On compactness and connectedness degrees of fuzzy sets in fuzzy topological spaces. (English) Zbl 0638.54008

General topology and its relations to modern analysis and algebra VI, Proc. 6th Symp., Prague/Czech. 1986, Res. Expo. Math. 16, 519-532 (1988).
[For the entire collection see Zbl 0632.00016.]
The author, continuing his previous papers, investigates essentially “how much compact” (resp. “how much connected”) a fuzzy subset M of a fuzzy topological space X is, introducing the new concept of compactness degree \(c_{\alpha}(M)\) (resp. connectedness degree \(a_{\alpha}(M))\) of M in X at a level \(\alpha\in (0,1]\). He points out that if M is crisp, then \(c_{\alpha}(M)=1\) (resp. \(s_{\alpha}(M)=1)\) if and only if M is compact (resp. connected). Several theorems and examples are presented.
Reviewer: S.Sessa


54D40 Remainders in general topology
54D05 Connected and locally connected spaces (general aspects)
54D30 Compactness


Zbl 0632.00016