基于D-S证据理论的三支决策推理模型  

Three-way Decision Inference Models Based on Dempster-Shafer Evidence Theory of Evidence

作　　者：张春英 冯晓泽 刘凤春 高瑞艳 任静 ZHANG Chun-ying;FENG Xiao-ze;LIU Feng-chun;GAO Rui-yan;REN Jing(College of Science,North China University of Science and Technology,Tangshan 063210,China;College of Qianan,North China University of Science and Technology,Tangshan 063210,China;Key Laboratory of Data Science and Application in Hebei Province,Tangshan 063210,China)

机构地区：[1]华北理工大学理学院,河北唐山063210 [2]华北理工大学迁安学院,河北唐山063210 [3]河北省数据科学与应用重点实验室,河北唐山063210

出　　处：《模糊系统与数学》2020年第6期85-98,共14页Fuzzy Systems and Mathematics

基　　金：河北省自然科学基金资助项目(F2018209374,F2016209344)。

摘　　要：三支决策是基于粗糙集的正域、负域和边界域提出的一种决策模型,D-S证据理论是基于基本概率分配函数融合多个证据进行决策推理的方法,两者都是处理不确定数据的方法。本文针对现实决策中往往有多种因素的复杂推理问题,提出构建基于D-S证据理论的三支决策推理模型。首先,讨论D-S证据理论与粗糙集理论的关系,利用粗糙集理论获取证据的基本概率分配函数;然后重新定义一个新的函数—信任程度函数,将经典三支决策中的条件概率函数替代,建立基于D-S证据理论的三支决策推理模型;其次,通过调节信任系数的取值,得到适合不同风险类型决策者的决策推理规则;最后,通过实例验证了模型的有效性和可行性。The three-way decision is a new decision model based on the rough set’positive,negative and boundary domain.Dempster-Shafer evidence theory(D-S evidence theory)is a method based on the basic probability assignment function to fuse multiple evidences for decision reasoning.Both are methods of dealing with uncertain data.For the complex reasoning problem that often has many factors in real decision making,the paper proposes a three-way decision inference model based on D-S evidence theory.Firstly,the relationship between D-S evidence theory and rough set theory is discussed,and the basic probability assignment function of evidence is obtained by rough set theory.Secondly,redefine a new function-trust degree function,replace the conditional probability function in the classic three-way decision,and establish a three-way decision inference model based on D-S evidence theory.Thirdly,by adjusting the value of trust coefficient,the decision inference rules suitable for decision makers of different risk types are obtained.Finally,an example is presented to verify the effectiveness and feasibility of this model.

关 键 词：D-S证据理论 粗糙集 三支决策 信任函数 信任系数 

分 类 号：O159[理学—数学]