基于属性关联的三角毕达哥拉斯模糊TOPSIS法  

Triangular Pythagorean Fuzzy TOPSIS Method Based on Interacting Attributes

作　　者：杜迎雪[1] 刘卫锋[1] 常娟[1] DU Ying-xue;LIU Wei-feng;CHANG Juan(School of Mathematics,Zhengzhou University of Aeronautics,Zhengzhou 450015,China)

机构地区：[1]郑州航空工业管理学院数学学院,河南郑州450015

出　　处：《数学的实践与认识》2021年第10期11-21,共11页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11501525);河南省杰出青年基金项目(2018JQ0004);河南省高等学校重点科研项目(20A110035);河南省高等学校重点科研项目计划基础研究专项(20zx003);郑州航院青年科研基金资助项目(2016113003)。

摘　　要：针对属性值为三角毕达哥拉斯模糊数,且属性之间有关联的多属性决策问题,提出了基于属性关联的三角毕达哥拉斯模糊TOPSIS法.首先,利用有序加权距离和三角毕达哥拉斯模糊数之间的距离,定义了三角毕达哥拉斯模糊集距离、三角毕达哥拉斯模糊集加权距离和三角毕达哥拉斯模糊有序加权距离等概念;当属性之间相互关联时,进而引入三角毕达哥拉斯模糊Choquet积分距离与三角毕达哥拉斯模糊广义Choquet积分距离;然后,将传统的TOPSIS法与Choquet积分距离相结合,提出属性关联的三角毕达哥拉斯模糊TOPSIS法,且通过分析各方案与正负理想之间的相对贴近度排序择优.最后,通过实例说明该方法的有效性与可行性.In view of the multi-attribute decision-making problem that the attribute value is triangular Pythagorean fuzzy number and the attributes are related,a triangular Pythagorean fuzzy TOPSIS method based on attribute association is proposed Firstly,Firstly,by using the distance between the ordered weighted distance and the triangular Pythagoras fuzzy number,the concepts of the triangular Pythagoras fuzzy set distance,the triangular Pythagoras fuzzy set weighted distance and the triangular Pythagoras fuzzy ordered weighted distance are defined.When the attributes are related to each other,the triangular Pythagorean fuzzy Choquet integral distance and triangular Pythagorean fuzzy ordered weighted Choquet integral distance are introduced;Then,the traditional TOPSIS method and Choquet integral integration distance are combined to give the steps of attribute related triangular Pythagorean fuzzy multi-attribute decision-making TOPSIS method,and through the analysis of the relative closeness degree between each scheme and positive and negative ideas,the optimization is selected;finally,the effectiveness of this method is illustrated by an example Feasibility.

关 键 词：毕达哥拉斯模糊集 三角毕达哥拉斯模糊数 TOPSIS法 CHOQUET积分 决策 

分 类 号：O225[理学—运筹学与控制论] O159[理学—数学]