基于FA-ER的装备保障资源供给能力评估方法

doi:10.3969/j.issn.1001-506X.2020.03.017

摘要/Abstract

摘要：

针对装备保障资源供给能力评估信息主观性和不确定性强、评估结果可信度低的问题,提出了一种基于萤火虫算法和证据推理(firefly algorithm-evidential reasoning, FA-ER)的评估方法。首先，通过直觉模糊熵处理不确定信息,确定初始权重范围。然后，基于后悔函数将证据推理方法的权重求解问题转化为非线性多目标优化问题。最后，采用萤火虫算法计算最优参数,确定最优评估模型并得到最终评估结果。算例分析结果表明,所提方法能够有效解决评估主观性强的问题,提高评估结果的准确度,对装备保障资源供给能力评估问题具有较好的适用性。

关键词: 装备保障资源, 供给能力评估, 萤火虫算法, 证据推理, 后悔函数

Abstract:

For the problems of strong subjectivity of evaluation information and low reliability of the results in the evaluation of the supply capability of equipment support resources, an evaluation method based on firefly algorithm and evidential reasoning (FA-ER) is proposed. The range of initial weights is determined by dealing with information under uncertainty according to intuitionistic fuzzy entropy. The weights calculation for evidential reasoning are transformed into a nonlinear multi-objective optimization problem by combining with the regret function. The firefly algorithm is used to solve optimal parameters, and then the optimal evaluation model and the final evaluation result are determined. The results of numerical example analysis show that the proposed method can effectively solve the problem of strong subjectivity of evaluation and improve the accuracy of evaluation results. The proposed method has good applicability to the evaluation of the supply capability of equipment support resources.

Key words: equipment support resources, supply capability assessment, firefly algorithm, evidential reasoning, regret function

中图分类号:

TP181

李岩, 陈云翔, 罗承昆, 蔡忠义. 基于FA-ER的装备保障资源供给能力评估方法[J]. 系统工程与电子技术, 2020, 42(3): 630-637.

Yan LI, Yunxiang CHEN, Chengkun LUO, Zhongyi CAI. Evaluation method for the supply capability of equipment support resources based on FA-ER[J]. Systems Engineering and Electronics, 2020, 42(3): 630-637.

