模糊三支形式概念分析与概念认知学习  

Fuzzy three-way formal concept analysisand concept-cognitive learning

作　　者：徐伟华 杨蕾 张晓燕[1] XU Weihua;YANG Lei;ZHANG Xiaoyan(College of Artificial Intelligence,Southwest University,Chongqing 400715,China;School of Science,Chongqing University of Technology,Chongqing 400054,China)

机构地区：[1]西南大学人工智能学院,重庆400715 [2]重庆理工大学理学院,重庆400054

出　　处：《西北大学学报（自然科学版）》2020年第4期516-528,共13页Journal of Northwest University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(61976245,61772002)。

摘　　要：目前,三支形式概念分析只适用于传统的形式背景,无法处理模糊环境中的形式背景。为了解决这个问题,文中结合三支形式概念分析与模糊集理论,提出了模糊三支算子及其逆算子,并对其相关重要性质进行了研究。在此基础上,定义了两类模糊三支概念,即属性导出模糊三支概念和对象导出模糊三支概念。随后,以对象导出的模糊三支概念为例,讨论了模糊三支概念的概念认知学习方法,实现了不完备模糊三支概念的认知学习。最后,为了更好地解释和理解所提出的理论,文中进行了案例分析并设计了认知学习算法,通过数值实验验证了所提出方法的有效性,进一步丰富了三支形式概念分析和概念认知学习理论。At present,the three-way formal concept analysis is only applicable to the traditional formal context,and can′t deal with the formal context in the fuzzy environment.In order to solve this problem,this paper combines the three-way formal concept analysis with the theory of fuzzy set,proposes the fuzzy three-way operator and its inverse operator,and studies its related important properties.On this basis,two kinds of fuzzy three-way concepts are defined,namely attribute-induced fuzzy three-way concepts and object-induced fuzzy three-way concepts.Then,taking the object-induced fuzzy three-way concept as an example,the concept-cognitive-learning approach to the fuzzy three-way concept is discussed,and the cognitive learning of the incomplete fuzzy three-way concept is realized in the environment.Finally,in order to explain and illustrate precisely the proposed theory,the paper gives a case study and designs an algorithm,at the same time,it uses some data sets for experimental evaluation.These results further enrich the theory of three-way formal concept analysis and concept-cognitive learning.

关 键 词：模糊三支概念 模糊三支算子 形式概念分析 概念认知学习 

分 类 号：O235[理学—运筹学与控制论] TP18[理学—数学]