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Article(id=1322595127294546391, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1322595047657296718, articleNumber=null, orderNo=null, doi=null, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1713369600000, receivedDateStr=2024-04-18, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793260850976, onlineDateStr=2026-10-29, pubDate=1742832000000, pubDateStr=2025-03-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793260850976, onlineIssueDateStr=2026-10-29, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793260850976, creator=13701087609, updateTime=1793260850976, updator=13701087609, issue=Issue{id=1322595047657296718, tenantId=1146029695717560320, journalId=1225396423026438145, year='2025', volume='45', issue='3', pageStart='1', pageEnd='288', issueExtLink='null', onlineDate='null', pubDate='1742832000000', pubDateStr='2025-03-25', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793260831989, creator='13701087609', updateTime=1793260831989, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=24, endPage=30, ext={EN=ArticleExt(id=1322595127458124248, articleId=1322595127294546391, tenantId=1146029695717560320, journalId=1225396423026438145, language=EN, title=Optimal Selection of the Mining Method Based on Game Theory-Subjective and Objective Multi-Attribute Combined Weighting, columnId=null, journalTitle=Mining Research and Development, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In view of the optimal selection of mining methods in underground metal mines, a game theory-subjective and objective multi-attribute combined weighting model was constructed. Taking the optimal selection of mining methods at the Sijiaying Iron Mine as an example, under the criteria of environment, economy, technology, and safety, 11 indicators closely related to mining methods were selected. The improved analytic hierarchy process (AHP) and CRITIC methods were used to determine the subjective and objective weights of each indicator, respectively. By applying game theory, the subjective and objective weights were integrated to obtain the comprehensive weights for all indicators, providing a basis for the selection of mining methods. The game theory-subjective and objective multi-attribute combined weighting model was used for optimal selection between two alternative mining methods. The comprehensive membership degree of the sub-level open stoping method with subsequent filling is 0.711, while that of the block caving method with subsequent filling is 0.692, with the former being chosen as the optimal scheme. The research results can offer a beneficial reference for decision-making in mining method optimization.

, authors=Jie REN, Jiaoqun LI, Zengxiang LU, Baoyang ZHAO, Ziyang LIU, authorsList=Jie REN, Jiaoqun LI, Zengxiang LU, Baoyang ZHAO, Ziyang LIU, authorCompany=null, correspAuthors=Jiaoqun LI, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1322595136568152595, articleId=1322595127294546391, tenantId=1146029695717560320, journalId=1225396423026438145, language=CN, title=基于博弈论-主客观多属性组合赋权的采矿方法优选, columnId=1226462294490657775, journalTitle=矿业研究与开发, columnName=采矿与矿山充填, runingTitle=null, highlight=null, articleAbstract=

针对地下金属矿山采矿方法的优选，构建了基于博弈论-主客观多属性组合赋权模型。以司家营铁矿采矿方法优选为例，在环境、经济、技术和安全4个准则层下，选择11个与采矿方法密切相关的评价指标。采用改进层次分析法和CRITIC法分别确定各指标的主、客观权重，并运用博弈论思想，将主、客观权重进行融合，获得各指标的综合权重，从而为采矿方法优选提供依据。应用基于博弈论-主客观多属性组合赋权模型，对司家营铁矿的两种备选采矿方法进行了优选，阶段空场嗣后充填采矿法的综合隶属度为0.711，分段空场嗣后充填采矿法的综合隶属度为0.692，因此前者为该矿的最优采矿方法。所建立的模型为采矿方法的优选提供了一种新的手段。

, authors=任杰, 李角群, 路增祥, 赵宝洋, 刘子阳, authorsList=任杰, 李角群, 路增祥, 赵宝洋, 刘子阳, authorCompany=null, correspAuthors=李角群, authorNote=

任杰（2000—），男，内蒙古赤峰人，硕士研究生，主要从事采矿方法优选研究。E-mail:

, correspAuthorsNote=
李角群（1970—），男，辽宁鞍山人，博士，教授，主要从事矿山数字化技术及矿业软件开发方面的教学与科研工作。E-mail:
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任杰（2000—），男，内蒙古赤峰人，硕士研究生，主要从事采矿方法优选研究。E-mail:

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任杰（2000—），男，内蒙古赤峰人，硕士研究生，主要从事采矿方法优选研究。E-mail:

