基于极性框架的粗糙模糊形式概念分析  

L-rough Fuzzy Formal Concept Analysis Based on Polarity Framework

作　　者：燕健 王拥军[1] 王宝山 周恒[1] YAN Jian;WANG Yong-jun;WANG Bao-shan;ZHOU Heng(School of Mathematical Science,Beihang University,Beijing 100191,China)

机构地区：[1]北京航空航天大学数学科学学院,北京100191

出　　处：《模糊系统与数学》2022年第4期131-142,共12页Fuzzy Systems and Mathematics

基　　金：国家自然基金资助项目(11871083)。

摘　　要：借助于范畴论中的伴随概念,本文提出用极性模糊伴随三元组生成模糊形式概念分析的基本框架。继而借用L-粗糙算子,构建粗糙模糊形式概念分析理论。这一新框架与已有的多伴随框架不同:对象集与属性集的模糊子集被建立在同一个真值结构之上;从两个模糊子集之间伴随三元组诱导的模糊伽罗华连接,变为三个模糊子集之间极性诱导的模糊伴随三元组。从而将多伴随框架中真值结构与模糊子集之间过于复杂的设定与伴随关系简化。基于以上结果,本文构造了一个病毒传播-医疗资源储备策略实例,用以论证极性模糊伴随三元组框架的优势以及应用前景。Follow the perspective of adjoint,one of the most important notions in category theory,this paper presents a new fuzzy formal concept analysis framework generated on a polarity fuzzy adjoint triples.With a pair of L-rough operators,the L-rough fuzzy formal concept analysis theory is also constructed.The most significant improvements of our framework compared with multi-adjoint framework lie in the settings of truth structures and adjoint situation.In multi-adjoint framework,there are multiple pairs of adjoint-triples in its truth structures consists of two lattices and a poset.In our polar fuzzy adjoint-triples framework,adjoint situation becomes fuzzy adjoint triples among three fuzzy subsets induced by the two lattice structures united by polarity.From above results,a well-designed Virus Spread-Medical Resource Reserve Strategy example is provided to demonstrate advantages in polarity fuzzy adjoint-triples framework.

关 键 词：极性模糊伴随三元组 模糊形式概念分析 L-粗糙算子 完备剩余格 

分 类 号：O159[理学—数学] O154[理学—基础数学]