系统工程与电子技术 ›› 2021, Vol. 43 ›› Issue (2): 476-486.doi: 10.12305/j.issn.1001-506X.2021.02.22
白静(
), 陈业华(), 石蕊*(), 张亚明()
收稿日期:2020-02-27
出版日期:2021-02-01
发布日期:2021-03-16
通讯作者:
石蕊
E-mail:bjr@stumail.ysu.edu.cn;chenyh@ysu.edu.cn;shirui@ysu.edu.cn;yaming99@ysu.edu.cn
作者简介:白静(1989-),女,讲师,博士,主要研究方向为应急决策、智能决策。E-mail:基金资助:
Jing BAI(), Yehua CHEN(), Rui SHI*(), Yaming ZHANG()
Received:2020-02-27
Online:2021-02-01
Published:2021-03-16
Contact:
Rui SHI
E-mail:bjr@stumail.ysu.edu.cn;chenyh@ysu.edu.cn;shirui@ysu.edu.cn;yaming99@ysu.edu.cn
摘要：
针对多部门协同应急决策带有不确定性和偏好性的多属性决策问题,提出了一种基于概率语言赋权交叉熵信度分配的应急决策方法。首先,采用能充分表达不确定决策信息的概率语言术语集(probabilistic linguistic term set, PLTS)刻画属性指标,并将其作为证据推理算法中的证据信息。同时,从认知科学的角度考虑由部门跨领域及专业偏好等特点造成的证据不确信问题,对证据折扣系数表达式进行改进,构建基于概率语言赋权交叉熵的Mass函数。然后,利用递归算法对多部门多指标形成的证据信息进行合成,得到各方案的综合评估信息。最后,通过算例分析验证了方法的有效性和实用性。
中图分类号:
白静, 陈业华, 石蕊, 张亚明. 基于概率语言赋权交叉熵信度分配的应急决策[J]. 系统工程与电子技术, 2021, 43(2): 476-486.
Jing BAI, Yehua CHEN, Rui SHI, Yaming ZHANG. Emergency decision-making based on the reliability distribution of weighted cross entropy in probabilistic language[J]. Systems Engineering and Electronics, 2021, 43(2): 476-486.
表1
各部门对于决策指标的相对权重"
| 指标el | 消防部门k1 | 交管部门k2 | 电信部门k3 |
| e1 | 0.43 | 0.36 | 0.21 |
| e2 | 0.32 | 0.47 | 0.21 |
| e3 | 0.53 | 0.28 | 0.19 |
表2
消防部门k1原始评估信息"
| 方案 | e1 | e2 | e3 |
| a1 | S1(0.3) | S-3(0.2) | S1(0.3) |
| S2(0.7) | S-2(0.2) | S2(0.7) | |
| - | S-1(0.6) | - | |
| a2 | S2(0.5) | S-3(0.2) | S2(0.8) |
| S3(0.5) | S-2(0.6) | S3(0.2) | |
| - | S-1(0.2) | - | |
| a3 | S-1(0.6) | S1(0.3) | S-1(0.7) |
| S0(0.4) | S2(0.2) | S0(0.3) | |
| - | S3(0.5) | - | |
| a4 | S0(0.4) | S1(0.2) | S-2(0.4) |
| S1(0.6) | S2(0.2) | S-1(0.6) | |
| - | S3(0.6) | - | |
| a5 | S2(0.7) | S0(0.4) | S1(0.2) |
| S3(0.3) | S1(0.4) | S2(0.8) | |
| - | S2(0.2) | - |
表3
交管部门k2原始评估信息"
| 方案 | e1 | e2 | e3 |
| a1 | S1(0.2) | S0(0.3) | S1(0.1) |
| S2(0.8) | S1(0.7) | S2(0.4) | |
| - | - | S3(0.5) | |
| a2 | S-2(0.2) | S-1(0.7) | S1(0.7) |
| S-1(0.6) | S0(0.3) | S2(0.2) | |
| S0(0.2) | - | S3(0.1) | |
| a3 | S-2(0.6) | S1(0.1) | S1(0.8) |
| S-1(0.5) | S2(0.1) | S2(0.1) | |
| - | S3(0.8) | S3(0.1) | |
| a4 | S2(0.3) | S1(0.1) | S0(0.1) |
| S3(0.7) | S2(0.1) | S1(0.7) | |
| - | S3(0.8) | S2(0.2) | |
| a5 | S2(0.6) | S1(0.6) | S0(0.6) |
| S3(0.4) | S2(0.2) | S1(0.4) | |
| - | S3(0.2) | - |
表4
电信部门k3原始评估信息"
| 方案 | e1 | e2 | e3 |
| a1 | S2(0.2) | S1(0.3) | S1(0.2) |
| S3(0.8) | S2(0.7) | S2(0.8) | |
| a2 | S2(0.6) | S2(0.2) | S2(0.2) |
| S3(0.4) | S3(0.8) | S3(0.8) | |
