多分S-近似空间  

Polytomous S-approximation spaces

作　　者：谢晓洁 廖淑娇 XIE Xiaojie;LIAO Shujiao(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou,Fujian 363000,China;Fujian Key Laboratory of Granular Computing and Application,Zhangzhou,Fujian 363000,China;Institute of Meteorological Big Data-Digital Fujian,Zhangzhou,Fujian 363000,China;Fujian Key Laboratory of Data Science and Statistics,Zhangzhou,Fujian 363000,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000 [2]福建省粒计算及其应用重点实验室,福建漳州363000 [3]数字福建气象大数据研究所,福建漳州363000 [4]数据科学与统计重点实验室,福建漳州363000

出　　处：《闽南师范大学学报（自然科学版）》2024年第4期94-107,共14页Journal of Minnan Normal University：Natural Science

基　　金：国家自然科学基金项目(12101289,12271191);福建省自然科学基金项目(2023J01122,2023J01125,2023J05175,2022J01306,2022J05169);福建省本科高校教育教学研究(FBJG20220091)。

摘　　要：基于知识空间理论的多分推广,提出了多分S-近似空间的概念,研究多分S-近似空间模型上、下近似在不同运算和不同决策映射下的性质.进一步,定义上、下近似多分知识状态,利用上、下近似算子的性质研究上、下近似多分知识状态集族形成多分知识结构的条件,特别地,探讨多分知识结构分别满足交封闭和并封闭的条件.多分S-近似空间为多分知识结构的构建及其应用提供了一种新的研究思路和方法,所得成果将丰富和发展S-近似空间理论和知识空间理论.Based on the polytomous generalization of knowledge space theory,the concept of polytomous S-approximation spaces is proposed.After that,the properties of upper and lower approximations under different operations and decision mappings are investigated.Moreover,the concept of upper and lower approximation polytomous knowledge states is introduced,and the conditions under which the family of upper and lower approximation polytomous knowledge state sets can form polytomous knowledge structures are explored.In particular,the conditions of the polytomous knowledge structure to satisfy intersection and union closure are discussed.Polytomous S-approximation spaces provide a new research approach and method for the construction and application of polytomous knowledge structures,and the results obtained will enrich and develop the S-approximation spaces theory and knowledge space theory.

关 键 词：S-近似空间 上近似 下近似 多分知识结构 

分 类 号：TP182[自动化与计算机技术—控制理论与控制工程]