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Boolean fuzzy sets. (English) Zbl 0760.03016
Boolean fuzzy sets were introduced by the first author [ibid. 37, 287-307 (1990; Zbl 0712.03045)] as a result of application of Boolean analysis to a generalization of the notion of set. This paper discusses mainly the notions of function and membership for Boolean fuzzy sets. Similar results for Zadeh’s fuzzy sets were presented by M. A. Erceg [ibid. 3, 75-92 (1980; Zbl 0421.03044)]. Local and global interpretation of Boolean fuzzy sets on the real line are also discussed, with application to arithmetic of fuzzy numbers.

MSC:
03E72 Theory of fuzzy sets, etc.
03H05 Nonstandard models in mathematics
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