图/表 11

图1

图2

表1

表2

表3

表4

图3

图4

表5

图5

图6

参考文献 30

1	单志伟. 装备综合保障工程[M]. 北京: 国防工业出版社, 2007: 332- 335.
	SHAN Z W . Equipment comprehensive protection project[M]. Beijing: National Defense Industry Press, 2007: 332- 335.
2	杨晶, 黎放, 狄鹏. 改进BP网络的舰船装备保障资源保障能力评估[J]. 火力与指挥控制, 2012, 37 (2): 65- 67, 71. doi: 10.3969/j.issn.1002-0640.2012.02.018
	YANG J , LI F , DI P . Support ability evaluation of ship equipment support ability resources based on improved BP network[J]. Fire Control & Command Control, 2012, 37 (2): 65- 67, 71. doi: 10.3969/j.issn.1002-0640.2012.02.018
3	KHALEIE S , FASANGHARI M , TAVASSOLIE E . Supplier selection using a novel intuitionist fuzzy clustering approach[J]. Applied Soft Computing, 2012, 12 (6): 1741- 1754. doi: 10.1016/j.asoc.2012.01.017
4	刘满凤, 任海平. 基于一类新的直觉模糊熵的多属性决策方法研究[J]. 系统工程理论与实践, 2015, 35 (11): 2909- 2916. doi: 10.12011/1000-6788(2015)11-2909
	LIU M F , REN H P . A study of multi-attribute decision making based on a new intuitionistic fuzzy entropy measure[J]. Systems Engineering-Theory & Practice, 2015, 35 (11): 2909- 2916. doi: 10.12011/1000-6788(2015)11-2909
5	BASKIR M B , TURKSEN I B , SAATCIOGLU O . An alternative fuzzy evaluation framework for supplier[J]. International Journal of Applied Management Science, 2017, 9 (3): 169- 187. doi: 10.1504/IJAMS.2017.086638
6	TOORANLOO H S , IRANPOUR A . Supplier selection and evaluation using interval-valued intuitionistic fuzzy AHP method[J]. International Journal of Procurement Management, 2017, 10 (5): 539- 554. doi: 10.1504/IJPM.2017.086399
7	SEN D K , DATTA S , MAHAPATRA S S , et al. Sustainable supplier selection in intuitionistic fuzzy environment: a decision making perspective[J]. Benchmarking: An International Journal, 2018, 25 (2): 545- 574. doi: 10.1108/BIJ-11-2016-0172
8	FATRIAS D , KAMIL I , MEILANI D . An integrative multi-criteria decision making techniques for supplier evaluation problem with its application[J]. IOP Conference Series: Materials Science and Engineering, 2018, 319, 012076. doi: 10.1088/1757-899X/319/1/012076
9	陈国钦, 张尊泉, 张伟. 基于证据理论的雷达装备规划保障资源能力评估方法[J]. 现代电子技术, 2005, 28 (21): 11- 13. doi: 10.3969/j.issn.1004-373X.2005.21.004
	CHEN G Q , ZHANG Z Q , ZHANG W . One method to assess the ability of planning guaranteed resources of radar equipment based on DS evidence theory[J]. Modern Electronic Technique, 2005, 28 (21): 11- 13. doi: 10.3969/j.issn.1004-373X.2005.21.004
10	胡丽芳, 初军田, 李强. 一种基于投影多属性决策的证据推理方法[J]. 控制与决策, 2015, 30 (2): 261- 265.
	HU L F , CHU J T , LI Q . An evidence reasoning approach based on projection multi-attributedecision making[J]. Control and Decision, 2015, 30 (2): 261- 265.
11	ZHOU M , LIU X B , YANG J B . Evidential reasoning approach for MADM based on incomplete interval value[J]. Journal of Intelligent & Fuzzy Systems, 2017, 33 (6): 3707- 3721.
12	周志杰, 刘涛源, 李方志, 等. 一种基于证据推理的装备保障资源评估方法[J]. 控制与决策, 2018, 33 (6): 1048- 1054.
	ZHOU Z J , LIU T Y , LI F Z . An evaluation method of equipment support resources based on evidential reasoning[J]. Control and Decision, 2018, 33 (6): 1048- 1054.
13	MOHAMMADI S E , MAKUI A . Multi-attribute group decision making approach based on interval-valued intuitionistic fuzzy sets and evidential reasoning methodology[J]. Soft Computing, 2017, 21 (17): 5061- 5080. doi: 10.1007/s00500-016-2101-6
14	刘文清, 王应明, 蓝以信. 不完全信息下基于证据推理的直觉模糊多属性决策方法[J]. 统计与决策, 2018, 34 (15): 42- 45.
	LIU W Q , WANG Y L , LAN Y X . An intuitionistic fuzzy multiple attribute decision making method based on evidential reasoning under incomplete information[J]. Statistics & Decision, 2018, 34 (15): 42- 45.
15	FU C , CHANG W J , XU D L , et al. An evidential reasoning approach based on criterion reliability and solution reliability[J]. Computers & Industrial Engineering, 2019, 128, 401- 417.
16	YANG X S . Firefly algorithm, stochastic test functions and design optimization[J]. International Journal of Bio-inspired Computation, 2010, 2 (2): 78- 84. doi: 10.1504/IJBIC.2010.032124
17	ZHOU M , LIU X B , CHEN Y W . Evidential reasoning rule for MADM with both weights and reliabilities in group decision making[J]. Knowledge-Based Systems, 2018, 143, 142- 161. doi: 10.1016/j.knosys.2017.12.013
18	YANG J B . Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties[J]. European Journal of Operational Research, 2001, 131 (1): 31- 61.
19	李欣屹, 王强, 周洪斌, 等. 基于ANP-灰色模糊的航空装备维修保障能力评估[J]. 火力与指挥控制, 2018, 43 (3): 100- 106. doi: 10.3969/j.issn.1002-0640.2018.03.022
	LI X Y , WANG Q , ZHOU H B , et al. Research on evaluation of aeronautic equipment maintenance support capability based on ANP-GF[J]. Fire Control & Command Control, 2018, 43 (3): 100- 106. doi: 10.3969/j.issn.1002-0640.2018.03.022
20	YANG J B, LIU J, WANG J, et al. Belief rule-base inference methodology using the evidential reasoning approach-RIME[J]. IEEE Trans.on Systems Man and Cybernetics Part A: Systems and Humans, 2006, 36(2): 266-285.
21	陈云翔, 王攀, 罗承昆. 基于证据理论的偏好型直觉模糊群决策方法[J]. 控制与决策, 2017, 32 (5): 947- 953.
	CHEN Y X , WANG P , LUO C K . Method for intuitionistic fuzzy group decision-making with preference based on evidence theory[J]. Control and Decision, 2017, 32 (5): 947- 953.
22	BURILLO P , BUSTINCE H . Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets[J]. Fuzzy Sets and Systems, 1996, 78, 305- 316. doi: 10.1016/0165-0114(96)84611-2
23	王新霞, 陈孝国. 直觉模糊熵的改进研究[J]. 齐齐哈尔大学学报, 2015, 31 (4): 11- 13.
	WANG X X , CHEN X G . Study on improvement of intuitionistic fuzzy entropy[J]. Journal of Qiqihar University, 2015, 31 (4): 11- 13.
24	徐倩, 唐胜景, 郭杰, 等. 基于后悔函数的多目标优化决策问题研究[J]. 北京理工大学学报, 2010, 30 (7): 803- 806, 834.
	XU Q , TANG S J , GUO J . Decision-making problem analysis for multi-objective optimization based on regret-function[J]. Transaction of Beijing Institute of Technology, 2010, 30 (7): 803- 806, 834.
25	ZHOU Z J, HU G Y. A model for hidden behaviour prediction of complex systems based on belief rule base and power set[J]. IEEE Trans.on Systems, Man, and Cybernetics, 2017, 99: 1-7.
26	张仲敏, 李俊山, 宋凭, 等. 一种基于模糊层次分析的多Agent电子对抗装备状态智能评判方法[J]. 兵工学报, 2014, 35 (4): 516- 522. doi: 10.3969/j.issn.1000-1093.2014.04.013
	ZHANG Z M , LI J S , SONG P . A multi-agent intelligent decision approach based on fuzzy analytic hierarchy process for service status of electronic countermeasures equipment[J]. Acta Armamentarii, 2014, 35 (4): 516- 522. doi: 10.3969/j.issn.1000-1093.2014.04.013
27	SHATHANAA R , RAMASUBRAMANIAN N . Group influence based improved firefly algorithm for design space exploration of datapath resource allocation[J]. Applied Intelligence, 2019, 49 (6): 2084- 2100. doi: 10.1007/s10489-018-1371-3
28	ZHANG F Q , HUI J Z , ZHU B , et al. An improved firefly algorithm for collaborative manufacturing chain optimization problem[J]. Proceedings of the Institution of Mechanical Engineers, 2019. doi: 10.1177/0954405418789981
29	ZHOU L Y , DING L X , MA M D , et al. An accurate partially attracted firefly algorithm[J]. Computing, 2019, 101 (5): 477- 493. doi: 10.1007/s00607-018-0645-2
30	KHALIFEHZADEH S , FAKHRZAD M B . A modified firefly algorithm for optimizing a multi stage supply chain network with stochastic demand and fuzzy production capacity[J]. Computers & Industrial Engineering, 2019, 133, 42- 56.

