基于毕达哥拉斯模糊数双向投影的VIKOR决策方法  

VIKOR Decision Making Method Based on Bidirectional Projection of Pythagorean Fuzzy Numbers

作　　者：罗静[1] 沈淑霞 王贵君[1] LUO Jing;SHEN Shu-xia;WANG Gui-jun(School of Mathematics Sciences,Tianjin Normal University,Tianjin 300387,China;Business School,City College of Dongguan University of Technology,Dongguan 523419,China)

机构地区：[1]天津师范大学数学科学学院,天津300387 [2]东莞理工学院城市学院商学院,广东东莞523419

出　　处：《模糊系统与数学》2022年第1期1-10,共10页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61374009)。

摘　　要：毕达哥拉斯(Pythagorean)模糊集(PFS)不仅是传统直觉模糊集的一种推广,而且它能在更广泛的区域上处理多属性模糊信息的决策问题,尤其是通过正、负理想值的投影更能有效地发挥作用。本文首先回顾了Pythagorean模糊数(PFN)的基本定义和相关运算,并基于PFN和最小元(0,1)的距离作比较提出PFN、PFS的模和投影概念,进而讨论该模的基本性质。其次,针对传统VIKOR决策方法的缺陷(只考虑正理想值刻画模糊信息)引入正、负理想值的双向投影概念,并根据双向投影给出新的群体效用值、个体遗憾值、折衷评价值、熵权和权重的数学表示。最后,依据毕达哥拉斯模糊数的双向投影提出新的VIKOR决策方法,并依据实例验证新的VIKOR决策方法的有效性。Pythagorean fuzzy sets(PFS) are not only a generalization of traditional intuitionistic fuzzy sets, but also can deal with the decision-making problems of multi-attribute fuzzy information in a wider area. Especially, by projecting positive and negative ideal value, it can play a more effective role. In this paper, the basic definition and related operations of Pythagorean fuzzy number(PFN) are first reviewed, the concepts of module and projection of PFS are proposed by the close distance between PFN and minimum element(0,1), and then the basic properties of this module are discussed. Secondly, aiming at some defects of traditional VIKOR decision-making method(only considering positive ideal value to describe fuzzy information), the concept of bidirectional projection of positive and negative ideal value is introduced, some new mathematical expressions of the group utility value, individual regret value, compromise evaluation value, entropy weight and weight are given by two-way projection. Finally, a new VIKOR decision-making method is put forward by the bidirectional projection of Pythagorean fuzzy numbers, and the effectiveness of the proposed method is verified by an example.

关 键 词：毕达哥拉斯模糊数(PFN) 模 双向投影 正、负理想值 VIKOR决策方法 

分 类 号：O159[理学—数学]