| a3 | S1(0.3) | S1(0.3) | S1(0.3) |
| S2(0.7) | S2(0.7) | S2(0.7) | |
| a4 | S1(0.3) | S1(0.3) | S1(0.3) |
| S2(0.7) | S2(0.7) | S2(0.7) | |
| a5 | S1(0.3) | S2(0.2) | S2(0.5) |
| S2(0.5) | S3(0.8) | S3(0.5) | |
| S3(0.2) | - | - |
表5
消防部门k1规范化后的决策信息"
| 方案 | e1 | e2 | e3 |
| a1 | S1(0.3) | S-3(0.2) | S1(0.3) |
| S2(0.7) | S-2(0.2) | S2(0.7) | |
| S3(0) | S-1(0.6) | S3(0) | |
| - | S0(0) | - | |
| - | S1(0) | - | |
| - | S2(0) | - | |
| a2 | S0(0) | S-3(0.2) | S1(0) |
| S1(0) | S-2(0.6) | S2(0.8) | |
| S2(0.5) | S-1(0.2) | S3(0.2) | |
| S3(0.5) | - | - | |
| a3 | S-2(0) | - | S-1(0.7) |
| S-1(0.6) | S1(0.3) | S0(0.3) | |
| S0(0.4) | S2(0.2) | S1(0) | |
| S1(0) | S3(0.5) | S2(0) | |
| S2(0) | - | S3(0) | |
| a4 | S0(0.4) | S1(0.2) | S-2(0.4) |
| S1(0.6) | S2(0.2) | S-1(0.6) | |
| S2(0) | S3(0.6) | S0(0) | |
| S3(0) | - | S1(0) | |
| - | - | S2(0) | |
| a5 | S1(0) | S0(0.4) | S0(0) |
| S2(0.7) | S1(0.4) | S1(0.2) | |
| S3(0.3) | S2(0.2)S3(0) | S2(0.8)S3(0) |
表6
交管部门k2规范化后的决策信息Normalized decision information of traffic control department k2"
| 方案 | e1 | e2 | e3 |
| a1 | S1(0.2) | S-3(0) | S1(0.1) |
| S2(0.8) | S-2(0) | S2(0.4) | |
| S3(0) | S-1(0)S0(0.3) | S3(0.5) | |
| - | S1(0.7)S2(0) | - | |
| a2 | S-2(0.2) | S-3(0) | S1(0.7) |
| S-1(0.6) | S-2(0) | S2(0.2) | |
| S0(0.2) | S-1(0.7) | S3(0.1) | |
| S1(0) | S0(0.3) | - | |
| S2(0) | - | - | |
| a3 | S-2(0.6) | S1(0.1) | S-1(0) |
| S-1(0.5) | S2(0.1) | S0(0) | |
| S0(0) | S3(0.8) | S1(0.8) | |
| S1(0) | - | S2(0.1) | |
| S2(0) | - | S3(0.1) | |
| a4 | S0(0) | - | S-2(0) |
| S1(0) | S1(0.1) | S-1(0) | |
| S2(0.3) | S2(0.1) | S0(0.1) | |
| S3(0.7) | S3(0.8) | S1(0.7) | |
| - | - | S2(0.2) | |
| a5 | S1(0) | S0(0) | S0(0.6) |
| S2(0.6) | S1(0.6) | S1(0.4) | |
| S3(0.4) | S2(0.2) | S2(0) | |
| - | S3(0.2) | S3(0) |
表7
电信部门k3规范化后的决策信息"
| 方案 | e1 | e2 | e3 |
| a1 | S1(0) | S-3(0) | S1(0.2) |
| S2(0.2) | S-2(0) | S2(0.8) | |
| S3(0.8) | S1(0) | S3(0) | |
| - | S0(0) | - | |
| - | S1(0.3) | - | |
| - | S2(0.7) | - | |
| a2 | S-2(0) | S-3(0) | S1(0) |
| S-1(0) | S-2(0) | S2(0.2) | |
| S0(0) | S-1(0) | S3(0.8) | |
| S1(0) | S0(0) | - | |
| S2(0.6) | S1(0) | - | |
| S3(0.4) | S2(0.2) | - | |
| - | S3(0.8) | - | |
| a3 | S-2(0) | S1(0.3) | S-1(0) |
| S-1(0) | S2(0.7) | S0(0) | |
| S0(0) | S3(0) | S1(0.3) | |
| S1(0.3) | - | S2(0.7) | |
| S2(0.7) | - | S3(0) | |
| a4 | S0(0) | S1(0.3) | S-2(0) |
| S1(0.3) | S2(0.7) | S-1(0) | |
| S2(0.7) | S3(0) | S0(0) | |
| S3(0) | - | S1(0.3) | |