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Optimization study of the mining methods for the upper orebody of the second west mining area in Longshou Mine[D]. Mianyang: Southwest University of Science and Technology, 2019., articleTitle=Optimization study of the mining methods for the upper orebody of the second west mining area in Longshou Mine, refAbstract=null), Reference(id=1322595779781439654, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322595127294546391, doi=null, pmid=null, pmcid=null, year=2022, volume=38, issue=7, pageStart=51, pageEnd=55, url=null, language=null, rfNumber=[22], rfOrder=42, authorNames=陈树林, 李亮, 薛丽娟, journalName=现代矿业, refType=null, unstructuredReference=陈树林，李亮，薛丽娟，等.FAHP在尖山地采矿山采矿方法优选中的应用[J].现代矿业，2022，38(7)：51-55., articleTitle=FAHP在尖山地采矿山采矿方法优选中的应用, refAbstract=null), Reference(id=1322595779848548520, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322595127294546391, doi=null, pmid=null, pmcid=null, year=2022, volume=38, issue=7, pageStart=51, pageEnd=55, url=null, language=null, rfNumber=[22], rfOrder=43, authorNames=CHEN Shulin, LI Liang, XUE Lijuan, journalName=Modern Mining, refType=null, unstructuredReference=CHEN Shulin, LI Liang, XUE Lijuan, et al. Application of FAHP in mining method optimization of Jianshan Mine[J]. Modern Mining, 2022, 38(7):51-55., articleTitle=Application of FAHP in mining method optimization of Jianshan Mine, refAbstract=null)], funds=[Fund(id=1322595771581575291, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322595127294546391, awardId=HG2023215, language=CN, fundingSource=河钢集团重点科技项目(HG2023215), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1322595766393221194, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322595127294546391, xref=null, ext=[AuthorCompanyExt(id=1322595766405804107, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322595127294546391, companyId=1322595766393221194, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=School of Mining Engineering, University of Science and Technology Liaoning, Anshan, Liaoning 114051, China), AuthorCompanyExt(id=1322595766418387020, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322595127294546391, companyId=1322595766393221194, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=辽宁科技大学 矿业工程学院，辽宁　鞍山市　114051)])], figs=[ArticleFig(id=1322595770302312558, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322595127294546391, language=EN, label=Fig.1, caption=Index system of multi-attribute decision matrix for the optimal selection of mining method, figureFileSmall=up4uRNdgeX/41j/K2Sa9sQ==, figureFileBig=lFCNE16LmEzTw66E7cRCiQ==, tableContent=null), ArticleFig(id=1322595770382004335, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322595127294546391, language=CN, label=图1, caption=采矿方法多属性决策矩阵优选指标体系, figureFileSmall=up4uRNdgeX/41j/K2Sa9sQ==, figureFileBig=lFCNE16LmEzTw66E7cRCiQ==, tableContent=null), ArticleFig(id=1322595770486861936, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322595127294546391, language=EN, label=Table 1, caption=

A−P compare matrix

, figureFileSmall=null, figureFileBig=null, tableContent=
A-PP1P2P3P4ci
P112227
P201225
P300123
P400011
), ArticleFig(id=1322595770553970801, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322595127294546391, language=CN, label=表1, caption=

A−P 比较矩阵

, figureFileSmall=null, figureFileBig=null, tableContent=
A-PP1P2P3P4ci
P112227
P201225
P300123
P400011
), ArticleFig(id=1322595770621079667, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322595127294546391, language=EN, label=Table 2, caption=

A−P complete judgement matrix

, figureFileSmall=null, figureFileBig=null, tableContent=
A-PP1P2P3P4
P11.0001.4622.6038.997
P20.6841.0001.7806.154
P30.3840.5621.0003.457
P40.1110.1630.2891.000
), ArticleFig(id=1322595770734325876, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322595127294546391, language=CN, label=表2, caption=

A−P 完全判断矩阵

, figureFileSmall=null, figureFileBig=null, tableContent=
A-PP1P2P3P4
P11.0001.4622.6038.997
P20.6841.0001.7806.154
P30.3840.5621.0003.457
P40.1110.1630.2891.000
), ArticleFig(id=1322595770973401205, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322595127294546391, language=EN, label=Table 3, caption=

The weights calulated by improved analytic hierarchy process

, figureFileSmall=null, figureFileBig=null, tableContent=
准则A-P准则P1-X准则P2-X准则P3-X准则P4-X
P10.459X10.900X30.423X60.501X80.459
P20.314X20.100X40.289X70.345X90.314
P30.176——X50.289X80.154X100.176
P40.051——————X110.051
), ArticleFig(id=1322595771057287286, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322595127294546391, language=CN, label=表3, caption=

