The Fundamental Conception of Similarity Relation and Its Weak Equivalence Properties
相似关系的基本概念及其弱等价性质

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),similarity system are built on the basis of five most basic conceptions (set, subset, set of sets, set union and one one mapping) and macro downward compatibility and system principle, such conceptions play a significant role in establishing similarity system analysis.