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

Shostak, A. P.

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

MSC:

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

Keywords:

fuzzy compactness; fuzzy connectedness; compactness degree; connectedness degree

Citations:

Zbl 0632.00016