\(r\)-fuzzy \(\delta\)-\(\ell\)-open sets and fuzzy upper (lower) \(\delta\)-\(\ell\)-continuity via fuzzy idealization

Volume 25, Issue 1, pp 1--9 http://dx.doi.org/10.22436/jmcs.025.01.01

Publication Date: April 25, 2021 Submission Date: January 31, 2021 Revision Date: April 02, 2021 Accteptance Date: April 09, 2021

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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 study, the concepts of \(r\)-fuzzy \(\delta\)-\(\ell\)-open and \(r\)-fuzzy strong \(\beta\)-\(\ell\)-open sets are defined in a fuzzy ideal topological space \((X,\tau,\ell)\) based on the sense of \v{S}ostak. Some properties of these sets along with their mutual relationships are discussed with the help of examples. Also, the concepts of fuzzy upper and lower \(\delta\)-\(\ell\)-continuous (resp. strong \(\beta\)-\(\ell\)-continuous) multifunctions are introduced and studied. Moreover, the decomposition of fuzzy upper (resp. lower) semi-\(\ell\)-continuity and the decomposition of fuzzy upper (resp. lower) \(\alpha\)-\(\ell\)-continuity are obtained. Finally, we constructed a new form of \(r\)-fuzzy connected set called \(r\)-fuzzy \(\ell\)-connected and studied some of its properties via fuzzy ideals.

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Keywords

• Fuzzy ideal topological space
• \(r\)-fuzzy \(\delta\)-\(\ell\)-open (resp. strong \(\beta\)-\(\ell\)-open) set
• fuzzy upper and lower \(\delta\)-\(\ell\)-continuity (resp. strong \(\beta\)-\(\ell\)-continuity)
• connectedness

MSC

•  54A40
•  54C08
•  54C60

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