基于云模型与PROMETHEE方法的语言型Z-number多属性决策
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安徽大学数学科学学院,合肥 230601

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国家自然科学基金青年基金(61806001)资助项目; 国家自然科学基金面上基金(71871001)资助项目。


Linguistic Z-numbers Multi-attribute Decision-Making Method Based on Normal Cloud Model and PROMETHEE Method
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School of Mathematical Sciences, Anhui University, Hefei 230601, China

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    摘要:

    针对属性权重未知,属性值为语言型Z-number的多属性决策问题,提出了一种基于云模型与丰富度评估的偏好排序组织方法(Preference ranking organization method for enrichment evaluation, PROMETHEE)的决策方法。首先,引入语言尺度函数,然后利用其建立转化模型完成语言型Z-number向云模型的转化。此外,通过定义云可能度函数,建立属性权重求解公式及构建正弦偏好函数,进而计算方案的优先指数,通过计算方案的正负方向优序级别值得到备选方案综合优序级别值,进而得到方案排序。最后通过算例及比较分析验证本方法的有效性和可行性。

    Abstract:

    To solve the multi-attribute decision-making (MADM) problem in which the weights of the attributes are unknown under linguistic Z-numbers environment, a novel decision-making method based on normal cloud model and preference ranking organization method for enrichment evaluation (PROMETHEE) method is proposed. Firstly, the conversion model based on linguistic scale function is proposed to convert linguistic Z-numbers to normal cloud models. Then, this paper defines a new cloud likelihood function, and utilizes the proposed function to establish a weight formula to measure the importance of each attribute in MADM. Moreover, a sine preference function is designed to acquire the preference values of alternatives, and the positive, negative and net flow on the basis of aggregated preference values can be calculated, and the corresponding ranking result of each alternative is acquired. Finally, the validity and feasibility of the proposed method can be illustrated by the problem of air pollution potential evaluation and comparative analysis with other existing three methods.

    表 4 4种决策方法结果对比Table 4 Ranking results by the four methods
    表 2 各个方案之间的优先指数Table 2 Comparison of priority index of each alternative
    图1 Z-number Z1=(s3,s6)的标准云模型表示Fig.1 Z-number Z1 = (s3,s6) described by normal cloud
    表 1 专家语言型Z-number评价矩阵Table 1 Linguistic Z-number evaluation matrix given by the expert
    表 3 不同方案与理想间的相对贴近度值Table 3 Values of relative closeness between each alternative with ideal
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李燕飞,郭海艳,吴涛,毛军军.基于云模型与PROMETHEE方法的语言型Z-number多属性决策[J].数据采集与处理,2021,36(3):556-564

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  • 收稿日期:2020-07-28
  • 最后修改日期:2020-09-16
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  • 在线发布日期: 2021-06-16