A Study of Congruence Structure in Algebraic Quotient Space

SUN Ye; WANG Jia-yang; ZHANG Si-tong

doi:10.3969/j.issn.0372-2112.2017.10.017

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A Study of Congruence Structure in Algebraic Quotient Space

更新时间：2025-07-16

- A Study of Congruence Structure in Algebraic Quotient Space
- Acta Electronica Sinica Vol. 45, Issue 10, Pages: 2434-2438(2017)
- 作者机构：
  
  中南大学信息科学与工程学院,湖南,长沙,410083
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.61172031);2017 Changsha Energy-saving Project of Hunan Province
- DOI：10.3969/j.issn.0372-2112.2017.10.017
  CLC： TP18
- Published：2017
- 稿件说明：
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SUN Ye, WANG Jia-yang, ZHANG Si-tong. A Study of Congruence Structure in Algebraic Quotient Space[J]. Acta Electronica Sinica, 2017, 45(10): 2434-2438.
DOI：

SUN Ye, WANG Jia-yang, ZHANG Si-tong. A Study of Congruence Structure in Algebraic Quotient Space[J]. Acta Electronica Sinica, 2017, 45(10): 2434-2438. DOI： 10.3969/j.issn.0372-2112.2017.10.017.

摘要

商空间理论是粒计算最为重要的模型之一，现有的商空间模型的结构一般为拓扑结构.当论域结构是代数结构时，拓扑结构中的等价关系已经不再适用，所以使用比等价关系约束更为严格的同余关系.当给定关系是非同余等价关系时，则引入同余闭包和同余内核的概念来逼近非同余等价关系.本文系统的论证了同余闭包和同余内核的求法以及一些相关性质与结论.以此为基础，对代数商空间模型合成进行系统的研究，为使用商空间理论解决代数结构的复杂问题提供了理论基础.

Abstract

Quotient space theory is one of the most important models of granular computing.The structure in the existing quotient space model is usually a topology.If the domain structure is an algebraic structure

the equivalence relation in topological structure is no longer applicable.So the congruence relation in use is stricter than the equivalence relation.When a given relation is a non congruent equivalence relation

it introduces the concept of congruence closure and congruence interior to approximate the relation.The method

the properties and the conclusions are systematically demonstrated in the paper.On this basis

the algebraic quotient space model is systematically studied.The paper provides theoretical basis for solving complicated problems with the algebraic structure using quotient space theory.

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