基于交叉熵和Shapley值的犹豫模糊多属性决策方法  

ethod for Multiple Attribute Decision Making Based On Shapley Value and Cross-entropy with Hesitant Fuzzy Set

作　　者：于倩 侯福均[2] 曹俊 廖娅 YU Qian;HOU Fu-jun;CAO Jun;LIAO Ya(School of Business and Administration,Chongqing University of Science&Technology,Chongqing 401331,China;School of Management and Economics,Beijing Institute of Technology,Beijing 100081,China)

机构地区：[1]重庆科技学院工商管理学院,重庆401331 [2]北京理工大学管理与经济学院,北京100081

出　　处：《运筹与管理》2019年第11期60-67,共8页Operations Research and Management Science

基　　金：重庆市教委科技项目(KJQN201901505);重庆市教委重点项目(19SKGH181)

摘　　要：针对属性值以犹豫模糊集形式给出的多属性决策问题,将Shapley理论和模糊测度进行结合,提出了两种更加能全面融合信息的诱导型广义犹豫模糊混合Shapley平均(I-GHFHSA)算子和诱导型广义犹豫模糊混合Shapley几何(I-GHFHSG)算子,同时详细研究了它们的相关特性。这两种算子综合考虑了数据不同组合的重要性、数据间的关联性,以及数据位置之间的相互依赖性。考虑到有时会存在属性权重以及数据位置权重未知的多属性决策问题,将交叉熵理论和Shapley函数进行结合,建立了最优模糊测度确定模型。最后提出了一种基于I-GHFHSA算子和I-GHFHSG算子的犹豫模糊多属性决策方法,并通过实际案例验证了其可行性和合理性。Based on the combination of Shapley theory and fuzzy measures, an induced generalized hesitant fuzzy hybrid Shapley average(I-GHFHSA)operator and an induced generalized hesitant fuzzy hybrid Shapley geometric(I-GHFHSG)operator are proposed for hesitant fuzzy multi-attribute decision making to utilize information more completely. And some related properties of these operators are studied in detail. The proposed operators can not only globally reflect the interactive characteristics among the hesitant fuzzy arguments themselves and their ordered positions,but also consider the importance of the arguments and their ordered positions. Moreover, considering the existence of the situations where the fuzzy measures of attributes and ordered set are incompletely known,a series of programming models based on cross-entropy and Shapley function are constructed to determine the optimal fuzzy measures. Furthermore, a multi-attribute decision making approach in the form of hesitant fuzzy information based on the proposed operators is presented. Finally, an illustrative example is used to verify the feasibility and rationality of the method.

关 键 词：多属性决策 Shapley函数 模糊测度 犹豫模糊集 交叉熵 

分 类 号：C934[经济管理—管理学]