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