基于二元关系的一种新运算

A new operation based on binary relation

本文提出了二元关系的一种新运算,称之为内核运算。其思想是通过删除给定集合X上的二元关系R的若干序,使之满足某些特殊性质。文中严格定义了反自反内核、对称内核、反对称内核、传递内核,给出了相应的构造方法,同时进行了严格论证。最后讨论了内核运算的一些性质以及与闭包运算的关系。

This paper introduces a new operation based on binary relation called kernel operation.The idea is to delete some pairs in binary relation R on a given set X to satisfy some pairs' special properties(e.g.anti-reflexive,anti- symmetric,etc.) It stricdy defines terms like anti- reflexive kernel,symmetric kernel,anti-symmetric kernel and transitive kernel,and gives some mediods to construct all kinds of kernels(except transitive kernel) with strict proof.It also discusses some characteristics of the kernel operation and its relationship with the closure operation.