本文首先介绍了增量聚类算法的分类以及研究现状，提出了增量聚类算法等价性概念；
This paper firstly introduces the classification of incremental clustering algorithms and the research state, defines the concept of algorithm equivalence.
最后，利用半基的概念还给出了半紧致性的一个等价形式。
Finally. We give a identical form of semi-compact to use concept of semi-base.
模糊传递性是模糊序关系的核心，也是模糊等价关系，模糊相似关系等概念的基础。
The fuzzy transitivity is the core of fuzzy ordering relation, and the basis of fuzzy equal relation.
本文的第二部分首先给出了射影系统的概念并且描述了线性码和射影系统之间的等价性，因而我们就可以用几何语言给出线性码一个新的描述。
In the first, the projective system was given in section two, and the equivalence between linear codes and projective was proofed. So we can use geometric language to describe linear codes.
本文基于决策系统的一致性，定义概念“关键属性”，并证明关键属性集合与属性核之间的等价性。
In this paper, the notion of key feature is defined based on the consistency of a decision system, then the equivalence relation between the set of all key features and the feature core is discovered.
证明了等价关系族构成的有界格，建立了函数复合的最大公因式、最小公倍式等概念，并对其存在唯一性作出证明。
This paper establishes the concept of maximal common factor and minimal common multiple for compound function and proves their unique existence.
证明了等价关系族构成的有界格，建立了函数复合的最大公因式、最小公倍式等概念，并对其存在唯一性作出证明。
This paper establishes the concept of maximal common factor and minimal common multiple for compound function and proves their unique existence.
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