| 基于距离与关联系数的概率语言群决策方法 |
| Probabilistic linguistic group decision-making method based on the distance and relational coefficient |
| 摘要点击 78 全文点击 0 投稿时间：2025-01-24 修订日期：2025-09-15 |
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| 中文关键词 概率语言术语集; 多属性群决策; 平方和距离; 专家权重; 灰色关联分析法 |
| 英文关键词 probabilistic linguistic term sets; multi-attribute group decision making; sum of squares distance; expert weight; grey relational analysis method |
| 基金项目 国家社会科学基金后期资助项目（项目编号20FGLB023） |
| 投稿方向 决策 |
| 作者 | 单位 | 邮编 | | Tian Jing-Feng | 华北电力大学数理系 | 071003 | | 王紫祎 | 华北电力大学数理系 | | | 哈明虎* | 河北工程大学数理科学与工程学院 | 056038 |
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| 中文摘要 |
| 由于已有的概率语言多属性群决策(PL-MAGDM)方法既未讨论用概率语言术语集中的内部元素与均值之间的偏差来度量两个概率语言术语集间的距离, 也未考虑概率语言环境下专家之间的关联系数. 因此, 本文进一步研究了PL-MAGDM问题. 首先, 给出了概率语言术语集离差平方和的定义, 据此构建了概率语言术语集间的平方和距离和概率语言矩阵间的距离测度. 其次, 基于灰色关联分析的思想和概率语言矩阵间的距离测度, 定义了专家之间的关联系数, 提出了基于关联系数确定专家权重的方法. 再次, 将平方和距离应用到离差最大化法中确定属性权重, 应用到概率语言灰色关联分析法中求解最优方案. 最后, 以上述为基础, 提出了基于距离(即平方和距离)与关联系数的PL-MAGDM方法, 并通过绿色供应商的案例验证了所提方法的有效性与可行性, 该方法也可为其他面临不确定决策情境的问题提供可行的参考方法. |
| 英文摘要 |
| Since the existing probabilistic linguistic multi-attribute group decision-making (PL-MAGDM) methods neither discuss measuring the distance between two probabilistic linguistic term sets using the deviation between internal elements and the mean, nor consider the relational coefficient among experts in the probabilistic linguistic environment, this paper further studies the PL-MAGDM problem. Firstly, the definition of the sum of squared deviations of a probabilistic linguistic term set is given, and based on this, the sum of squared distances between probabilistic linguistic term sets and the distance measure between probabilistic linguistic matrices are constructed. Secondly, based on the idea of grey relational analysis and the distance measure between probabilistic linguistic matrices, the relational coefficient among experts is defined, and a method for determining the expert weights based on the relational coefficient is proposed. Thirdly, the sum of squared distances is applied to the deviation maximization method to determine the attribute weights and to the probabilistic linguistic grey relational analysis method to solve the optimal solution. Finally, based on the above, a PL-MAGDM method based on distance (sum of squares distance) and relational coefficient is proposed, and the effectiveness and feasibility of the proposed method are verified through a case of green suppliers. This method can also provide a feasible reference method for other problems facing uncertain decision-making situations. |
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