﻿ 考虑多角度效用的应急案例调整方法
 文章快速检索 高级检索
 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

### 引用本文 [复制中英文]

[复制中文]
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.
[复制英文]

### 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

 [1] FAN Z, LI Y, WANG X, et al. Hybrid similarity measure for case retrieval in CBR and its application to emergency response towards gas explosion[J]. Expert Systems with Applications, 2014, 41(5): 2526–2534. DOI:10.1016/j.eswa.2013.09.051 [2] LIAO Z, MAO X, HANNAM P M, et al. Adaptation methodology of CBR for environmental emergency preparedness system based on an improved genetic algorithm[J]. Expert Systems With Applications, 2012, 39(8): 7029–7040. DOI:10.1016/j.eswa.2012.01.044 [3] FAN Z, LI Y, ZHANG Y, et al. Generating project risk response strategies based on CBR: A case study[J]. Expert Systems with Applications, 2015, 42(6): 2870–2883. DOI:10.1016/j.eswa.2014.11.034 [4] ZHANG B, LI X, WANG S, et al. A novel case adaptation method based on an improved integrated genetic algorithm for power grid wind disaster emergencies[J]. Expert Systems with Applications, 2015, 42(21): 7812–7824. DOI:10.1016/j.eswa.2015.05.042 [5] SHEPPERD M, SCHOFIELD C. Estimating software project effort using analogies[J]. IEEE Transactions on Software Engineering, 1997, 23(11): 736–743. DOI:10.1109/32.637387 [6] ANGELIS L, STAMELOS I. A simulation tool for efficient analogy based cost estimation[J]. Empirical Software Engineering, 2000, 5(1): 35–68. DOI:10.1023/A:1009897800559 [7] KWONG C K, SMITH G F, LAU W S, et al. Application of case based reasoning injection molding[J]. Journal of Materials Processing Technology, 1997, 63(1): 463–467. [8] JI S, PARK M, LEE H, et al. Case adaptation method of case-based reasoning for construction cost estimation in Korea[J]. Journal of Construction Engineering and Management, 2012, 138(1): 43–52. DOI:10.1061/(ASCE)CO.1943-7862.0000409 [9] QI J, HU J, PENG Y, et al. Incorporating adaptability-related knowledge into support vector machine for case-based design adaptation[J]. Engineering Applications of Artificial Intelligence, 2015, 37: 170–180. DOI:10.1016/j.engappai.2014.09.010 [10] HU J, QI J, PENG Y, et al. New CBR adaptation method combining with problem-solution relational analysis for mechanical design[J]. Computers in Industry, 2015, 66: 41–51. DOI:10.1016/j.compind.2014.08.004 [11] BUTDEE S. Adaptive aluminum extrusion die design using case-based reasoning and artificial neural networks[J]. Advanced Materials Research, 2012, 383: 6747–6754. [12] QI J, HU J, PENG Y, et al. A new adaptation method based on adaptability under k-nearest neighbors for case adaptation in case-Based design[J]. Expert Systems with Applications, 2012, 39(7): 6485–6502. DOI:10.1016/j.eswa.2011.12.055 [13] XIE X, LIN L, ZHONG S, et al. Handling missing values and unmatched features in a CBR system for hydro-generator design[J]. Computer-Aided Design, 2013, 45(6): 963–976. DOI:10.1016/j.cad.2013.02.004 [14] LI H, SUN J. Gaussian case-based reasoning for business failure prediction with empirical data in China[J]. Information Sciences, 2009, 179(1): 89–108. [15] 邓聚龙. 灰色控制系统[J]. 华中工学院学报, 1982, 10(3): 9–18. DENG J L. Grey control system[J]. The Journal of Huazhong University of Science and Technology, 1982, 10(3): 9–18. [16] 李永海, 樊治平, 李铭洋. 解决广义不确定型决策问题的案例决策方法[J]. 系统工程学报, 2014, 29(1): 21–29. LI Y H, FAN Z P, LI M Y. Case-based decision analysis method for general uncertain decision making problem[J]. Journal of Systems Engineering, 2014, 29(1): 21–29. [17] WANG Y M, YANG J B, XU D L, et al. The evidential reasoning approach for multiple attribute decision analysis using interval belief degree[J]. European Journal of Operational Research, 2006, 175(1): 35–66. DOI:10.1016/j.ejor.2005.03.034 [18] LI S, HO H. Predicting financial activity with evolutionary fuzzy case-Based reasoning[J]. Expert Systems with Applications, 2009, 36(1): 411–422. DOI:10.1016/j.eswa.2007.09.049 [19] YU W, LIU Y. Hybridization of CBR and numeric soft computing techniques for mining of scarce construction databases[J]. Automation in Construction, 2006, 15(1): 33–46. DOI:10.1016/j.autcon.2005.01.007