中文摘要：

模糊集合论是模糊理论的数学基础,其公理化可以从不同的逻辑语言出发。经典逻辑是较为简洁的一种方法。夏平基于扎德的模糊集概念创立了第一个公理化模糊集合论Za。这个公理化是ZF的。将它扩张为NBG是一种自然的考虑。这样的扩张将作为从非经典逻辑如模糊逻辑出发建立集合论的一个基础。

英文摘要：

Fuzzy set theory（FST） is the foundation of fuzzy theory.The axiomatization of FST is almostly based on varieties of logic languages.Classical logic is a concise approach.Chapin gave the first axiomatization of FST named Za based on Zadeh＇s concept of fuzzy sets.Za is a ZF-like axiomatization and an extension to NBG shall be discussed naturally.The extension will be a foundation of those constructions of set theory based on non-classical logic,such as fuzzy logic.