Health Assessment of Equipment Based on IVIF

doi:10.3969/j.issn.1009-086x.2026.01.014

Abstract

Abstract:

To address the issues of weight allocation for parameters affecting the equipment health and the fusion of evaluation values for each parameter， a health assessment method of equipment based on technique for order preference by similarity to an ideal solution （TOPSIS）-rank-sum ratio （RSR） algorithm and interval-valued intuitionistic fuzzy （IVIF） was proposed according to the characteristics of equipment and its life extension requirements. Firstly， IVIF was introduced to determine the weight of decision experts， and the index weight was determined according to the evaluation hesitation degree and similarity degree， obtaining a weighted normalized matrix. Then， the TOPSIS was established， and the RSR assessment framework was integrated with TOPSIS to realize the health assessment of equipment and decision-making. Finally， simulation cases were utilized to evaluate， rank， and grade the health status of multiple equipment of the same model， and two known evaluation methods were compared to verify the feasibility of the proposed method.

Key words: health assessment, rank-sum ratio（RSR）, technique for order preference by similarity to an ideal solution（TOPSIS）, interval-valued intuitionistic fuzzy（IVIF）, equipment life extension

摘要：

为解决影响装备健康状态参数的权重分配及各参数评估值的融合问题，根据装备特点和其自身延寿需求，提出基于区间直觉模糊集（interval-valued intuitionistic fuzzy，IVIF）和融合逼近理想解排序法（technique for order preference by similarity to an ideal solution，TOPSIS）与秩和比法（rank-sum ratio，RSR）的装备健康状态评估方法。引入IVIF确定决策专家自身权重，根据其评估犹豫度及相似度综合确定指标权重，获取加权规范化矩阵；建立TOPSIS-RSR的评估框架实现对装备的健康状态评估及决策；利用仿真案例对多个同型号装备健康状态进行评估排序分级，对比2种已知评估方法验证方法了的可行性。

关键词: 健康评估, 秩和比, 逼近理想解排序法, 区间直觉模糊, 装备寿命延长

CLC Number:

TG760.89

Yao LEI, Jianyin ZHAO, Weimin LÜ. Health Assessment of Equipment Based on IVIF[J]. Modern Defense Technology, 2026, 54(1): 138-148.

雷瑶, 赵建印, 吕卫民. 基于直觉模糊集的装备健康状态评估方法[J]. 现代防御技术, 2026, 54(1): 138-148.

Figures/Tables 15

Fig. 1 Equipment health status evaluation framework

Table 1 Scale for the importance weights of the DMs

语言术语	IVIF值
	$μ ˜ A ˜ x$	$v ˜ A ˜ x$
	$μ A ˜ L, μ A ˜ U$	$v A ˜ L, v A ˜ U$
非常专业	$0.95,1.00$	$0.00,0.00$
较为专业	$0.80,0.85$	$0.05,0.10$
专业	$0.60,0.65$	$0.10,0.15$
较不专业	$0.30,0.35$	$0.25,0.30$
非常不专业	$0.20,0.25$	$0.30,0.35$
极不专业	$0.00,0.05$	$0.45,0.50$

Table 1 Scale for the importance weights of the DMs

语言术语	IVIF值
	$μ ˜ A ˜ x$	$v ˜ A ˜ x$
	$μ A ˜ L, μ A ˜ U$	$v A ˜ L, v A ˜ U$
非常专业	$0.95,1.00$	$0.00,0.00$
较为专业	$0.80,0.85$	$0.05,0.10$
专业	$0.60,0.65$	$0.10,0.15$
较不专业	$0.30,0.35$	$0.25,0.30$
非常不专业	$0.20,0.25$	$0.30,0.35$
极不专业	$0.00,0.05$	$0.45,0.50$

Table 2 Linguistic scale used for pairwise comparisons ［29］

语言术语	IVIF值		IVIF相对值
	$μ ˜ A ˜ x$	$υ ˜ A ˜ x$	$μ ˜ A ˜ x$	$υ ˜ A ˜ x$
	$μ A ˜ L, μ A ˜ U$	$υ A ˜ L, υ A ˜ U$	$μ A ˜ L, μ A ˜ U$	$υ A ˜ L, υ A ˜ U$
同等重要（EI）	$0.38,0.42$	$0.22,0.58$	$0.22,0.58$	$0.38,0.42$
介值（IV）	$0.29,0.41$	$0.12,0.58$	$0.12,0.58$	$0.29,0.41$
中等重要（MMI）	$0.10,0.43$	$0.57,0.03$	$0.57,0.03$	$0.10,0.43$
介值（IV2）	$0.03,0.47$	$0.03,0.53$	$0.03,0.53$	$0.03,0.47$
更加重要（SMI）	$0.13,0.53$	$0.07,0.47$	$0.07,0.47$	$0.13,0.53$
介值（IV3）	$0.32,0.62$	$0.08,0.38$	$0.08,0.38$	$0.32,0.62$
非常重要（VSMI）	$0.52,0.72$	$0.08,0.28$	$0.08,0.28$	$0.52,0.72$
介值（IV4）	$0.75,0.85$	$0.05,0.15$	$0.05,0.15$	$0.75,0.85$
极其重要（EMI）	$1.00,1.00$	$0,0$	$0,0$	$1.00,1.00$

