燕山大学学报2024，Vol.48Issue(2)：129-137,9.DOI:10.3969/j.issn.1007-791X.2024.02.004
属性偏序形式结构的数学形式化
Mathematical formalization of attribute partial order formal structure
摘要
Abstract
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Key words
formal context/mathematical formalization/attribute partial order formal structure/granular computing/concept cognitive learning分类
信息技术与安全科学引用本文复制引用
任蕴丽,宋佳霖,郑存芳,洪文学..属性偏序形式结构的数学形式化[J].燕山大学学报,2024,48(2):129-137,9.基金项目
国家自然科学基金资助项目(81803958,62176229) （81803958,62176229）
河北省自然科学基金资助项目(F2016203443,F2020203010) （F2016203443,F2020203010）
