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**A new form of fuzzy \(\alpha \)-compactness.**
*(English)*
Zbl 1108.54009

Summary: A new form of \(\alpha \)-compactness is introduced in \(L\)-topological spaces by means of \(\alpha \)-open \(L\)-sets and their inequality where \(L\) is a complete de Morgan algebra. This notion doesn’t rely on the structure of the basis lattice \(L\). It can also be characterized by means of \(\alpha \)-closed \(L\)-sets and their inequality. When \(L\) is a completely distributive de Morgan algebra, many characterizations are presented and the relation between our new notion and other types of compactness are discussed. Countable \(\alpha \)-compactness and the \(\alpha \)-LindelĂ¶f property are also investigated.