Table 2 Linguistic scale used for pairwise comparisons ［29］

语言术语	IVIF值		IVIF相对值
	$μ ˜ A ˜ x$	$υ ˜ A ˜ x$	$μ ˜ A ˜ x$	$υ ˜ A ˜ x$
	$μ A ˜ L, μ A ˜ U$	$υ A ˜ L, υ A ˜ U$	$μ A ˜ L, μ A ˜ U$	$υ A ˜ L, υ A ˜ U$
同等重要（EI）	$0.38,0.42$	$0.22,0.58$	$0.22,0.58$	$0.38,0.42$
介值（IV）	$0.29,0.41$	$0.12,0.58$	$0.12,0.58$	$0.29,0.41$
中等重要（MMI）	$0.10,0.43$	$0.57,0.03$	$0.57,0.03$	$0.10,0.43$
介值（IV2）	$0.03,0.47$	$0.03,0.53$	$0.03,0.53$	$0.03,0.47$
更加重要（SMI）	$0.13,0.53$	$0.07,0.47$	$0.07,0.47$	$0.13,0.53$
介值（IV3）	$0.32,0.62$	$0.08,0.38$	$0.08,0.38$	$0.32,0.62$
非常重要（VSMI）	$0.52,0.72$	$0.08,0.28$	$0.08,0.28$	$0.52,0.72$
介值（IV4）	$0.75,0.85$	$0.05,0.15$	$0.05,0.15$	$0.75,0.85$
极其重要（EMI）	$1.00,1.00$	$0,0$	$0,0$	$1.00,1.00$

Table 3 Parameter values of health assessment for the equipment to be evaluated

待估装备	性能指标
待估装备	X₁	X₂	X₃	X₄	X₅	X₆
1	26.430	-7.790	-11.060	-4.443	-6.191	3.779
2	27.430	-7.998	-11.400	-4.565	-6.376	3.818
3	27.370	-7.939	-11.090	-4.697	-6.376	3.813
4	27.400	-8.266	-11.280	-4.716	-6.503	3.872
5	27.430	-8.261	-11.280	-4.716	-6.499	3.867
6	27.430	-8.266	-11.250	-4.716	-6.494	3.852
7	27.120	-8.090	-10.710	-4.912	-6.308	3.720
8	26.810	-8.098	-11.120	-4.648	-6.547	4.057
9	26.560	-8.017	-11.180	-4.458	-6.425	4.067
10	26.620	-8.061	-11.150	-4.599	-6.386	4.028

Table 4 Professionalism and weight of expert evaluation opinions

评估专家	语言术语	IVIF值		意见权重
		$μ ˜ A ˜ x$	$υ ˜ A ˜ x$
		$μ A ˜ L, μ A ˜ U$	$υ A ˜ L, υ A ˜ U$
1	专业	$0.60,0.65$	$0.10,0.15$	0.303 3
2	专业	$0.60,0.65$	$0.10,0.15$	0.303 3
3	非常专业	$0.95,1.00$	$0,0$	0.393 4

Table 4 Professionalism and weight of expert evaluation opinions

评估专家	语言术语	IVIF值		意见权重
		$μ ˜ A ˜ x$	$υ ˜ A ˜ x$
		$μ A ˜ L, μ A ˜ U$	$υ A ˜ L, υ A ˜ U$
1	专业	$0.60,0.65$	$0.10,0.15$	0.303 3
2	专业	$0.60,0.65$	$0.10,0.15$	0.303 3
3	非常专业	$0.95,1.00$	$0,0$	0.393 4

Table 5 Expert opinions on importance assessment of parameters

专家	参数评估
1	性能参数	X₁	X₂	X₃	X₄	X₅	X₆
	X₁	EI	IV2	MMI	IV2	IV4	IV3
	X₂		EI			IV3	MMI
	X₃		MMI	EI	MMI	VSMI	IV2
	X₄		MMI		EI	IV3	IV
	X₅					EI
	X₆					IV	EI
2	性能参数	X₁	X₂	X₃	X₄	X₅	X₆
	X₁	EI	MMI		IV2	IV2	IV3
	X₂		EI		IV	IV	SMI
	X₃	IV	IV	EI	IV3	IV3	VSMI
	X₄				EI		IV
	X₅				IV	EI	MMI
	X₆						EI
3	性能参数	X₁	X₂	X₃	X₄	X₅	X₆
	X₁	EI			IV2	IV2	IV
	X₂	IV2	EI	MMI	IV3	VSMI	SMI
	X₃	IV		EI	SMI	IV3	IV2
	X₄				EI	IV
	X₅					EI
	X₆				MMI	IV2	EI

