Abstract

Abstract This paper presents a new representation of α-openness, α-continuity, α-irresoluteness, and α-compactness based on L-fuzzy α-open operators introduced by Nannan and Ruiying [1] and implication operation. The proposed representation extends the properties of α-openness, α-continuity, α-irresoluteness, and α-compactness to the setting of L-fuzzy pretopological spaces based on graded concepts. Moreover, we introduce and establish the relationships among the new concepts.

Highlights

  • This paper presents a new representation of α-openness, α-continuity, α-irresoluteness, and αcompactness based on L-fuzzy α-open operators introduced by Nannan and Ruiying [1] and implication operation

  • Continuity is an important concept in topology, which has developed extensively with the emergence of fuzzy mathematics

  • Α-continuity, α-irresoluteness, and α-compactness degree based on the implication operation and L-fuzzy α-open operators

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Summary

Introduction

Continuity is an important concept in topology, which has developed extensively with the emergence of fuzzy mathematics. The proposed representation extends the properties of α-openness, α-continuity, α-irresoluteness, and α-compactness to the setting of L-fuzzy pretopological spaces based on graded concepts. Α-continuity, α-irresoluteness, and α-compactness degree based on the implication operation and L-fuzzy α-open operators.

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