直觉模糊集的Choquet积分相关测度及其决策应用  

Choquet integral correlation measures of intuitionistic fuzzy sets and its application in decision making

作　　者：刘卫锋[1] 何霞[1] 常娟[1] LIU Wei-feng;HE Xia;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

出　　处：《控制与决策》2019年第9期1937-1945,共9页Control and Decision

基　　金：国家自然科学基金青年基金项目(11501525);河南省杰出青年基金项目(2018JQ0004);航空科学基金项目(2016ZD55019);河南省高等学校重点科研项目(18A110032)

摘　　要：Qu给出的直觉模糊集的Choquet积分相关系数的计算公式与相关系数的性质相矛盾.为此,通过一个实例说明Qu定义的直觉模糊Choquet积分相关系数定义存在的问题,并结合相关系数的性质证明,分析问题出现的原因;然后,针对存在的问题,以直觉模糊集的Choquet积分相关指标为基础,给出新的直觉模糊集的Choquet积分信息能量的概念,定义新的直觉模糊集的Choquet积分相关系数,并讨论相关系数的性质;最后,利用新定义的直觉模糊集的Choquet积分相关测度,推导出方案与正理想方案之间的Choquet积分相关系数计算公式,据此提出一种直觉模糊多属性决策方法,并通过实例分析以及方法对比,说明所提出方法的可行性和有效性.The Choquet integral correlation coefficient between intuitionistic fuzzy sets and the computing formula are obtained by Qu, but the results have contradiction with the nature of the Choquet integral correlation coefficient between intuitionistic fuzzy sets. It is found from the practical example that the range of the Choquet integral correlation coefficient between intuitionistic fuzzy sets is not appropriate, and through the study on the proof of its nature of the Choquet integral correlation coefficient, the cause of the problem existed is analyzed. Then based on the Choquet integral correlation of intuitionistic fuzzy sets, the new Choquet integral information energy of the intuitionistic fuzzy set and the Choquet integral correlation coefficient between intuitionistic fuzzy sets are defined, and their natures are also discussed. Finally, the Choquet correlation coefficient between the alternative and the positive ideal alterative is derived, and a method is developed to solve the multiple attribute decision making problem using the Choquet correlation coefficient, and an example is used to illustrate the feasibility and effectiveness of the proposed method.

关 键 词：直觉模糊集 相关系数 模糊测度 CHOQUET积分 决策 应用 

分 类 号：O223[理学—运筹学与控制论] C934[理学—数学]