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《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (3): 118-126.doi: 10.6040/j.issn.1671-9352.7.2023.4667

•   • 上一篇    

基于改进距离测度的概率犹豫模糊多属性群决策新方法

刘梦迪1,2(),张贤勇1,2,*(),莫智文1,2   

  1. 1. 四川师范大学数学科学学院, 四川 成都 610066
    2. 四川师范大学智能信息与量子信息研究所, 四川 成都 610066
  • 收稿日期:2023-04-26 出版日期:2024-03-20 发布日期:2024-03-06
  • 通讯作者: 张贤勇 E-mail:719867875@qq.com;xianyongzh@sina.com
  • 作者简介:刘梦迪(1999—), 女, 硕士研究生, 研究方向为模糊集理论与决策分析. E-mail: 719867875@qq.com
  • 基金资助:
    四川省科技计划资助项目(2021YJ0085);四川省科技计划资助项目(2022ZYD0001);四川省自然科学基金资助项目(24NSFSCI1487);四川省自然科学基金资助项目(2022NSFSC0929)

A new probabilistic hesitant fuzzy multi-attribute group decision making method based on improved distance measures

Mengdi LIU1,2(),Xianyong ZHANG1,2,*(),Zhiwen MO1,2   

  1. 1. School of Mathematical Sciences, Sichuan Normal University, Chengdu 610066, Sichuan, China
    2. Institute of Intelligent Information and Quantum Information, Sichuan Normal University, Chengdu 610066, Sichuan, China
  • Received:2023-04-26 Online:2024-03-20 Published:2024-03-06
  • Contact: Xianyong ZHANG E-mail:719867875@qq.com;xianyongzh@sina.com

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摘要：

针对概率犹豫模糊环境下属性权重已知的多属性群决策问题, 考虑概率犹豫模糊集的犹豫度, 提出基于改进距离测度的概率犹豫模糊多属性群决策新方法。结合传统的概率犹豫模糊距离测度, 通过信息融合定义融入犹豫度的概率犹豫模糊距离测度: 汉明距离、欧氏距离、广义欧氏距离, 并通过组合系数来实现理论扩张和融合优化, 同时研究距离测度的大小关系及参数单调性。将融入犹豫度的距离测度与基于理想解相似度的逼近理想解排序法(technique for order preference by similarity to ideal solution, TOPSIS)结合构建多属性群决策新方法, 采用公司选址案例进行决策选择, 通过参数分析和决策比较来揭示所建方法的有效性。相关研究系统深化概率犹豫模糊距离测度, 并丰富了多属性群决策方法。

关键词: 多属性群决策, 概率犹豫模糊集, 犹豫度, 信息融合, 距离测度

Abstract:

Aiming at the multi-attribute group decision making problem with known attribute weights under probabilistic hesitant fuzzy environments, hesitation degrees of probabilistic hesitant fuzzy sets are considered, and thus a new method of probabilistic hesitant fuzzy multi-attribute group decision making is proposed based on improved distance measures. Firstly, combining the traditional probabilistic hesitant fuzzy distance measures, improved probabilistic hesitant fuzzy distance measures with hesitation degrees are defined through information fusion, including the Hamming distance, Euclidean distance, and generalized Euclidean distance. These new measures depend on combination coefficients to achieve the theoretical expansion and fusion optimization, and size relationships and parameter monotonicity of distance measures are studied. Secondly, according to the improved distance measures, a new method of multi-attribute group decision making is constructed by using the technique for order preference by similarity to ideal solution(TOPSIS) method, and an example of company location is used to make decision selection. The effectiveness of the proposed method is revealed by parameter analysis and decision comparison. Related researches systematically deepen probabilistic hesitant fuzzy distance measures, and effectively enrich multi-attribute group decision-making methods.

