On the axiomatic theory of fuzzy sets (Q1319439)

This is an axiomatization of fuzzy set theory in the realm of classical logic which follows the style of \textit{P. Bernays} [Axiomatic set theory (1968; Zbl 0733.03038)] in having fuzzy sets and (crisp) classes as well as (ternary) fuzzy set membership and class membership as separate primitive notions. Also \(=\), \(\subseteq\), \(\subset\), \(\cup\), \(\cap\) are used separately for fuzzy sets and for classes. The axioms include: class comprehension, replacement for fuzzy sets, fuzzy power set, union, foundation, and class choice. Unfortunately, the presentation is notationally complicated and not free of minor errors. Only the most basic facts, from the axiomatic point of view, are developed.