基于累积效应的区间粗糙数距离  

Interval Rough Number Distance Based on Cumulative Effects

作　　者：颜廷娇 吕跃进[1] 杨少康 

机构地区：[1]广西大学数学与信息科学学院,广西南宁530004

出　　处：《模糊系统与数学》2018年第1期1-9,共9页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(71361002)

摘　　要：区间粗糙数是一种新的用来描述不确定问题的不确定数,合理定义两个区间粗糙数之间的距离成为解决属性值为区间粗糙数的多属性决策问题的重要组成部分。本文基于集合的思想建立区间粗糙数与区间数之间的联系,进而基于累积效应构建新的区间粗糙数之间的距离,证明新定义满足距离的三个公理化条件,并示例说明新定义的距离相较于原有距离的优越性。最后将新定义的距离与基于贴近度的理想解法相结合应用到属性值为区间粗糙数的多属性决策问题中,并以数值实验验证其可行性。The interval rough number is a new kind of uncertain numbers which is used to describe the fuzzy problem. It is an important part to define the distance between two interval rough numbers in the multiple attribute decision making problems which the attribute values are in the forms of interval rough numbers. Based on the idea of the set, the relationship between the interval rough number and the interval number is established, and the distance between two interval rough numbers is construc- ted based on the cumulative effects. In addition, the distance is proved to meet the three axioms of distance, and the example illustrates the superiority of the new distance compared to the existing dis- tance. Finally, the new distance is combined with the TOPSIS method to solve the multiple attribute decision making problems, and the numerical experiment is used to verify its feasibility.

关 键 词：区间粗糙数 区间数 距离 理想解法 多属性决策 

分 类 号：TP391[自动化与计算机技术—计算机应用技术] C934[自动化与计算机技术—计算机科学与技术]