| 基于偏序集的PROMETHEE方法优化研究 |
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| 引用本文： | 张飞,岳立柱,王国辉.基于偏序集的PROMETHEE方法优化研究[J].运筹与管理,2020,29(1):10-16. |
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| 作者姓名： | 张飞 岳立柱 王国辉 |
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| 作者单位： | 1. 辽宁工程技术大学 公共管理与法学院,辽宁 阜新 123000;2. 辽宁工程技术大学 工商管理学院,辽宁 葫芦岛 125105;3. 辽宁省重要技术创新与研发基地建设工程中心,辽宁 沈阳 110000 |
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| 基金项目： | 国家社科基金资助项目(17BSH076);辽宁省教育厅科学研究项目(LJ2019JW002) |
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| 摘 要： | 尽管PROMETHEE是当前最受欢迎的多准则决策方法之一,但在实践应用过程中,模型的应用范围与质量依然受制于指标权重问题。一些常用的赋权方法,不仅没有解决不确定权重问题,反而增加了决策风险。在偏序集相关定理的基础上,给出权重的定性信息即权重次序,由流出矩阵、流入矩阵和净流矩阵等定义,得到了PROMETHEE的偏序集表达形式。当流入和流出之和为常数时,证明了模型存在对偶性质。根据对偶性质,简化了PROMETHEE方法的分析步骤,删减模型冗余信息。应用偏序集表示的PROMETHEE,突破了模型没有具体权重便无法应用的思维定势,解决了模型赋权困难,增强了模型的鲁棒性,拓展了模型处理数据类型的范围。
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| 关 键 词： | PROMETHEE 偏序集 权重 HASSE图 |
| 收稿时间： | 2018-05-31 |
Study on PROMETHEE Method Optimization Based on Poset |
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| ZHANG Fei,YUE Li-zhu,WANG Guo-hui.Study on PROMETHEE Method Optimization Based on Poset[J].Operations Research and Management Science,2020,29(1):10-16. |
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| Authors: | ZHANG Fei YUE Li-zhu WANG Guo-hui |
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| Affiliation: | 1. Department of Public Administration and Law of LiaoNing Technical University, FuXin 123000, China;2. College of Business Administration, LiaoNing Technical University, HuLudao 125105, China;3. LiaoNing Important Technology Innovation and R&D Base Construction Engineering Center, ShenYang 110000, China |
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| Abstract: | Although PROMETHEE is one of the most popular multi-criteria decision making methods at present, its application scope and quality are still subject to the index weight in the practical application. Some frequently-used weighting methods not only fail to solve the problem of uncertain weight, but also increase the decision-making risk. On the basis of the correlation theorems of Poset, coupled with the qualitative information of weight-weight order, the Poset expression of PROMETHEE is obtained by means of such definitions as outflow matrix, inflow matrix and net current matrix. If the sum of inflow and outflow is constant, it proves that the model has the duality. According to the dual nature, the analysis steps of the PROMETHEE method are simplified with the redundant information deleted. The PROMETHEE model expressed by Poset breaks the mind-set that the method cannot be used without specific weights, with the difficulty of model weighting overcome. Meanwhile, it also enhances the robustness of the model and expands the data type scope. |
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| Keywords: | PROMETHEE Poset weight HASSE map |
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