The general fuzzy filter approach to fuzzy topology. I (Q1920352)

The author introduces and investigates a general notion of fuzzy filters (representable by prefilter families), types of fuzzy filters, (sub-)bases of fuzzy filters, fuzzy ultrafilters, principal fuzzy filters and fuzzy filter monad, extending the notions in [\textit{P. Eklund} and the author, in `Applications of category theory to fuzzy subsets', Theory Decis. Libr., Ser. B 14, 110-136 (1992; Zbl 0772.54006); Completions and compactifications by means of monads, in: `Fuzzy Logic: State of Art' (Kluwer, Dordrecht, 1993), 39-56]. The partially ordered monad defined in [the author, in: `Recent developments of general topology and its applications, Internat. conf. in memory of Felix Hausdorff (1868-1942)', Math. Res. 67, 136-149 (1992; Zbl 0803.54013)], turns out to be a submonad of the partially ordered fuzzy filter monad defined by means of the fuzzy filters.