﻿ 考虑多角度效用的应急案例调整方法
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 浙江大学学报(理学版)  2017, Vol. 44 Issue (3): 314-321  DOI:10.3785/j.issn.1008-9497.2017.03.012 0

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ZHANG Kai, WANG Yingming. Emergency alternative adaptation method with considering multi-angle utility[J]. Journal of Zhejiang University(Science Edition), 2017, 44(3): 314-321. DOI: 10.3785/j.issn.1008-9497.2017.03.012.
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文章历史

1. 福建船政交通职业学院 信息工程系，福建 福州 350007;
2. 福州大学 决策科学研究所，福建 福州 350116

Emergency alternative adaptation method with considering multi-angle utility
ZHANG Kai1 , WANG Yingming2
1. Department of Information Engineering, Fujian Chuanzheng Communications College, Fuzhou 350007, China;
2. Decision Sciences Institute, Fuzhou University, Fuzhou 350116, China
Abstract: To improve the pertinence of the emergency plan, a method for plan adaptation based on those of similar emergency cases from multiple views is proposed. The comprehensive similarity between the current case and a candidate is calculated by three similarity computation methods while the case correlation degree is evaluated by the grey correlation method. Then, the similar case set and the associated weights are determined according to the comprehensive similarity, grey correlation degree and the case implementation effect of each candidate. Finally, the evidence reasoning is adopted to integrate the emergency plans of these similar cases to get the adaptive plan. A case is given to illustrate the feasibility and validity of the proposed method.
Key words: emergency    case adaptation    evidence reasoning    hybrid weight
0 引言

1 问题描述

2 应急案例调整方法 2.1 计算综合相似度

(1) 欧氏距离的相似度计算公式：

 ${{d'}_{0jl}} = \frac{{\left| {{x_{0l}} - {x_{jl}}} \right|}}{{x_l^{\max } - x_l^{\min }}},$ (1)

 ${\rm{Si}}{{\rm{m}}_1}\left( {{C_0},{C_j}} \right) = \frac{1}{{1 + \sqrt {\sum\limits_{l = 1}^h {{{\left( {w_l^P{{d'}_{0jl}}} \right)}^2}} } }}.$ (2)

(2) 高斯距离的相似度计算公式：

 ${g_{0jl}} = \exp \left[ { - \frac{{{{d'}_{0jl}}}}{{\sqrt 2 \times {\sigma _l}}}} \right],$ (3)

 ${\rm{Si}}{{\rm{m}}_2}\left( {{C_0},{C_j}} \right) = \sum\limits_{l = 1}^h {w_l^P{g_{ojl}}} .$ (4)

(3) FAN的相似度计算公式：

 ${{d''}_{0jl}} = \frac{{\sqrt {{{\left( {{x_{0l}} - {x_{jl}}} \right)}^2}} }}{{\max \left\{ {\sqrt {{{\left( {{x_{0l}} - {x_{jl}}} \right)}^2}} } \right\}}},$ (5)
 ${\rm{Si}}{{\rm{m}}_3}\left( {{C_0},{C_j}} \right) = \sum\limits_{l = 1}^h {w_l^P \cdot \exp \left( { - {{d''}_{0jl}}} \right)} .$ (6)

 $\begin{array}{l} {\rm{Sim}}\left( {{C_0},{C_j}} \right) = \\ \;\;\;\;\;\;\frac{{{\rm{Si}}{{\rm{m}}_1}\left( {{C_0},{C_j}} \right) + {\rm{Si}}{{\rm{m}}_2}\left( {{C_0},{C_j}} \right) + {\rm{Si}}{{\rm{m}}_3}\left( {{C_0},{C_j}} \right)}}{3}. \end{array}$ (7)
2.2 计算案例关联度

 ${{x'}_{jl}} = \frac{{{x_{jl}}}}{{{x_{1l}}}};\;\;\;{{y'}_{jl}} = \frac{{{y_{jf}}}}{{{y_{1f}}}};$ (8)

 $\begin{array}{l} r\left( {{{x'}_{jl}},{{y'}_{jf}}} \right) = \\ \;\;\;\;\;\;\;\frac{{\mathop {\min }\limits_l \mathop {\min }\limits_j \left| {{{x'}_{jl}} - {{y'}_{jf}}} \right| + \rho \cdot \mathop {\max }\limits_l \mathop {\max }\limits_j \left| {{{x'}_{jl}} - {{y'}_{jf}}} \right|}}{{\left| {{{x'}_{jl}} - {{y'}_{jf}}} \right| + \rho \cdot \mathop {\max }\limits_l \mathop {\max }\limits_j \left| {{{x'}_{jl}} - {{y'}_{jf}}} \right|}}, \end{array}$ (9)