Key words: multi-attribute group decision making, probabilistic hesitant fuzzy set, hesitation degree, information fusion, distance measure

中图分类号: 

  • O159

图1

给定参数时距离测度三维图"

表1

公司选址的概率犹豫模糊决策矩阵"

Ai C1 C2 C3 C4
A1 {0.3|0.4, 0.75|0.6} {0.25|0.3, 0.55|0.7} {0.5|0.4, 0.65|0.6} {0.6|0.2, 0.85|0.8}
A2 {0.45|0.5, 0.6|0.5} {0.3|0.6, 0.4|0.4} {0.45|0.2, 0.5|0.8} {0.25|0.4, 0.45|0.6}
A3 {0.5|0.2, 0.6|0.8} {0.4|0.55, 0.6|0.45} {0.6|0.5, 0.7|0.5} {0.4|0.3, 0.6|0.7}
A4 {0.4|0.6, 0.8|0.4} {0.25|0.7, 0.5|0.3} {0.7|0.7, 0.9|0.3} {0.45|0.5, 0.7|0.5}

表2

方案Ai与V+、V-之间的距离"

α D1+ D2+ D3+ D4+ D1- D2- D3- D4-
1 0.099 8 0.193 4 0.091 2 0.100 5 0.153 6 0.011 0 0.108 4 0.128 1
2 0.103 7 0.224 2 0.106 4 0.122 6 0.183 0 0.014 0 0.121 6 0.140 0
4 0.125 4 0.265 7 0.138 4 0.140 4 0.212 3 0.017 0 0.138 1 0.163 7
5 0.117 9 0.270 2 0.126 6 0.136 5 0.220 0 0.017 8 0.142 8 0.172 1

表3

贴近度值Ωi及排序结果"

α Ω1 Ω2 Ω3 Ω4 排序结果
1 0.606 0 0.053 5 0.543 2 0.560 3 A1>A4>A3>A2
2 0.638 2 0.058 7 0.533 3 0.554 3 A1>A4>A3>A2
4 0.628 7 0.060 0 0.499 5 0.538 3 A1>A4>A3>A2
5 0.651 1 0.062 7 0.530 1 0.557 7 A1>A4>A3>A2

表4

参数对方案结果的影响值及排序结果"

α μ1, μ2 Ω1 Ω2 Ω3 Ω4 排序结果
1 μ1=1, μ2=0 0.626 1 0.022 9 0.537 5 0.537 1 A1>A3>A4>A2
μ1=0.8, μ2=0.2 0.617 8 0.028 3 0.540 5 0.537 9 A1>A3>A4>A2
μ1=0.4, μ2=0.6 0.600 4 0.039 6 0.547 1 0.539 4 A1>A3>A4>A2
μ1=0, μ2=1 0.580 4 0.008 2 0.545 9 0.544 4 A1>A3>A4>A2
2 μ1=1, μ2=0 0.649 7 0.031 1 0.529 4 0.544 3 A1>A4>A3>A2
μ1=0.8, μ2=0.2 0.644 8 0.037 4 0.530 3 0.541 4 A1>A4>A3>A2
μ1=0.4, μ2=0.6 0.634 2 0.048 8 0.532 2 0.534 5 A1>A4>A3>A2
μ1=0, μ2=1 0.622 2 0.059 8 0.534 6 0.525 0 A1>A3>A4>A2
4 μ1=1, μ2=0 0.655 5 0.043 3 0.529 8 0.552 8 A1>A4>A3>A2
μ1=0.8, μ2=0.2 0.938 8 0.087 1 0.643 3 0.604 6 A1>A3>A4>A2
μ1=0.4, μ2=0.6 0.646 0 0.056 0 0.528 4 0.539 0 A1>A4>A3>A2
μ1=0, μ2=1 0.638 5 0.063 0 0.526 8 0.519 8 A1>A3>A4>A2
5 μ1=1, μ2=0 0.655 4 0.047 3 0.529 9 0.555 7 A1>A4>A3>A2
μ1=0.8, μ2=0.2 0.652 7 0.051 1 0.529 4 0.552 3 A1>A4>A3>A2
μ1=0.4, μ2=0.6 0.653 9 0.057 4 0.539 3 0.550 2 A1>A4>A3>A2
μ1=0, μ2=1 0.639 7 0.063 2 0.525 9 0.519 8 A1>A3>A4>A2

