基于直觉模糊决策粗糙集的三支决策  

Three-way Decisions with Intuitionistic Fuzzy Decision-theoretic Rough Sets

作　　者：李召 李磊军[1,2] 米据生 李美争[3] LI Zhao;LI Lei-jun;MI Ju-sheng;LI Mei-zheng(College of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,China;Hebei Key Laboratory of Computational Mathematics and Applications,Shijiazhuang 050024,China;College of Computer and Cyberspace Security,Hebei Normal University,Shijiazhuang 050024,China)

机构地区：[1]河北师范大学数学科学学院,河北石家庄050024 [2]河北省计算数学与应用重点实验室,河北石家庄050024 [3]河北师范大学计算机与网络空间安全学院,河北石家庄050024

出　　处：《模糊系统与数学》2022年第6期122-136,共15页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61502144,62076088,12101182);河北省高等学校科学技术研究项目(BJ2019014)。

摘　　要：基于决策粗糙集的三支决策是解决风险决策问题的一种经典方法,利用贝叶斯决策理论生成决策规则。决策规则具有正域、边界域、负域三个区域特征,对应的决策分别为接受决策、延迟决策和拒绝决策。本文将决策粗糙集模型对象之间的等价关系转变为具有自反性和对称性的直觉模糊关系,通过直觉模糊事件概率度量,定义了贝叶斯决策理论中对象状态与对象描述之间的条件概率。将决策损失与直觉模糊数相结合计算对象分类的预期损失,进而由贝叶斯决策理论引导的最小风险决策规则推导出相应的正域、负域、边界域的决策规则。当决策损失满足一定大小关系时将决策规则进行化简,计算出简化决策规则中的阈值与决策损失之间的关系,并且由简化决策规则定义了直觉模糊决策粗糙集的上、下近似。最后将构造的直觉模糊决策粗糙集的三支决策模型应用到直觉模糊概率决策系统,在已知的决策损失下得到相应的决策规则。Three-way decisions with decision-theoretic rough set is a classical method to solve risk decision problems, which uses Bayesian decision theory to generate decision rules. The decision rules have the characteristics of positive region, boundary region and negative region, and the corresponding decisions are acceptable decision, delayed decision and rejected decision. In this paper, the equivalence relation between objects in decision-theoretic rough set model is transformed into the intuitionistic fuzzy relation with reflexivity and symmetry. Through the intuitionistic fuzzy event probability measure, the conditional probability between object state and object description in Bayesian decision theory is defined. The decision losses and intuitionistic fuzzy numbers are combined to calculate the expected losses of object classification, and then the corresponding decision rules of positive region, negative region and boundary region are derived by the minimum risk decision rule guided by Bayesian decision theory. When the decision losses meet a certain relationship, the decision rules are simplified, the relationship between the threshold and the decision loss in the simplified decision rules is calculated, and the upper and lower approximations of intuitionistic fuzzy decision-theoretic rough sets are defined by the simplified decision rules. Finally, the constructed model of three-way decisions with intuitionistic fuzzy decision-theoretic rough set was applied to the intuitionistic fuzzy probabilistic decision system, and the corresponding decision rules were obtained under the known decision loss.

关 键 词：决策粗糙集 三支决策 直觉模糊数 贝叶斯决策理论 直觉模糊事件概率度量 

分 类 号：O159[理学—数学]