In this study, a new form of fuzzy r-minimal structure [28] called a fuzzy soft r-minimal structure, is defined, which is an extension of the fuzzy soft topology introduced by Aygunoglu et al. [26]. In addition, the concepts of fuzzy soft r-minimal continuity and fuzzy soft r-minimal compactness are introduced in fuzzy soft r-minimal spaces. Some interesting properties and characterizations are also discussed. Finally, several types of fuzzy soft rminimal compactness are defined, and the relationships between them are characterized.
<abstract><p>As a weaker form of fuzzy soft $ r $-minimal continuity by Taha (2021), the notions of fuzzy soft almost (respectively (resp. for short) weakly) $ r $-minimal continuous mappings are introduced, and some properties are given. Also, we show that every fuzzy soft $ r $-minimal continuity is fuzzy soft almost (resp. weakly) $ r $-minimal continuity, but the converse need not be true. After that, we introduce a concept of continuity in a very general setting called fuzzy soft $ r $-minimal $ (\mathcal{A}, \mathcal{B}, \mathcal{C}, \mathcal{D}) $-continuous mappings and investigate some properties of these mappings.</p></abstract>
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