【摘要】 传递性是二元关系的一个重要性质，对传递性质的定义理解不透，往往会造成判断错误。文中结合二元关系的前域与值域，提出域矩阵和简化域矩阵。域矩阵既可以用于判断二元关系的传递性，又可以用于二元关系和其自身的复合运算；简化域矩阵减少了域矩阵规模，可以更简单、直观地判断二元关系的传递性和反对称性。基于域矩阵和简化域矩阵研究了二元关系传递性判断、反对称性判断和关系复合运算的相关理论。更多还原

【Abstract】 Transitivity is an important property of binary relation. The unclear understanding of the definition of transitivity often leads to wrong judgment. In this paper,the domain matrix and the simplified domain matrix are proposed,which can be used to judge the transitivity of the binary relation and the compound operation of the binary relation and itself. The simplified domain matrix reduces the scale of the domain matrix,and can be used to judge the transitivity and antisymmetry of binary relation more simply and intuitively. Based on the domain matrix and the simplified domain matrix,we studied the related theories of the judgment of the transitivity and the antisymmetry of binary relation and the relational compound operation.更多还原