基于语言值软集的多准则群决策方法及其应用  

Multiple Criteria Group Decision Making Method Based on Linguistic Value Soft Set and Its Application

作　　者：张家录 吴霞 ZHANG Jia-lu;WU Xia(College of Mathematics and Finance,Xiangnan University,Chenzhou 423000,China)

机构地区：[1]湘南学院数学与金融学院,湖南郴州423000

出　　处：《模糊系统与数学》2020年第4期122-132,共11页Fuzzy Systems and Mathematics

基　　金：湖南省哲学社会科学基金资助项目(16YBA329)。

摘　　要：在语言值评估集上引进适当的运算,建立语言值逻辑代数系统,并利用虚拟术语指标不丢失信息的特点,扩展语言值逻辑代数系统为连续语言值逻辑代数系统。通过加权平均算子将全部专家对各决策方案的语言值评估信息集结,得到专家群对全部决策方案就全部准则的集中评估,全部集中评估值构成决策方案上的语言值软集。建立优化模型计算最优准则权重,利用最优准则权重将专家关于各准则的语言值评估结果进行集结,得到各专家对全部决策方案的评估值,评估值全体可看成专家群上的语言值软集,这里参数集为决策方案集。建立基于决策方案上的语言值软集的粗糙近似模型——语言值粗糙近似模型,通过计算各专家对全部决策方案的评估值关于语言值粗糙近似模型的下近似和上近似,得到专家群上的语言值下近似软集和上近似软集。通过对全部决策方案评估集及其语言值粗糙下近似、上近似进行加权算术平均,分别得到三个决策方案上的语言值模糊集。通过三个语言值模糊集对全部决策方案排序。最后,应用基于语言值软集的多准则群决策方法对电子商务监管系统安全进行多准则综合决策评估,说明本文提出的多准则群决策方法是有效的和合理的。In this paper,the problem of multiple criteria group decision making with linguistic attribute values is studied. Some operations in evaluation set of linguistic value are introduced, a linguistic value logic algebra system is established. By used the feature that virtual term index does not lose information the linguistic value logic algebra system to a continuous linguistic value logic algebra system is extended. Used of the weighted average operator, the linguistic evaluation information of all experts for each decisions is aggregated, and a centralized evaluation for every decisions for every criteria by experts group is obtained. All centralized evaluation values constitute a linguistic soft set over the decisions set. The optimization model is established for computing the optimal criteria weight, the linguistic evaluation results of all experts for each criterion are aggregated by using the optimal criteria weight, and then the evaluation values of all decisions are obtained. The evaluation values can be regarded as a linguistic value soft set over the expert group, where the parameter set is the decisions set. Based on the linguistic value soft set over the decisions set, the rough approximation model is established. By computing the lower approximation and upper approximation of the evaluation value of all the decisions given by every expert, the lower approximation soft set and upper approximation soft set with linguistic value over expert groups are then formed. By weighted arithmetic mean of the evaluation sets of all decisions and their linguistic rough lower approximation and upper approximation, three linguistic value fuzzy sets are obtained respectively. All decisions are sorted by used of three linguistic value fuzzy sets. Finally, the effectiveness and rationality of the method is verified by the case study of the multiple criteria comprehensive decision evaluation of the security of e-commerce regulatory system.

关 键 词：虚拟术语指标 语言值软集 语言值粗糙近似模型 语言值下近似和上近似 多准则群决策 电子商务监管系统 

分 类 号：C934[经济管理—管理学] F274