指标	< μ_i, v_i, κ_i>
x₁	< 0.812 5, 0.175 0, 0.012 5>
x₂	< 0.787 5, 0.212 5, 0.000 0>
x₃	< 0.837 5, 0.162 5, 0.000 0>
x₄	< 0.825 0, 0.150 0, 0.025 0>
x₅	< 0.950 0, 0.050 0, 0.000 0>
x₆	< 0.862 5, 0.125 0, 0.012 5>

指标权重	ω₁	ω₂	ω₃	ω₄	ω₅	ω₆
初始权重	0.155 0	0.148 0	0.160 0	0.159 8	0.207 6	0.169 6
区间上限	0.350 7	0.438 8	0.190 0	0.190 0	0.231 7	0.358 7
区间下限	0.112 9	0	0.121 1	0.053 3	0.123 8	0

指标权重	ω₁	ω₂	ω₃	ω₄	ω₅	ω₆
权重值	0.112 9	0.112 9	0.113 6	0.115 0	0.350 7	0.194 9

差	基本满足	满足	好	H	效用值	后悔值
${\hat \beta }$₁	${\hat \beta }$₂	${\hat \beta }$₃	${\hat \beta }$₄	${\hat \beta }$_H	${\bar D}$(X)	F(${\bar D}$(X))
0.009 5	0.082 2	0.752 6	0.154 6	0.001 1	0.790 5	0.052 9

评价方法	${\bar D}$(X)	F(${\bar D}$(X))
FA-ER	0.790 5	0.052 9
P-CMA-ES-ER	0.784 5	0.064 9
专家打分法-ER	0.665 8	0.160 8
直觉模糊熵-ER	0.711 5	0.123 2
fuzzy sets—AHP	0.702 3	∅