基于前景理论的毕达哥拉斯模糊有序加权距离TOPSIS法  

Pythagorean Fuzzy Ordered Weighted Distance TOPSIS Based on Prospect Theory

作　　者：李美娟 卢锦呈[1] 蔡猷花 LI Meijuan;LU Jincheng;CAI Youhua(School of Economics&Management,Fuzhou University,Fuzhou 350108;Funding for Research Center of Fujian Economic High Quality Development Based on Social Science Planning of Fujian Province in China,Fuzhou 350108)

机构地区：[1]福州大学经济与管理学院,福州350108 [2]福建省社科研究基地福州大学福建经济高质量发展研究中心,福州350108

出　　处：《系统科学与数学》2021年第5期1291-1304,共14页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金项目(71872047);国家社科基金(18BGL121);福建省社会科学规划项目(FJ2018B029,FJ2019B086);福建省高校领军人才资助课题。

摘　　要：针对现有毕达哥拉斯模糊有序加权距离测度法在集结距离测度时忽略决策者主观偏好的问题,文章引入前景理论来反映决策者面临损失和收益时的主观价值感受,根据不同类型决策者构建了基于前景理论的毕达哥拉斯模糊有序加权距离测度方法(PTPFOWD),并构建了基于均衡视角的权重修正系数,以防止过度依赖决策者主观偏好造成的偏误,尽可能保留原始数据中的客观信息;同时,讨论了PTPFOWD与现有距离测度之间的联系,证明了相关定理.在此基础上,将PTPFOWD引入到TOPSIS法中,提出了基于PTPFOWD的TOPSIS法,以实现对多样性信息进行有序的集结.最后,通过实证分析来验证方法有效性.The existing methods of determining the weights for ordered weighted distance(OWD)depend on either the intrinsic information contained in original data and positional relationship or average weights.However,average weights may lead to the loss of lots of decision information,and focusing on intrinsic information would ignore the preference of decision maker(DM).To handle these deficiencies,the prospect theory is introduced to reflect the subjective value perception of DMs when facing the losses and gains,and the Pythagorean fuzzy ordered weighted distance based on prospect theory(PTPFOWD)is constructed depending on different types of DMs.Additionally,to avoid the deviation derived from the over-reliance on the preference of DMs,the weight correction coefficient based on equilibrium perspective is constructed,which is able to reflect objective information in the original data as much as possible.Moreover,the relationship between existing distance measures and PTPFOWD is discussed,and the relevant theorems are proved.And then,the proposed PTPFOWD is introduced to TOPSIS to achieve an orderly aggregation of diversity information.Finally,an empirical analysis is applied to verify the effectiveness of the proposed methods.

关 键 词：毕达哥拉斯模糊集 前景理论 有序加权距离 理想解法 

分 类 号：O159[理学—数学] O225[理学—基础数学]