表5

概率犹豫模糊群决策矩阵[15, 18]"

xi a1 a2 a3
x1 {0.55|0.15, 0.65|0.25, 0.76|0.1, 0.8|0.5} {0.2|0.05, 0.3|0.325, 0.4|0.125, 0.65|0.25, 0.75|0.25} {0.55|0.5, 0.75|0.25, 0.8|0.15, 0.94|0.1}
x2 {0.4|0.25, 0.58|0.25, 0.69|0.25, 0.95|0.25} {0.35|0.25, 0.6|0.075, 0.65|0.25, 0.7|0.35, 0.8|0.075} {0.45|0.25, 0.55|0.125, 0.56|0.25, 0.66|0.125, 0.85|0.25}
x3 {0.3|0.1, 0.5|0.35, 0.6|0.3, 0.68|0.25} {0.45|0.25, 0.55|0.125, 0.56|0.25, 0.66|0.125, 0.85|0.25} {0.45|0.25, 0.55|0.25, 0.68|0.25, 0.75|0.25}
x4 {0.15|0.1, 0.37|0.15, 0.4|0.25, 0.6|0.25, 0.73|0.25} {0.48|0.4, 0.55|0.25, 0.62|0.1, 0.66|0.25} {0.38|0.25, 0.5|0.125, 0.7|0.125, 0.75|0.25, 0.85|0.25}

表6

贴近度值及排序结果"

α μ1, μ2 Ω1 Ω2 Ω3 Ω4 排序结果
1 μ1=1, μ2=0 0.760 1 0.354 3 0.457 1 0.320 6 x1>x3>x2>x4
μ1=0.8, μ2=0.2 0.755 9 0.353 2 0.462 9 0.328 2 x1>x3>x2>x4
μ1=0.6, μ2=0.4 0.778 0 0.323 8 0.457 8 0.339 6 x1>x3>x4>x2
μ1=0.4, μ2=0.6 0.748 1 0.347 9 0.470 0 0.338 5 x1>x3>x2>x4
μ1=0.2, μ2=0.8 0.744 5 0.345 3 0.473 4 0.343 2 x1>x3>x2>x4
μ1=0, μ2=1 0.741 0 0.342 8 0.476 7 0.347 6 x1>x3>x4>x2
2 μ1=1, μ2=0 0.790 4 0.312 3 0.437 2 0.304 0 x1>x3>x2>x4
μ1=0.8, μ2=0.2 0.787 8 0.308 1 0.439 9 0.310 9 x1>x3>x4>x2
μ1=0.6, μ2=0.4 0.785 2 0.303 7 0.442 5 0.316 9 x1>x3>x4>x2
μ1=0.4, μ2=0.6 0.782 6 0.299 2 0.445 2 0.322 3 x1>x3>x4>x2
μ1=0.2, μ2=0.8 0.780 2 0.294 4 0.440 7 0.327 2 x1>x3>x4>x2
μ1=0, μ2=1 0.777 7 0.289 3 0.450 3 0.331 6 x1>x3>x4>x2
4 μ1=1, μ2=0 0.817 9 0.322 3 0.432 4 0.295 0 x1>x3>x2>x4
μ1=0.8, μ2=0.2 0.803 0 0.315 0 0.431 3 0.303 0 x1>x3>x2>x4
μ1=0.6, μ2=0.4 0.804 7 0.306 5 0.430 1 0.308 3 x1>x3>x4>x2
μ1=0.4, μ2=0.6 0.806 7 0.295 8 0.428 9 0.312 0 x1>x3>x4>x2
μ1=0.2, μ2=0.8 0.808 7 0.281 2 0.427 5 0.314 2 x1>x3>x4>x2
μ1=0, μ2=1 0.811 0 0.254 5 0.426 0 0.315 2 x1>x3>x4>x2
5 μ1=1, μ2=0 0.657 4 0.421 9 0.651 1 0.391 3 x1>x3>x2>x4
μ1=0.8, μ2=0.2 0.798 4 0.330 5 0.434 0 0.309 0 x1>x3>x2>x4
μ1=0.6, μ2=0.4 0.677 7 0.405 6 0.648 0 0.413 0 x1>x3>x4>x2
μ1=0.4, μ2=0.6 0.806 8 0.309 8 0.428 2 0.325 5 x1>x3>x4>x2
μ1=0.2, μ2=0.8 0.812 4 0.246 0 0.383 2 0.263 4 x1>x3>x4>x2
μ1=0, μ2=1 0.819 3 0.324 3 0.639 9 0.436 0 x1>x3>x4>x2
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