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Algebraic properties of fuzzy sets. (English) Zbl 0211.31002
Summary: Some new algebraic properties of the class of the “fuzzy sets” \(\mathcal F(I)\) are stressed; in particular it is pointed out that the class of the generalized characteristic functions furnished with the lattice operations proposed by Zadeh is a Brouwerian lattice. The possibility of inducing other different lattice operations to the whole class \(\mathcal F(I)\) or to a suitable subclass of it is considered. The problem of the relationship between “fuzzy sets” and classical set theory is finally remarked. A qualitative comparison with similar situations appearing in the axiomatic formulation of quantum mechanics and in the classical theory of probability is made.

MSC:
03E72 Theory of fuzzy sets, etc.
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
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