本文的主要目的是确立相似关系的准确数学概念。首先本文将等价关系合理推广为弱等价关系，其次为解决描述部分与整体的共同属性问题，本文引入了向下相容性概念，并证明了向下相容性具有弱等价性质。然后用集合、子集、幂集、并集、１—１映射这五个最基本的概念及向下相容性公理、系统原理初步界定和刻划了相似关系、相似映射、相似要素、相似基、相似元（相似点）、相似系统这六个相似方面的基本概念。这对建立相似系统的分析具有重要意义。

The major purpose of this paper is to establish a precise mathematical conception of similarity relation. First, the paper rationally extends equivalence to weak equivalence. Second, in order to describe the common attribute of the whole and parts, the paper introduces downward computability conception and proves that downward compatability has weak equivalence properties. Then six fundamental conceptions:similarity relation,similarity mapping,similarity factors,similarity base, similarity element (point),s...