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A fuzzy alternative set theory. (English) Zbl 0688.03035
The author introduces a theory which makes it possible to describe a larger extent of objects than Alternative Set Theory (AST). His theory admits not only urelements, but also fuzzy sets are taken into account. The author generalizes the common approach to fuzzy sets. Namely, besides giving the membership degrees to the elements of a fuzzy set, he adds to every fuzzy set a valuation object (describing the membership degrees) being another fuzzy set. This approach is somewhat similar to the construction of Boolean universes, but it is not clear that corresponding “fuzzy types” are well ordered. The author separates in his theory objects of AST, and thus he proves that his theory is an extension of AST. The described theory is in my opinion rather complicated, but the paper is written quite plainly.
Reviewer: K.Čuda

03E70 Nonclassical and second-order set theories
03E72 Theory of fuzzy sets, etc.