| - | - | S2(0.7) | |
| - | - | S2(0) | |
| a5 | S1(0.3) | S0(0)S1(0) | S0(0)S1(0) |
| S2(0.5) | S2(0.2) | S2(0.5) | |
| S3(0.2) | S3(0.8) | S3(0.5) |
表8
部门间指标评估的概率语言赋权交叉熵"
| 方案 | 指标el | 部门间概率语言赋权交叉熵 | |||||
| hk1, hk2 | hk1, hk3 | hk2, hk3 | hk2, hk1 | hk3, hk1 | hk3, hk2 | ||
| a1 | e1 | 0.002 | 0.088 | 0.104 | 0.002 | 0.112 | 0.127 |
| e2 | 0.119 | 0.113 | 0.060 | 0.098 | 0.152 | 0.066 | |
| e3 | 0.030 | 0.002 | 0.037 | 0.032 | 0.002 | 0.047 | |
| a2 | e1 | 0.094 | 0.002 | 0.091 | 0.085 | 0.002 | 0.104 |
| e2 | 0.091 | 0.130 | 0.106 | 0.126 | 0.199 | 0.140 | |
| e3 | 0.705 | 0.064 9 | 0.100 | 0.066 | 0.074 | 0.125 | |
| a3 | e1 | 0.065 | 0.095 | 0.115 | 0.052 | 0.109 | 0.145 |
| e2 | 0.018 | 0.050 | 0.107 | 0.021 | 0.051 | 0.096 | |
| e3 | 0.094 | 0.089 | 0.062 | 0.104 | 0.100 | 0.064 | |
| a4 | e1 | 0.095 | 0.062 | 0.081 | 0.110 | 0.067 | 0.074 |
| e2 | 0.008 | 0.065 | 0.107 | 0.010 | 0.064 | 0.096 | |
| e3 | 0.087 | 0.090 | 0.042 | 0.099 | 0.105 | 0.044 | |
| a5 | e1 | 0.002 | 0.013 | 0.013 | 0.002 | 0.012 | 0.013 |
| e2 | 0.023 | 0.093 | 0.062 | 0.024 | 0.116 | 0.074 | |
| e3 | 0.088 | 0.031 | 0.098 | 0.078 | 0.032 | 0.105 | |
表9
对各方案as部门给出的折扣信度分布函数"
| 方案 | 评估指标el | 评估等级置信度 | |||||||
| P(Θ) | -3 | -2 | -1 | 0 | 1 | 2 | 3 | ||
| a1 | e1 | 0.476 | 0 | 0 | 0 | 0 | 0.082 | 0.315 | 0.126 |
| e2 | 0.55 | 0.029 | 0.029 | 0.088 | 0.044 | 0.155 | 0.103 | 0 | |
| e3 | 0.480 | 0 | 0 | 0 | 0 | 0.096 | 0.347 | 0.076 | |
| a2 | e1 | 0.502 | 0 | 0.032 | 0.208 | 0.099 | 0 | 0.079 | 0.079 |
| e2 | 0.524 | 0.031 | 0.094 | 0.147 | 0.047 | 0 | 0.031 | 0.125 | |
| e3 | 0.197 | 0 | 0 | 0 | 0 | 0.507 | 0.157 | 0.139 | |
| a3 | e1 | 0.470 | 0 | 0.099 | 0.199 | 0.066 | 0.050 | 0.116 | 0 |
| e2 | 0.572 | 0 | 0 | 0 | 0 | 0.099 | 0.142 | 0.187 | |
| e3 | 0.140 | 0 | 0 | 0.294 | 0.239 | 0.069 | 0.047 | 0.211 | |
| a4 | e1 | 0.337 | 0 | 0 | 0 | 0.158 | 0.251 | 0.100 | 0.153 |
| e2 | 0.572 | 0 | 0 | 0 | 0 | 0.084 | 0.141 | 0.203 | |
| e3 | 0.451 | 0 | 0.070 | 0.105 | 0.018 | 0.190 | 0.167 | 0 | |
| a5 | e1 | 0.306 | 0 | 0 | 0 | 0 | 0.145 | 0.333 | 0.215 |
| e2 | 0.268 | 0 | 0 | 0 | 0.149 | 0.208 | 0.170 | 0.206 | |
| e3 | 0.447 | 0 | 0 | 0 | 0.104 | 0.110 | 0.253 | 0.087 | |
图1
不同风险系数下的效用值"
表10
各模型决策结果对比"
| 方法 | 排序结果 | 最优方案 |
| 文献[ | a5≻a4≻a3≻a2≻a1 | a5 |
| 文献[ | a4≻a5≻a2≻a3≻a1 | a4 |
| 文献[ | a4≻a5≻a3≻a1≻a2 | a4 |
| 本文模型(0≤δ < 0.25) | a4≻a5≻a3≻a2≻a1 | a4 |
| 本文模型(0.25≤δ≤1) | a4≻a5≻a3≻a1≻a2 | a4 |
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