IPOWA算子及其在正态随机多准则决策中的应用  

IPOWA Operator and Its Application in Normal Stochastic Multi-Criterion Decision-Making

作　　者：任剑[1,2] 成鹏飞[3] 周向红[3] CHENG Pengfei;REN Jian;ZHOU Xianghong(School of Business, Hunan University, Changsha 410082, China;Mobile E-business Collaborative Innovation Center of Hunan Province, Hunan University of Commerce, Changsha 410205, China;School of Management, Hunan University of Science and Technology, Xiangtan, Hunan 411201, China)

机构地区：[1]湖南大学工商管理学院,长沙410082 [2]湖南商学院湖南省移动电子商务协同创新中心,长沙410205 [3]湖南科技大学管理学院,湖南湘潭411201

出　　处：《计算机科学与探索》2017年第1期155-162,共8页Journal of Frontiers of Computer Science and Technology

基　　金：国家社会科学基金;教育部人文社会科学研究青年基金;中国博士后科学基金;湖南省哲学社会科学基金;湖南省社会科学成果评审委员会重大课题;湖南省教育厅科学研究优秀青年项目~~

摘　　要：现实中,很多现象近似服从正态分布。为了解决准则值为正态随机变量且决策者风险态度不确定的多准则决策问题,提出了一种基于区间可能有序加权平均(interval possible ordered weighted averaging,IPOWA)算子与可能性系数的方法。通过正态随机变量的线性组合方法,算出各方案的线性加权正态随机变量。根据正态随机变量的3σ原则,将线性加权正态随机变量转化为随机区间数。对随机区间数进行两两比较,得到可能度矩阵,利用区间可能有序加权平均算子,集结可能度矩阵中每行元素的值。采用风险态度的可能性系数,计算各方案的综合评价值,进而确定各方案的最终排序。最后,通过两个算例的对比分析,表明所提方法具有排序结果稳定,支持信息充分等特点。In reality, most of the phenomena can approximately obey the normal distribution. In order to solve multicriterion decision-making problems with normal stochastic criterion evaluations and uncertain risk attitude of decision makers, this paper proposes a method based on interval possible ordered weighted averaging (IPOWA) operator and possibility coefficients. Firstly, by the linear combination method of normal stochastic variables, the linear weighted normal stochastic variables of alternatives are gotten. Then, according to the 3σ principle of normal stochastic variables, the linear weighted normal stochastic variables are transformed into stochastic interval numbers.Furthermore, through the comparison of stochastic interval numbers, the possible degree matrix is attained. After that, using the IPOWA operator, the items of each row are integrated in the matrix. Accordingly, via the possibility coefficients of risk attitudes, the comprehensive evaluation values of alternatives are calculated. Moreover, the ranking order comes out. Finally, the comparative analysis of two illustrative examples shows the method has some features such as stable ranking result, sufficient support information and so on.

关 键 词：多准则决策 正态随机变量 区间可能有序加权平均算子 可能度矩阵 风险态度的可能性系数 

分 类 号：C934[经济管理—管理学]