一种基于犹豫模糊粗糙集的工厂代储器材品种决策方法

doi:10.12305/j.issn.1001-506X.2026.01.21

摘要/Abstract

摘要：

针对工厂代储器材保障模式特点和决策信息犹豫模糊特征，运用传统器材品种决策方法难以实现属性约简和规则提取，提出一种基于犹豫模糊粗糙集的器材品种决策方法。首先，从生产周期、关键性、存储要求、经济性、消耗性、通用性和保障装备现代化水平等方面对工厂代储器材品种决策影响因素进行分析。然后，提出基于决策习惯的不完备信息延拓方法。最后，构建基于相似度的模糊等价关系器材属性约简和规则提取模型，选取代储器材工厂作为案例，验证所提方法的有效性。所提方法较好地完成代储器材品种的选择。

关键词: 犹豫模糊集, 粗糙集, 品种选择, 属性约简, 决策规则

Abstract:

Aiming at the characteristics of the factory storage equipment guarantee mode and the hesitant fuzzy feature of decision-making information, it is difficult to achieve attribute reduction and rule extraction using traditional equipment variety decision-making methods. Firstly, a equipment variety decision-making method based on hesitant fuzzy rough sets is proposed. Analyze the influencing factors of factory storage equipment variety decision-making from the aspects of production cycle, criticality, storage requirements, economy, consumption, universality, and modernization level of guarantee equipment. Secondly, an incomplete information extension method based on decision-making habits is proposed. Finally, constructed a equipment attribute reduction and rule extraction model based on similarity-derived fuzzy equivalence relation. A certain storage equipment factory is selected as a case study, and verified the effectiveness of the proposed method. The proposed method effectively completed the selection of storage equipment varieties.

Key words: hesitant fuzzy set, rough set, variety selection, attribute reduction, decision-making rule

中图分类号:

E 92

崔志强, 贾红丽, 高丽丽, 郝冰. 一种基于犹豫模糊粗糙集的工厂代储器材品种决策方法[J]. 系统工程与电子技术, 2026, 48(1): 235-248.

Zhiqiang CUI, Hongli JIA, Lili GAO, Bing HAO. Decision-making method based on hesitant fuzzy rough set for the variety of equipment stored on behalf of the factory[J]. Systems Engineering and Electronics, 2026, 48(1): 235-248.

图/表 13

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表10

工厂代储器材决策规则"

