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Fuzzy soft upper and lower semi-continuous multifunctions. (English) Zbl 1438.54041

Summary: In this paper, we define the upper and lower inverse of a fuzzy soft multifunction and prove some basic identities. Then by using these ideas we introduce the concept of fuzzy soft continuity and obtain many interesting properties of fuzzy soft upper and lower semi-continuous multifunctions. Also, we define the notions of fuzzy soft lower \((\mathcal{A},\mathcal{B},\mathcal{C}, \mathcal{D},\mathcal{I})\)-continuity and fuzzy soft upper \((\mathcal{A},\mathcal{B}, \mathcal{C},\mathcal{D},\mathcal{I})\)-continuity. Moreover, we present different cases of upper and lower fuzzy soft continuous multifunctions.

MSC:

54A40 Fuzzy topology
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54D05 Connected and locally connected spaces (general aspects)
54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
54D30 Compactness
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