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On fuzzy convergence. (English) Zbl 0614.54008

First, summarizing his paper ”On the concept of fuzzy point” [Fuzzy Sets Syst. 18, 159-172 (1986; Zbl 0606.03014)], the author shows that a ”good definition of fuzzy point” is impossible if one wants \(\in\) to be a nonfuzzy relation between fuzzy points and fuzzy subsets. Instead, he admits that points and sets are nonfuzzy objects while \(\in\) is a fuzzy relation. So, interpreting in a multivalued logic the concepts of subsets, point, topology and two different formulas expressing the classical convergence, he obtains concepts of convergence for sequences of elements of a set w.r.t. a fuzzy topology. Finally, he investigates convergences preserving operators in functional spaces and the uniqueness of limits.
Reviewer: B.Behrens

MSC:

54A40 Fuzzy topology
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
03E72 Theory of fuzzy sets, etc.
03B50 Many-valued logic
03B52 Fuzzy logic; logic of vagueness

Citations:

Zbl 0606.03014
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Full Text: DOI

References:

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