基于距离测度的区间粗糙模糊数多属性决策方法  

Interval Rough Fuzzy Number Multiple Attribute Decision Making Method Based on Distance Measurement

作　　者：翁世洲 吕跃进[2,3] 曹志强 WENG Shi-zhou;LV Yue-jin;CAO Zhi-qiang(Department of Economic and Management,Guangxi Normal University for Nationalities,Chongzuo532200,China;College of Mathematics and Information Sciences,Guangxi University,Nanning 530004 China;Department of Mathematics and Physics,Liuzhou Institute of Technology,Liuzhou 545616,China)

机构地区：[1]广西民族师范学院经济与管理学院,广西崇左532200 [2]广西大学数学与信息科学学院,广西南宁530004 [3]柳州工学院数理教学部,广西柳州545616

出　　处：《模糊系统与数学》2022年第3期131-144,共14页Fuzzy Systems and Mathematics

基　　金：国家社科基金资助项目(21XGL016);广西民族师范学院校级科研项目(2020YB007);广西高校中青年教师基础能力提升项目(2022KY0764,2020KY20012)

摘　　要：将模糊集理论与区间粗糙数融合,提出了区间粗糙模糊数的概念,并定义了区间粗糙模糊数的运算法则。为对区间粗糙模糊数进行比较及排序,定义了区间粗糙模糊数的上近似距离和下近似距离,每个距离下分别讨论了最大、最小和平均三种情形,并通过调节因子α将上近似距离和下近似距离集成为区间粗糙模糊数的距离。为解决区间粗糙模糊数形式下的多属性决策问题,定义了信息系统的最优解、最劣解、正距离、负距离、优势度等概念,并借助熵权法确定属性权重,给出对象的加权综合优势度及排序结果。算例结果表明,最大距离、最小距离和平均距离三种情形下得到的结果无显著差异,且与决策者主观认知基本一致,验证了算法的合理性与稳健性。Combining fuzzy set theory with interval rough numbers,the concept of interval rough fuzzy numbers is proposed,and the calculation rule of interval rough fuzzy numbers is defined.In order to compare and sort different interval rough fuzzy numbers,the upper approximate distance and the lower approximate distance are determined,for each distance,three cases of maximum,minimum and average are discussed separately,and the upper approximate distance and the lower approximate distance are integrated into the distance of the interval rough fuzzy numbers through the adjustment factorα.In order to solve the multi-attribute decision-making problem in the form of interval rough fuzzy numbers,concepts such as the optimal solution,the worst solution,positive distance,negative distance,and dominance degree of the information system are defined,and the attributes weight are determined by the entropy weight method,and the weighted comprehensive dominance degree and ranking results of objects are given subsequently.The example demonstration show that the results obtained under the maximum distances,minimum distances and average distances are not significantly different,and are basically consistent with the subjective cognition of the decision maker,which verifies the rationality and robustness of the algorithm.

关 键 词：区间粗糙模糊数 上近似距离 下近似距离 综合优势度 排序方法 多属性决策 

分 类 号：C934[经济管理—管理学]