概率区间值模糊覆盖粗糙集及其三支决策  

Probability interval-valued fuzzy covering rough set and itsthree-way decision

作　　者：金雨馨 冯涛[1] 王荣欣[1] 张少谱 JIN Yuxin;FENG Tao;WANG Rongxin;ZHANG Shaopu(College of Science,Hebei University of Science and Technology,Shijiazhuang 050018,P.R.China;Department of Mathematics and Physics,Shijiazhuang Tiedao University,Shijiazhuang 050043,P.R.China)

机构地区：[1]河北科技大学理学院,石家庄050018 [2]石家庄铁道大学数理系,石家庄050043

出　　处：《重庆邮电大学学报(自然科学版)》2025年第1期131-146,共16页Journal of Chongqing University of Posts and Telecommunications(Natural Science Edition)

基　　金：国家自然科学基金项目(62076088);河北省自然科学基金项目(A2020208004,A2021210027);河北省教育厅基金项目(QN2020196)。

摘　　要：区间值模糊覆盖作为等价类的一种推广,对客观世界的描述更加准确实用。区间值模糊数可以由均值拓展而得,使其更具有解释性,基于概率的思想,对区间值模糊集的概率和条件概率进行改进,提高了概率的精确度。在区间值模糊覆盖近似空间中利用区间模糊相似度构造了二元关系,建立了概率区间值模糊覆盖粗糙集模型,并得到了它的三分类结果。为了提高决策的准确性,研究了基于三描述的损失函数,并重新定义了期望损失函数。给出了确定模型参数的方法,基于贝叶斯最小风险决策理论建立了三支决策模型。通过实例验证了该模型的有效性。Interval-valued fuzzy covering,as a generalization of equivalence classes,provides a more accurate and practical description of the objective world.Interval-valued fuzzy numbers can be derived from mean extension,making them more interpretable.Based on probabilistic concepts,the probability and conditional probability of interval-valued fuzzy sets are improved,enhancing the accuracy of probability.In the interval-valued fuzzy covering approximation space,a binary relation is constructed using interval fuzzy similarity,and a probability interval-valued fuzzy covering rough set model is established,with its three-classification results obtained.To improve decision accuracy,a loss function based on three descriptions is studied,and the expected loss function is redefined.A method for determining the model parameters is provided,and a three-branch decision model is established based on Bayesian minimum risk decision theory.The effectiveness of the model is verified through examples.

关 键 词：粗糙集 区间值模糊概率 概率区间值模糊覆盖粗糙集 区间值模糊损失函数 三支决策 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] O225[自动化与计算机技术—控制科学与工程]