基于粗糙集定义区间数环境下专家权重的新方法

摘要

Multiple attribute group decision-making (MAGDM) has become an emerging research area.How to determine the weights of experts is a fundamental topic.This paper presents a novel approach with a rough set group method,to determine the weights of decision makers (DMs),in which the decision information of each decision maker (DM) is expressed by a matrix of interval numbers.In this paper,we firstly build a lower rough group decision (LRGD) and an upper rough group decision (URGD) based on the rough group decision.Then we define a Lower positive ideal solution (Lower PIS) as the average matrix of LRGD and Upper positive ideal solution (Upper PIS) as the average matrix of URGD.The PIS is the average matrix of Lower PIS and Upper PIS,meanwhile,the negative ideal solution (NIS) has the maximum separation from positive ideal solution.After that,we define the weight of each DM by distances from DM's decision to PIS and NIS.Finally,an example "airquality monitoring stations" is provided to illustrate the calculation process of the propesed approach in details.%专家权重在多属性组决策问题中起到重要的作用,如何衡量专家的权重一直以来都是研究热点.提出一种基于粗糙集来定义区间数环境中专家权重的方法.首先建立一个粗糙群组下决策(LRGD)和一个粗糙群组上决策(URGD).然后,定义LRGD的区间中值矩阵为下理想决策(Lower PIS),URGD的区间中值矩阵为上理想决策(Upper PIS).正理想决策(PIS)是Lower PIS和Upper PIS的区间中值矩阵,同时,负理想决策(NIS)对正理想决策存在最远的欧式距离.之后,利用专家决策到PIS和NIS的欧式距离,得出专家权重.由“空气质量监测站”的算例来阐明提出方法的详细实施步骤.