属性偏序形式结构的数学形式化  

Mathematical formalization of attribute partial order formal structure

作　　者：任蕴丽[1,2] 宋佳霖[1] 郑存芳 洪文学[1] REN Yunli;SONG Jialin;ZHENG Cunfang;HONG Wenxue(School of Electrical Engineering,Yanshan University,Qinhuangdao,Hebei 066004,China;College of Mathematics and Information Technology,Hebei Normal University ofScience and Technology,Qinhuangdao,Hebei 066004,China;Department of Information and Engineering,Hebei University of Environmental Engineering,Qinhuangdao,Hebei 066102,China)

机构地区：[1]燕山大学电气工程学院,河北秦皇岛066004 [2]河北科技师范学院数学与信息科技学院,河北秦皇岛066004 [3]河北环境工程学院信息工程系,河北秦皇岛066102

出　　处：《燕山大学学报》2024年第2期129-137,共9页Journal of Yanshan University

基　　金：国家自然科学基金资助项目(81803958,62176229);河北省自然科学基金资助项目(F2016203443,F2020203010)。

摘　　要：属性偏序形式结构,作为一种基于人类认知原理和粒计算思想的知识发现和知识表示新理论,目前已有广泛的应用,但其理论基础缺乏抽象化数学化,这势必影响该理论的系统发展。针对上述问题,研究了属性偏序形式结构的数学形式化描述问题。首先,基于粒计算的思想提出了知识表示的形式化框架。在此基础上,通过定义对象集合的覆盖和最简覆盖,给出属性偏序形式结构的粒和粒群的概念,进而通过对粒衍生出粒群的充要条件的讨论,给出了属性偏序形式结构中的知识结构,从而完成属性偏序形式结构的数学形式化描述。最后,通过具体实例展示了利用数学形式化描述构造属性偏序形式结构的过程,并揭示了该过程所体现的人类认知规律。Attribute partial order formal structure,as a new theory of knowledge discovery and knowledge representation based on human cognitive principles and granular computing ideas,has been widely used at present.However,its theoretical basis is lack of abstraction and mathematization,which is bound to affect the systematic development of this theory.Regarding the above problem,the mathematical formal description of attribute partial order formal structure is studied.Firstly,a formal framework of knowledge representation is proposed based on the idea of granular computing.On this basis,by defining the cover and the simplest cover of an object set,the concepts of granule and granular group of attribute partial order formal structure are given.And then through the discussion of the sufficient and necessary condition for a granule to derive a granular group,the knowledge structure in attribute partial order formal structure is given,so as to complete the mathematical formal description of attribute partial order formal structure.Finally,through specific examples,the process of constructing attribute partial order formal structure by using mathematical formal description is demonstrated,and the human cognitive law embodied in this process is revealed as well.

关 键 词：形式背景 数学形式化 属性偏序形式结构 粒计算 概念认知学习 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]