不完备决策背景下对象导出三支概念格的规则提取  

Rule Acquisition Based on Object-induced Three-way Concept Lattice in Incomplete Formal Decision Context

作　　者：王田燕 万仁霞 苗夺谦 赵杰[1] WANG Tianyan;WAN Renxia;MIAO Duoqian;ZHAO Jie(School of Mathematics and Information Science,North Minzu University,Yinchuan 750021,China;Ningxia Key Laboratory of Intelligent Information and Big Data Processing,Yinchuan 750021,China;Faculty of Computer Science and Technology,Tongji University,Shanghai 201804,China)

机构地区：[1]北方民族大学数学与信息科学学院,宁夏银川750021 [2]宁夏智能信息与大数据处理重点实验室,宁夏银川750021 [3]同济大学计算机科学与技术系,上海201804

出　　处：《山西大学学报(自然科学版)》2025年第1期89-100,共12页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(62066001);宁夏科技领军人才项目(2022GKLRLX08);宁夏自然科学基金(2021AAC03203)。

摘　　要：规则提取是形式概念分析研究的一个重要内容,而三支形式概念分析又是形式概念理论分析发展的一个重要成果。针对当前的三支形式概念分析研究并没有充分考虑形式背景不完备的情况,本文探讨在不完备决策背景下对象导出三支概念格的决策规则的提取问题。首先刻画了乐观型的不完备决策背景和悲观型的不完备决策背景,在这两种背景下给出三支概念格之间的细于关系;然后分别给出了在乐观型和悲观型的决策背景下对象导出三支概念格及决策规则的提取;最后讨论了对象导出三支概念格、乐观型对象导出三支概念格和悲观型对象导出三支概念格之间的规则提取关系,得出了不完备决策背景下,对象导出三支正规则集合与悲观型对象导出三支正规则集合相同以及决策近似概念格细于悲观型背景下的决策概念格等结论。研究结果可为不完备形式背景下的三支概念格及规则提取等相关研究提供有益的理论支持。Rule extraction plays an important role in formal concept research,while three-way formal concept analysis represents a significant advancement in the development of formal concept analysis theory.Considering that current research on three-way formal concept analysis does not adequately address incomplete formal contexts,this paper delves into the issue of extracting decision rules from object-induced three-way concept lattices under incomplete decision contexts.Firstly,the optimistic and pessimistic decision contexts of incomplete decision contexts are characterized and the detailed relations between three-way concepts in these two contexts are then provided.The extraction of the three-way concept lattice and decision rules for both optimistic and pessimistic decision objects are subsequently presented.Finally,the relationships in rule acquisition among object-induced three-way concept lattices,optimistic object-induced three-way concept lattices and pessimistic object-induced three-way concept lattices are discussed.The study concluded that in an incomplete decision context,the set of object-induced three-way positive rules is identical to the set of pessimistic object-induced three-way positive rules,and that the decision approximate concept lattice is finer than the decision concept lattice in a pessimistic context.These findings provide valuable theoretical support for the study of three-way concept lattices and rule extraction in contexts involving incomplete information.

关 键 词：不完备决策背景 规则提取 对象导出三支概念格 乐观型 悲观型 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]