Table 6 Comprehensive IVIF value based on expert opinions

专家	性能参数	综合IVIF值
		$μ ˜ A ˜ x$	$υ ˜ A ˜ x$	$π ˜ A ˜ x$
		$μ A ˜ L, μ A ˜ U$	$υ A ˜ L, υ A ˜ U$	$π A ˜ L, π A ˜ U$
1	X₁	0.519 5，0.796 0	0.004 9，0.204 0	0，0.475 6
	X₂	0.275 0，0.745 9	0.010 5，0.254 1	0，0.714 5
	X₃	0.362 4，0.738 4	0.006 0，0.261 6	0，0.631 6
	X₄	0.340 5，0.720 3	0.009 2，0.278 2	0.001 5，0.650 3
	X₅	0.240 6，0.579 9	0.163 4，0.417 1	0.003 0，0.596 0
	X₆	0.282 1，0.704 3	0.027 7，0.292 1	0.003 6，0.690 2
2	X₁	0.296 1，0.721 2	0.008 3，0.276 7	0.002 1，0.695 6
	X₂	0.357 9，0.708 7	0.026 6，0.286 2	0.005 1，0.615 5
	X₃	0.554 8，0.767 4	0.017 5，0.230 2	0.002 4，0.427 7
	X₄	0.303 0，0.706 4	0.038 3，0.287 9	0.005 7，0.658 7
	X₅	0.298 2，0.677 9	0.019 2，0.318 1	0.004 7，0.682 6
	X₆	0.233 2，0.674 2	0.067 5，0.323 4	0.002 4，0.699 3
3	X₁	0.335 8，0.789 9	0.002 3，0.206 7	0.003 4，0.661 9
	X₂	0.521 4，0.845 0	0.004 3，0.155 0	0，0.474 3
	X₃	0.425 0，0.814 0	0.003 2，0.184 8	0.001 2，0.571 8
	X₄	0.335 2，0.774 4	0.007 0，0.224 1	0.001 5，0.657 8
	X₅	0.279 6，0.769 4	0.010 6，0.228 4	0.002 2，0.709 8
	X₆	0.282 8，0.792 7	0.002 4，0.203 8	0.003 5，0.714 8
综合	X₁	0.387 3，0.773 1	0.004 3，0.224 9	0.002 0，0.608 4
	X₂	0.324 9，0.782 0	0.009 8，0.216 8	0.001 8，0.663 5
	X₃	0.451 0，0.779 3	0.006 5，0.219 5	0.001 2，0.542 5
	X₄	0.327 3，0.739 2	0.012 7，0.258 1	0.002 7，0.660 0
	X₅	0.273 8，0.683 7	0.029 1，0.303 1	0.013 2，0.697 1
	X₆	0.267 9，0.735 2	0.013 9，0.261 4	0.003 4，0.718 2

