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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
1 TORRA V . Hesitant fuzzy sets[J]. International journal of intelligent systems, 2010, 25 (6): 529- 539.
2 XU Zeshui , WEI Zhou . Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment[J]. Fuzzy Optimization and Decision Making, 2017, 16 (4): 481- 503.
doi: 10.1007/s10700-016-9257-5
3 华维灿, 孙刚, 王贵君. 基于概率犹豫模糊相似度的交互式群体决策方法[J]. 浙江大学学报(理学版), 2022, 49 (4): 398- 407.
HUA Weican , SUN Gang , WANG Guijun . An interactive group decision making method based on probabilistic hesitation fuzzy similarity[J]. Journal of Zhejiang University(Science Edition), 2022, 49 (4): 398- 407.
4 武文颖, 李应, 金飞飞, 等. 基于概率犹豫信息集成方法的群决策模型[J]. 模式识别与人工智能, 2017, 30 (10): 894- 906.
WU Wenying , LI Ying , JIN Feifei , et al. Group decision making model based on probabilistic hesitant fuzzy information aggregation operations[J]. Pattern Recognition and Artificial Intelligence, 2017, 30 (10): 894- 906.
5 饶益, 陈云翔, 蔡忠义, 等. 考虑专家偏好的基于概率犹豫模糊熵的多属性决策方法[J]. 火力与指挥控制, 2021, 46 (4): 4- 13.
RAO Yi , CHEN Yunxiang , CAI Zongyi , et al. Method for multi-attribute decision making considering expert preference based on probabilistic hesitant fuzzy entropy[J]. Fire Control & Command Control, 2021, 46 (4): 4- 13.
6 OHLAN A . Novel entropy and distance measures for interval-valued intuitionistic fuzzy sets with application in multi-criteria group decision-making[J]. International Journal of General Systems, 2022, 51 (4): 413- 440.
doi: 10.1080/03081079.2022.2036138
7 MAHANTA J , PANDA S . Distance measure for Pythagorean fuzzy sets with varied applications[J]. Neural Computing and Applications, 2021, 33 (24): 17161- 17171.
doi: 10.1007/s00521-021-06308-9
8 HAO Zhinan , XU Zeshui , ZHAO Hua , et al. The context-based distance measure for intuitionistic fuzzy set with application in marine energy transportation route decision making[J]. Applied Soft Computing, 2021, 101, 107044.
doi: 10.1016/j.asoc.2020.107044
9 金贵, 周礼刚, 吴澎, 等. 属性权重未知情形下的q阶orthopair犹豫模糊TOPSIS法[J]. 计算机工程与应用, 2022, 58 (6): 256- 263.
JIN Gui , ZHOU Ligang , WU Peng , et al. q-Rung orthopair hesitant fuzzy TOPSIS method under unknown attribute weigh[J]. Computer Engineering and Applications, 2022, 58 (6): 256- 263.
10 谭春桥, 支帅. 基于直觉犹豫模糊集的TOPSIS法[J]. 运筹与管理, 2018, 27 (3): 66- 73.
TAN Chunqiao , ZHI Shuai . TOPSIS method with intuitionistic hesitant fuzzy sets[J]. Operations Research and Management Science, 2018, 27 (3): 66- 73.
11 王志平, 傅敏, 王沛文. 概率犹豫模糊环境下基于前景理论和TOPSIS法的多属性群决策模型[J]. 科学技术与工程, 2022, 22 (4): 1329- 1337.
WANG Zhiping , FU Min , WANG Peiwen . Multi-attribute group decision making model based on prospect theory and TOPSIS in probabilistic hesitant fuzzy environment[J]. Science Technology and Engineering, 2022, 22 (4): 1329- 1337.
12 梁薇, 王应明. 考虑群体一致性的区间犹豫模糊TOPSIS决策方法[J]. 系统科学与数学, 2020, 40 (7): 1146- 1156.
LIANG Wei , WANG Yingming . Interval-valued hesitant fuzzy TOPSIS decision making method with group consistency[J]. Journal of Systems Science and Mathematical Sciences, 2020, 40 (7): 1146- 1156.
13 骆华. 基于改进距离的概率犹豫模糊多属性决策方法[J]. 武汉理工大学学报(信息与管理工程版), 2020, 42 (3): 239- 245.
LUO Hua . Probabilistic hesitant fuzzy multi-attribute decision-making method based on improved distance[J]. Journal of Wuhan University of Technology(Information and Management Engineering Edition), 2020, 42 (3): 239- 245.
14 曾维丹. 概率犹豫模糊集的距离测度及其应用研究[D]. 成都: 西华大学, 2020.
ZENG Weidan. The distance of the probability hesitant fuzzy set and it's application[D]. Chengdu: Xihua University, 2020.
15 方冰, 韩冰, 闻传花. 基于新型距离测度的概率犹豫模糊多属性群决策方法[J]. 控制与决策, 2022, 37 (3): 729- 736.
FANG Bing , HAN Bing , WEN Chuanhua . Probabilistic hesitant fuzzy multi-attribute group decision-making based on new distance measure[J]. Control and Decision, 2022, 37 (3): 729- 736.
16 SU Zhan , XU Zeshui , ZHAO Hua , et al. Entropy measures for probabilistic hesitant fuzzy information[J]. IEEE Access, 2019, 7, 65714- 65727.
17 SONG Chenyang , XU Zeshui , ZHAO Hua . New correlation coefficients between probabilistic hesitant fuzzy sets and their applications in cluster analysis[J]. International Journal of Fuzzy Systems, 2019, 21 (2): 355- 368.
18 刘玉敏, 朱峰, 靳琳琳. 基于概率犹豫模糊熵的多属性决策方法[J]. 控制与决策, 2019, 34 (4): 861- 870.
LIU Yumin , ZHU Feng , JIN Linin . Multi-attribute decision method based on probabilistic hesitant fuzzy entropy[J]. Control and Decision, 2019, 34 (4): 861- 870.
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