 $\begin{array}{l} r\left( {{{\bar x}_j},{{y'}_{jf}}} \right):\\ \;\;\;\;\;\;\;\;\;\;\;\;\;r\left( {{{\bar x}_j},{{y'}_{jf}}} \right) = \sum\limits_{l = 1}^g {w_l^Pr\left( {{{x'}_{jl}},{{y'}_{jf}}} \right)} ; \end{array}$ (10)

 $r\left( {{{\bar x}_j},{{\bar y}_j}} \right) = \frac{{\sum\limits_{f = 1}^g {r\left( {{{\bar x}_j},{{y'}_{jf}}} \right)} }}{g}.$ (11)
2.3 计算历史案例中方案实施效果的效用值

 ${{r'}_{js}} = \frac{{{r_{js}}}}{{\mathop {\max }\limits_{1 \le j \le m} \left\{ {{r_{js}}} \right\}}};$ (12)

 ${{r'}_{je}} = \frac{p}{5}.$ (13)

 ${u_j} = \sum\limits_{s = 1}^e {w_s^R{{r'}_{js}}} ,$ (14)

2.4 确定相似历史案例集及案例权重

 ${t_j} = \frac{{\sum\limits_{p = 1}^3 {{t_{jp}}} }}{3}.$ (15)

 $\begin{array}{*{20}{c}} {{w_j} = \alpha {{w'}_j} + \lambda {{w''}_j} + \gamma {{w'''}_j},}\\ {{{w'}_j} = = \frac{{{\rm{Sim}}\left( {{C_0},{C_j}} \right)}}{{\sum\limits_{j = 1}^q {{\rm{Sim}}\left( {{C_0},{C_j}} \right)} }},{{w''}_j} = \frac{{{r_j}}}{{\sum\limits_{j = 1}^q {{r_j}} }},{{w'''}_j} = \frac{{{u_j}}}{{\sum\limits_{j = 1}^q {{u_j}} }},} \end{array}$ (16)

2.5 调整应急案例

(1) 当yjf为精确数时，将方案属性转换为{(Hn, βj, n); (Hn+1, βj, n+1)}(n=1, 2, …, 5) 的形式：

 ${\beta _{j,n}} = \frac{{{D_{f,n}} - {y_{jf}}}}{{{D_{f,n + 1}} - {D_{f,n}}}},\;\;\;{\beta _{j,n + 1}} = \frac{{{y_{jf}} - {D_{f,n}}}}{{{D_{f,n + 1}} - {D_{f,n}}}}.$ (17)

(2) 当yjf为区间数时，设yjf=[yjf-, yjf+]，则方案属性的置信度形式根据yjf横跨几个评价等级确定.

Df, nyjfDf, n+1，则将其转换为{(Hn, [βj, n-, βj, n+]); (Hn+1, [βj, n+1-, βj, n+1+])}形式，即

 $\beta _{j,n}^ - = \frac{{{D_{f,n + 1}} - y_{jf}^ + }}{{{D_{f,n + 1}} - {D_{f,n}}}},\;\;\;\beta _{j,n}^ + = \frac{{{D_{f,n + 1}} - y_{jf}^ - }}{{{D_{f,n + 1}} - {D_{f,n}}}};$ (18)
 $\beta _{j,n + 1}^ - = \frac{{y_{jf}^ - - {D_{f,n}}}}{{{D_{f,n + 1}} - {D_{f,n}}}},\;\;\;\beta _{j,n + 1}^ + = \frac{{y_{jf}^ + - {D_{f,n}}}}{{{D_{f,n + 1}} - {D_{f,n}}}}.$ (19)

Df, n-1yjfDf, n+2，则将其转换为{(Hn-1, [βj, n-1-, βj, n-1+])；(Hn, [βj, n-, βj, n+]); (Hn+1, [βj, n+1-, βj, n+1+])；(Hn+2, [βj, n+2-, βj, n+2+])}形式，即

 $\beta _{j,n - 1}^ - = 0,\;\;\;\beta _{j,n}^ + = \frac{{{D_{f,n + 1}} - y_{jf}^ - }}{{{D_{f,n + 1}} - {D_{f,n}}}};$ (20)
 $\beta _{j,n}^ - = 0,\;\;\;\;\beta _{j,n}^ + = {I_{n - 1,n}} + {I_{n,n + 1}};$ (21)
 $\beta _{j,n + 1}^ - = 0,\;\;\;\;\beta _{j,n + 1}^ + = {I_{n,n + 1}} + {I_{n + 1,n + 2}};$ (22)
 $\beta _{j,n + 2}^ - = 0,\;\;\;\beta _{j,n + 2}^ + = \frac{{y_{jf}^ + - {D_{f,n + 1}}}}{{{D_{f,n + 2}} - {D_{f,n + 1}}}};$ (23)

yjf为缺失值，将其表示为{(H, 1)}，其中H表示无知评价等级.

