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札德是提出模糊集合论的第一人。Zadeh was the first who developed his Fuzzy-set Theory.

这个问题类似早期集合论发生的情况。The problem is akin to what happened in early set theory.

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于1965年创立了模糊集合论，对语言学的研究产生了重要影响。Zadeh, an American scholar, set up his Fuzzy sets in 1965.

方法集合论与点集拓扑学中的方法。Methods Using method of the theory of set and general topology.

非良基集合论是研究循环的或超常集合的理论。Non-well-founded set theory is to study circular or hyper sets.

现行实数理论与ZFC公理集合论中都有矛盾。There are contradictions in current theories of real number and ZFC.

讨论了集合论和概率论的进一步发展对博弈论产生的影响。Further developments of set theory, probability theory and their influences on Game theory.

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模糊语言学就是在运用模糊集合论研究模糊语言中产生的一门新兴学科。Vague linguistics is a new branch which arose in the research of the application of"Fuzzy Sets".

模糊语言学是模糊集合论与现代语言学相结合形成的一门新学科。Fuzzy linguistics is a new discipline formed by combination of fuzzy sets and modern linguistics.

应用集合论在特征信息描述的基础上，探讨了特征映射机理。Based on the description of these features, the principle of features mapping is studied by set theory.

运用集合论中的偏序关系，提出了一种传感器任务分配的模型。A sensor task-assigning model based on semi-order relation in set theory has been presented in this paper.

然而，事实并非如此，在模糊集合论中正是可信性测度才扮演了概率测度的角色。However, it is the credibility measure which plays the role of probability measure in fuzzy set theory actually.

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知识集合论提出后，在图书馆学界引起了一定的争议。After the theory of knowledge set is put forward, it cause certain dispute in the educational circles of the library.

它是用来考察你们对集合论语言是否足够适应以便开始学习拓扑学。It is designed to determine whether you are comfortable enough with the language of set theory to begin the study of topology.

“知识集合论”的概念具有模糊性、宽泛性，因此对图书馆缺乏专指性。Because of the distinctness and broadness of the concept of knowledge set theory, it does not disclose the essence of libraries.

数学家就是个典型，他们会通过想象来证实基本原理尤其是集合论。Mathematicians typically justify their fundamental axioms, in particular those of set theory, by informal appeals to the imagination.

本文从集合论的角度建立了模糊掩模的数学模型，认为模糊掩模是传统掩模的自然扩展。As a mathematical model created based on the set theory, fuzzy masking can be treated as a natural extention of the traditional masking.

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文中证明古典集合论与近代公理集合论中的任何一个无穷集合都是自相矛盾的非集。In this paper, we prove that there is an inconsistency in any infinite set of the classical set theory or the modern axiomatic set theory.

在讨论数学的任何分支时，无论是分析，代数或分析，利用集合论的记号和术语是有帮助的。In discussing any branch of mathematics, be it analysis, algebra, or geometry, it is helpful to use the notation and terminology of set theory.

这套最小化的假定，可望能以比现在更自然更令人信服的方法解决集合论中的悖论。One effect to be hoped for, in such a minimization, is a more natural and conclusive solution than we now have for the antinomies of set theory.