直觉模糊向量β覆盖L粗糙集  

Intuitionistic Fuzzy Vector β Covering L Rough Sets

作　　者：林依婷 马周明 李进金 LIN Yi-ting;MA Zhou-ming;LI Jin-jin(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000,China;Digital Fujian Meteorological Big Data Research Institute,Zhangzhou 363000,China;Fujian Key Laboratory of Granular Computing and Applications,Zhangzhou 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]数字福建气象大数据研究所,福建漳州363000 [3]福建省粒计算及其应用重点实验室,福建漳州363000

出　　处：《模糊系统与数学》2022年第6期26-39,共14页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(62076088,61672272,11871259);福建省自然科学基金资助项目(2020J01792,2020J01812,2021J01979,2021J01983)。

摘　　要：直觉模糊覆盖粗糙集作为模糊粗糙集的一类推广,自提出以来就备受关注。为了更好的刻画直觉模糊环境中的目标概念,同时兼顾不同对象容错能力的差异性,本文提出了直觉模糊向量β覆盖L粗糙集,讨论了它们的相关性质、不确定性度量及其属性约简方法。首先研究了直觉模糊向量β覆盖及其邻域的相关特征。其次在直觉模糊β覆盖粗糙集的基础上给出了直觉模糊β覆盖L-1粗糙集,讨论了二者之间的联系。在直觉模糊向量β邻域的基础上,定义了直觉模糊向量β覆盖L-2粗糙集,探讨了其相关性质并讨论了它和其它模型之间的相关联系。最后研究了模型相关的直觉模糊粗糙性、相似性、辨识性度量等不确定性刻画方式,并给出相关属性约简算法。通过例子验证了模型的有效性与适用性。结论表明,就已有的直觉模糊β覆盖粗糙集而言,直觉模糊β覆盖L-1粗糙集与目标概念之间具有更高的相似性;直觉模糊向量β覆盖L-2粗糙集具有更好的适用性,并在一定的程度上具有更高的精确度。The intuitionistic fuzzy covering rough set as a kind of generalization of fuzzy rough set has attracted much attention since it was proposed. In order to better characterize concepts of target in the intuitionistic fuzzy environment, and take into account the differences in the fault tolerance of different objects, this paper proposes an intuitionistic fuzzy vector β covering L rough set model, and discusses its correlation properties, uncertainty measures and attribute reduction methods. Firstly, the correlation characteristics of intuitionistic fuzzy vector β covering and its neighborhood are studied. Secondly, on the basis of the intuitionistic fuzzy β covering rough set, the intuitionistic fuzzy β covering L-1 rough set is given, and the connection between the two is discussed. And on the basis of intuitionistic fuzzy vector β neighborhoods, intuitionistic fuzzy vector β rough sets and their properties are discussed, and the correlations between the model and other models are revealed. Finally, the uncertainty measure methods such as roughness, similarity, recognition metrics of intuitionistic fuzzy related to the model are studied, and a reduction algorithm for related attributes is proposed. Examples are given to illustrate the effectiveness and applicability of the model. The conclusion shows that the intuitionistic fuzzy covering of the L-1 rough set has a higher similarity with the corresponding target concept in terms of the existing intuitionistic fuzzy covering rough set, and the intuitionistic fuzzy vector covering the L-2 rough set has better applicability and higher accuracy to some extent.

关 键 词：直觉模糊集 直觉模糊向量β覆盖 直觉模糊粗糙集 不确定性度量 属性约简 

分 类 号：O159[理学—数学]