 ${m_{j,n}} = {m_j}\left( {{H_n}} \right) \in \left[ {m_{j,n}^ - ,m_{j,n}^ + } \right] = \left[ {{w_j}\beta _{j,n}^ - ,{w_j}\beta _{j,n}^ + } \right],$ (24)
 ${{\bar m}_{j,H}} = 1 - {w_j},$ (25)
 ${{\tilde m}_{j,H}} = \left[ {{w_j}\beta _{j,H}^ - ,{w_j}\beta _{j,H}^ + } \right].$ (26)

 ${\rm{Max}}\;{u_{\max }} = \sum\limits_{n = 1}^4 {{D_{f,n}}{\beta _n}} + {D_{f,5}}\left( {{\beta _5} + {\beta _H}} \right),$ (27-1)
 ${\rm{s}}.\;\;{\rm{t}}.\;\;\;\;\;{\beta _n} = \frac{{{m_n}}}{{1 - {{\bar m}_H}}},$ (27-2)
 ${\beta _H} = \frac{{{{\tilde m}_H}}}{{1 - {{\tilde m}_H}}},$ (27-3)
 $\begin{array}{l} {m_n} = K\left[ {\prod\limits_{j = 1}^q {\left( {{m_{j,n}} + {{\bar m}_{j,H}} + {{\tilde m}_{j,H}}} \right)} - } \right.\\ \;\;\;\;\;\;\;\;\left. {\prod\limits_{j = 1}^q {\left( {{{\bar m}_{j,H}} + {{\tilde m}_{j,H}}} \right)} } \right], \end{array}$ (27-4)
 ${{\tilde m}_H} = K\left[ {\prod\limits_{j = 1}^q {\left( {{{\bar m}_{j,H}} + {{\tilde m}_{j,H}}} \right)} - \prod\limits_{j = 1}^q {{{\bar m}_{j,H}}} } \right],$ (27-5)
 ${{\bar m}_H} = K\left[ {\prod\limits_{j = 1}^q {{{\bar m}_{j,H}}} } \right],$ (27-6)
 $\begin{array}{l} K = \left[ {\sum\limits_{n = 1}^5 {\prod\limits_{j = 1}^q {\left( {{m_{j,n}} + {{\bar m}_{j,H}} + {{\tilde m}_{j,H}}} \right)} } - } \right.\\ \;\;\;\;\;\;{\left. {4\prod\limits_{j = 1}^q {\left( {{{\bar m}_{j,H}} + {{\tilde m}_{j,H}}} \right)} } \right]^{ - 1}}, \end{array}$ (27-7)
 ${{\bar m}_{j,n}} \le {m_{j,n}} \le m_{j,n}^ + ,$ (27-8)
 $\tilde m_{j,H}^ - \le {{\tilde m}_{j,H}} \le \tilde m_{j,H}^ + ,$ (27-9)
 $\sum\limits_{n = 1}^5 {{m_{j,n}} + {{\bar m}_{j,H}} + {{\tilde m}_{j,H}}} = 1.$ (27-10)

 $\min \;{u_{\min }} = {D_{f,1}}\left( {{\beta _1} + {\beta _H}} \right) + \sum\limits_{n = 2}^5 {{D_{f,n}}{\beta _n}} .$ (28)
3 算例分析

4 性能分析

 ${\rm{Accuracy}} = 1 - {\rm{MAPE}} = 1 - \frac{1}{g}\sum\limits_{n = 1}^g {\left( {\frac{{\left| {{y_{0f}} - {{\bar y}_{0f}}} \right|}}{{{y_{0f}}}}} \right)} ,$ (29)

4.1 不同集结权重的分析

 图 1 C30在不同(α, λ, γ)时的精确度 Fig. 1 The accuracy of C30 with the different (α, λ, γ)
 图 2 C29在不同(α, λ, γ)时的精确度 Fig. 2 The accuracy of C29 with the different (α, λ, γ)
4.2 调整精确度分析

 图 3 4种方法在10个案例上的调整精确度排名 Fig. 3 Ranking of adjusting accuracy of ten casesusing four methods

5 结论