Table 6 Comprehensive IVIF value based on expert opinions

专家	性能参数	综合IVIF值
		$μ ˜ A ˜ x$	$υ ˜ A ˜ x$	$π ˜ A ˜ x$
		$μ A ˜ L, μ A ˜ U$	$υ A ˜ L, υ A ˜ U$	$π A ˜ L, π A ˜ U$
1	X₁	0.519 5，0.796 0	0.004 9，0.204 0	0，0.475 6
	X₂	0.275 0，0.745 9	0.010 5，0.254 1	0，0.714 5
	X₃	0.362 4，0.738 4	0.006 0，0.261 6	0，0.631 6
	X₄	0.340 5，0.720 3	0.009 2，0.278 2	0.001 5，0.650 3
	X₅	0.240 6，0.579 9	0.163 4，0.417 1	0.003 0，0.596 0
	X₆	0.282 1，0.704 3	0.027 7，0.292 1	0.003 6，0.690 2
2	X₁	0.296 1，0.721 2	0.008 3，0.276 7	0.002 1，0.695 6
	X₂	0.357 9，0.708 7	0.026 6，0.286 2	0.005 1，0.615 5
	X₃	0.554 8，0.767 4	0.017 5，0.230 2	0.002 4，0.427 7
	X₄	0.303 0，0.706 4	0.038 3，0.287 9	0.005 7，0.658 7
	X₅	0.298 2，0.677 9	0.019 2，0.318 1	0.004 7，0.682 6
	X₆	0.233 2，0.674 2	0.067 5，0.323 4	0.002 4，0.699 3
3	X₁	0.335 8，0.789 9	0.002 3，0.206 7	0.003 4，0.661 9
	X₂	0.521 4，0.845 0	0.004 3，0.155 0	0，0.474 3
	X₃	0.425 0，0.814 0	0.003 2，0.184 8	0.001 2，0.571 8
	X₄	0.335 2，0.774 4	0.007 0，0.224 1	0.001 5，0.657 8
	X₅	0.279 6，0.769 4	0.010 6，0.228 4	0.002 2，0.709 8
	X₆	0.282 8，0.792 7	0.002 4，0.203 8	0.003 5，0.714 8
综合	X₁	0.387 3，0.773 1	0.004 3，0.224 9	0.002 0，0.608 4
	X₂	0.324 9，0.782 0	0.009 8，0.216 8	0.001 8，0.663 5
	X₃	0.451 0，0.779 3	0.006 5，0.219 5	0.001 2，0.542 5
	X₄	0.327 3，0.739 2	0.012 7，0.258 1	0.002 7，0.660 0
	X₅	0.273 8，0.683 7	0.029 1，0.303 1	0.013 2，0.697 1
	X₆	0.267 9，0.735 2	0.013 9，0.261 4	0.003 4，0.718 2

Table 7 Weights of important parameter values

性能

参数

X₁

X₂

X₃

X₄

X₅

X₆

Table 8 Weighted normalized parameter values

性能指标	待估装备
性能指标	1	2	3	4	5	6	7	8	9	10
X₁	0.165 4	0.171 7	0.171 3	0.171 5	0.171 7	0.171 7	0.169 8	0.167 8	0.166 3	0.166 6
X₂	0.167 4	0.171 8	0.170 6	0.177 6	0.177 5	0.177 6	0.173 8	0.174 0	0.172 2	0.173 2
X₃	0.181 1	0.186 7	0.181 6	0.184 7	0.184 7	0.184 2	0.175 4	0.182 1	0.183 1	0.182 6
X₄	0.166 1	0.170 7	0.175 6	0.176 3	0.176 3	0.176 3	0.183 6	0.173 8	0.166 6	0.171 9
X₅	0.158 8	0.163 5	0.163 5	0.166 8	0.166 7	0.166 6	0.161 8	0.167 9	0.164 8	0.163 8
X₆	0.149 2	0.150 8	0.150 6	0.152 9	0.152 7	0.152 1	0.146 9	0.160 2	0.160 6	0.159 1

Table 9 Estimated equipment posting progress

待估装备	1	2	3	4	5	6	7	8	9	10
$C j$	0.190 2	0.467 6	0.473 2	0.656 6	0.652 5	0.637 4	0.501 7	0.626 6	0.477 1	0.537 1

Table 9 Estimated equipment posting progress

待估装备	1	2	3	4	5	6	7	8	9	10
$C j$	0.190 2	0.467 6	0.473 2	0.656 6	0.652 5	0.637 4	0.501 7	0.626 6	0.477 1	0.537 1

Table 10 RSRi distribution and corresponding Probit（pi ） alues

待估装备	D₁	D₂	D₃	D₄	D₅	D₆	D₇	D₈	D₉	D₁₀
$f ↓ i$	1	2	3	10	9	8	5	7	4	6
p	0.09	0.18	0.27	0.91	0.82	0.72	0.45	0.63	0.36	0.54
Probit（p_i ）	3.66	4.09	4.39	6.34	5.91	5.61	4.89	5.35	4.65	5.11

Table 10 RSRi distribution and corresponding Probit（pi ） alues

待估装备	D₁	D₂	D₃	D₄	D₅	D₆	D₇	D₈	D₉	D₁₀
$f ↓ i$	1	2	3	10	9	8	5	7	4	6
p	0.09	0.18	0.27	0.91	0.82	0.72	0.45	0.63	0.36	0.54
Probit（p_i ）	3.66	4.09	4.39	6.34	5.91	5.61	4.89	5.35	4.65	5.11

Table 11 Critical value of probit in common grades

分档数	Probit（p_i ）
3	4，6
4	3.5，5，6.5
5	3.2，4.4，5.6，6.8

Table 12 Results of equipment evaluation

待估装备	1	2	3	4	5
状态	合格	良好	良好	优秀	良好
待估装备	6	7	8	9	10
状态	良好	良好	良好	良好	良好

Fig. 2 Ranking and comparison results

Table 13 Compare the results of the parameters

对比参数

Kendall's tau

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