条件	决策	说明
$ \widetilde r_{1,{x_k}}^{{c_1}} \geqslant 0.775 \wedge \widetilde r_{1,{x_k}}^{{c_2}} \geqslant 0.775 \wedge \widetilde r_{1,{x_k}}^{{c_3}} \geqslant 0.775 $	配置	$ {x_1} \in \underline {\Re _{{c_1} \cup {c_2} \cup {c_3}}^\lambda } (X_1^d) $
$ \widetilde r_{2,{x_k}}^{{c_1}} \geqslant 0.775 \wedge \widetilde r_{2,{x_k}}^{{c_2}} \geqslant 0.775 \wedge \widetilde r_{2,{x_k}}^{{c_3}} \geqslant 0.775 $	配置	$ {x_2} \in \underline {\Re _{{c_1} \cup {c_2} \cup {c_3}}^\lambda } (X_1^d) $
$ \widetilde r_{3,{x_k}}^{{c_1}} \geqslant 0.775 \wedge \widetilde r_{3,{x_k}}^{{c_2}} \geqslant 0.775 \wedge \widetilde r_{3,{x_k}}^{{c_3}} \geqslant 0.775 $	配置	$ {x_3} \in \underline {\Re _{{c_1} \cup {c_2} \cup {c_3}}^\lambda } (X_1^d) $
$ \widetilde r_{4,{x_k}}^{{c_1}} \geqslant 0.775 \wedge \widetilde r_{4,{x_k}}^{{c_2}} \geqslant 0.775 \wedge \widetilde r_{4,{x_k}}^{{c_3}} \geqslant 0.775 $	配置	$ {x_4} \in \underline {\Re _{{c_1} \cup {c_2} \cup {c_3}}^\lambda } (X_1^d) $
$ \widetilde r_{7,{x_k}}^{{c_1}} \geqslant 0.775 \wedge \widetilde r_{7,{x_k}}^{{c_2}} \geqslant 0.775 \wedge \widetilde r_{7,{x_k}}^{{c_3}} \geqslant 0.775 $	配置	$ {x_7} \in \underline {\Re _{{c_1} \cup {c_2} \cup {c_3}}^\lambda } (X_1^d) $
$ \widetilde r_{8,{x_k}}^{{c_1}} \geqslant 0.775 \wedge \widetilde r_{8,{x_k}}^{{c_2}} \geqslant 0.775 \wedge \widetilde r_{8,{x_k}}^{{c_3}} \geqslant 0.775 $	不配置	$ {x_8} \in \underline {\Re _{{c_1} \cup {c_2} \cup {c_3}}^\lambda } (X_0^d) $
$ \widetilde r_{10,{x_k}}^{{c_1}} \geqslant 0.775 \wedge \widetilde r_{10,{x_k}}^{{c_2}} \geqslant 0.775 \wedge \widetilde r_{10,{x_k}}^{{c_3}} \geqslant 0.775 $	不配置	$ {x_{10}} \in \underline {\Re _{{c_1} \cup {c_2} \cup {c_3}}^\lambda } (X_0^d) $
$ \widetilde r_{11,{x_k}}^{{c_1}} \geqslant 0.775 \wedge \widetilde r_{11,{x_k}}^{{c_2}} \geqslant 0.775 \wedge \widetilde r_{11,{x_k}}^{{c_3}} \geqslant 0.775 $	不配置	$ {x_{11}} \in \underline {\Re _{{c_1} \cup {c_2} \cup {c_3}}^\lambda } (X_0^d) $
$ \widetilde r_{12,{x_k}}^{{c_1}} \geqslant 0.775 \wedge \widetilde r_{12,{x_k}}^{{c_2}} \geqslant 0.775 \wedge \widetilde r_{12,{x_k}}^{{c_3}} \geqslant 0.775 $	不配置	$ {x_{12}} \in \underline {\Re _{{c_1} \cup {c_2} \cup {c_3}}^\lambda } (X_0^d) $

表10

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器材类型	确定方法
关键件	器材发生故障或损坏将导致装备无法完成预定任务、丧失关键功能，甚至导致整个装备系统停机
重要件	器材发生故障或损坏将显著影响装备运转和性能发挥，降低任务执行效率或部分功能受限，但不会导致整个装备系统停机
一般件	器材发生故障或损坏将导致装备性能轻微降低，对装备的正常运行影响较小，通常不会影响任务的完成或装备的基本功能

器材品种	生产周期/月	器材价格/元	保障装备使用时间/年
x₁	15	5 099 302	4
x₂	+	3 800 000	1
x₃	12	1 855 400	3
x₄	5	1 469 000	4
x₅	4	357 082.5	8
x₆	6	51 250	8
x₇	+	45 000	1
x₈	1	43 651.88	4
x₉	+	13 500	1
x₁₀	2	204.75	25
x₁₁	1	54	16
x₁₂	2	46.2	9

