代数商空间的同余结构研究

发布时间：2018-04-30 15:53

本文选题：粒计算 + 商空间　；参考：《电子学报》2017年10期

【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 for granular computing. When the domain structure is an algebraic structure, the equivalence relation in the topological structure is no longer applicable, so the congruence relation, which is more strict than the equivalence relation constraint, is used. When a given relation is a noncongruence equivalence relation, the concepts of congruence closure and congruence kernel are introduced to approximate the noncongruence equivalence relationship. In this paper, we systematically demonstrate the solution of congruence closure and congruence kernel, and some related properties and conclusions. On this basis, the synthesis of algebraic quotient space model is systematically studied, which provides a theoretical basis for solving the complex problems of algebraic structure by using quotient space theory.
【作者单位】：中南大学信息科学与工程学院;
【基金】：国家自然科学基金(No.61172031) 2017年长沙市节能专项项目资助
【分类号】：TP18

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