\tau_{2}, \tau_{2}^*)\) are introduced and studied. Some interesting relationship between these mappings and other mappings introduced previously are investigated with the help of examples. In the end, the notion of \((r,s)\)-fuzzy GS-connected sets is introduced and studied with help of \((r,s)\)-generalized fuzzy semi-closed sets.

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Keywords

• Double fuzzy topological space
• \((r,s)\)-generalized fuzzy semi-closed set
• \((r,s)\)-fuzzy GS-connected
• DFGS-continuity
• DFGS-irresolute

MSC

•  54A40
•  54C08
•  54D05

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