保障装备使用时间/年	赋值
1	0.9
2	0.8
3	0.8
4	0.7
5	0.7
6~10	0.6
11~15	0.4
16~20	0.2
>20	0.1

论域	生产周期	关键程度	存储要求	经济性	消耗量	通用性	使用程度	是否存储
x₁	0.9	0.85，0.9，0.95	0.5，0.5，0.6	0.95	0.85，0.9，0.9	0.85，0.9，0.95	0.7	1
x₂	0.9，*，0.95	0.85，*，0.95	0.5，0.5，0.6	0.95	0.85，0.9，0.9	0.85，*，0.95	0.9	1
x₃	0.75	0.85，0.9，0.95	0.5，0.6，0.65	0.9	0.8，0.85，*	0.85，0.9，0.95	0.8	1
x₄	0.3	0.5，0.7，0.8	*，0.85，0.9	0.9	0.6，0.7，0.7	0.6，0.7，0.7	0.7	1
x₅	0.3	0.4，0.5，0.7	0.1，0.15，0.2	0.8	0.8，0.8，0.9	0.1，0.2，0.2	0.6	0
x₆	0.35	0.4，0.6，0.7	0.3，0.4，0.45	0.75	0.7，*，0.8	0.6，0.6，0.7	0.6	1
x₇	0.3，0.3，0.4	0.45，0.5，0.7	0.8，*，0.9	0.7	0.6，0.7，0.7	0.6，0.7，0.7	0.9	1
x₈	0.05	0.2，0.3，0.35	0.2，0.3，0.35	0.7	0.25，0.3，0.3	0.4，0.5，0.5	0.7	0
x₉	0.2，0.2，0.3	0.6，0.7，0.75	0.5，0.55，0.7	0.5	0.5，0.5，0.6	0.2，0.3，0.3	0.9	1
x₁₀	0.1	0.2，*，0.3	0.2，0.3，0.35	0.1	0.2，0.2，0.3	0.1，0.1，0.2	0.1	0
x₁₁	0.05	0.1，0.2，0.3	0.05，0.1，0.15	0.05	0.15，0.2，0.2	*，0.1，0.1	0.2	0
x₁₂	0.1	0.1，0.3，0.35	0.2，0.3，0.35	0.05	0.2，0.2，0.3	0.4，0.5，0.5	0.6	0

论域	生产周期	关键程度	存储要求	经济性	消耗量	通用性	使用程度	是否存储
x₁	0.9	0.85，0.9，0.95	0.5，0.5，0.6	0.95	0.85，0.9，0.9	0.85，0.9，0.95	0.7	1
x₂	0.9，0.9，0.95	0.85，0.9，0.95	0.5，0.5，0.6	0.95	0.85，0.9，0.9	0.85，0.92，0.95	0.9	1
x₃	0.75	0.85，0.9，0.95	0.5，0.6，0.65	0.9	0.8，0.85，0.9	0.85，0.9，0.95	0.8	1
x₄	0.3	0.5，0.7，0.8	0.8，0.85，0.9	0.9	0.6，0.7，0.7	0.6，0.7，0.7	0.7	1
x₅	0.3	0.4，0.5，0.7	0.1，0.15，0.2	0.8	0.8，0.8，0.9	0.1，0.2，0.2	0.6	0
x₆	0.35	0.4，0.6，0.7	0.3，0.4，0.45	0.75	0.7，0.75，0.8	0.6，0.6，0.7	0.6	1
x₇	0.3，0.3，0.4	0.45，0.5，0.7	0.8，0.85，0.9	0.7	0.6，0.7，0.7	0.6，0.7，0.7	0.9	1
x₈	0.05	0.2，0.3，0.35	0.2，0.3，0.35	0.7	0.25，0.3，0.3	0.4，0.5，0.5	0.7	0
x₉	0.2，0.2，0.3	0.6，0.7，0.75	0.5，0.55，0.7	0.5	0.5，0.5，0.6	0.2，0.3，0.3	0.9	1
x₁₀	0.1	0.2，0.25，0.3	0.2，0.3，0.35	0.1	0.2，0.2，0.3	0.1，0.1，0.2	0.1	0
x₁₁	0.05	0.1，0.2，0.3	0.05，0.1，0.15	0.05	0.15，0.2，0.2	0.1，0.1，0.1	0.2	0
x₁₂	0.1	0.1，0.3，0.35	0.2，0.3，0.35	0.05	0.2，0.2，0.3	0.4，0.5，0.5	0.6	0