改进层次分析法的赋权计算结果

, figureFileSmall=null, figureFileBig=null, tableContent=
准则A-P准则P1-X准则P2-X准则P3-X准则P4-X
P10.459X10.900X30.423X60.501X80.459
P20.314X20.100X40.289X70.345X90.314
P30.176——X50.289X80.154X100.176
P40.051——————X110.051
), ArticleFig(id=1322595771149561975, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322595127294546391, language=EN, label=Table 4, caption=

Quantitative results of qualitative indicators

, figureFileSmall=null, figureFileBig=null, tableContent=
指标类型很低低较低一般较高高很高
效益型指标1234567
成本型指标7654321
), ArticleFig(id=1322595771241836664, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322595127294546391, language=CN, label=表4, caption=

定性指标量化结果

, figureFileSmall=null, figureFileBig=null, tableContent=
指标类型很低低较低一般较高高很高
效益型指标1234567
成本型指标7654321
), ArticleFig(id=1322595771325722745, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322595127294546391, language=EN, label=Table 5, caption=

Evaluation index of primary mining methods

, figureFileSmall=null, figureFileBig=null, tableContent=
方法x1x2x3/(元/t)x4/%x5/%x6/(t/d)x7/(m/kt)x8x9x10x11
M16765.307.312.63633.395655
M25639.797.811.03002.206566
), ArticleFig(id=1322595771426386042, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322595127294546391, language=CN, label=表5, caption=

初选采矿方法的评价指标

, figureFileSmall=null, figureFileBig=null, tableContent=
方法x1x2x3/(元/t)x4/%x5/%x6/(t/d)x7/(m/kt)x8x9x10x11
M16765.307.312.63633.395655
M25639.797.811.03002.206566
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基于博弈论-主客观多属性组合赋权的采矿方法优选
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任杰 , 李角群 , 路增祥 , 赵宝洋 , 刘子阳
矿业研究与开发 | 采矿与矿山充填 2025,45(3): 24-30
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矿业研究与开发 |采矿与矿山充填 2025 , 45 (3) : 24 -30
基于博弈论-主客观多属性组合赋权的采矿方法优选
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任杰 , 李角群 , 路增祥, 赵宝洋, 刘子阳
作者信息
  • 辽宁科技大学 矿业工程学院，辽宁　鞍山市　114051
通讯作者:
李角群（1970—），男，辽宁鞍山人，博士，教授，主要从事矿山数字化技术及矿业软件开发方面的教学与科研工作。E-mail:
作者简介:

任杰（2000—），男，内蒙古赤峰人，硕士研究生，主要从事采矿方法优选研究。E-mail:

Optimal Selection of the Mining Method Based on Game Theory-Subjective and Objective Multi-Attribute Combined Weighting
Jie REN , Jiaoqun LI , Zengxiang LU, Baoyang ZHAO, Ziyang LIU
Affiliations
  • School of Mining Engineering, University of Science and Technology Liaoning, Anshan, Liaoning 114051, China
出版时间: 2025-03-25
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摘要
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针对地下金属矿山采矿方法的优选，构建了基于博弈论-主客观多属性组合赋权模型。以司家营铁矿采矿方法优选为例，在环境、经济、技术和安全4个准则层下，选择11个与采矿方法密切相关的评价指标。采用改进层次分析法和CRITIC法分别确定各指标的主、客观权重，并运用博弈论思想，将主、客观权重进行融合，获得各指标的综合权重，从而为采矿方法优选提供依据。应用基于博弈论-主客观多属性组合赋权模型，对司家营铁矿的两种备选采矿方法进行了优选，阶段空场嗣后充填采矿法的综合隶属度为0.711，分段空场嗣后充填采矿法的综合隶属度为0.692，因此前者为该矿的最优采矿方法。所建立的模型为采矿方法的优选提供了一种新的手段。

采矿方法优选  /  博弈论  /  CRITIC法  /  层次分析法

In view of the optimal selection of mining methods in underground metal mines, a game theory-subjective and objective multi-attribute combined weighting model was constructed. Taking the optimal selection of mining methods at the Sijiaying Iron Mine as an example, under the criteria of environment, economy, technology, and safety, 11 indicators closely related to mining methods were selected. The improved analytic hierarchy process (AHP) and CRITIC methods were used to determine the subjective and objective weights of each indicator, respectively. By applying game theory, the subjective and objective weights were integrated to obtain the comprehensive weights for all indicators, providing a basis for the selection of mining methods. The game theory-subjective and objective multi-attribute combined weighting model was used for optimal selection between two alternative mining methods. The comprehensive membership degree of the sub-level open stoping method with subsequent filling is 0.711, while that of the block caving method with subsequent filling is 0.692, with the former being chosen as the optimal scheme. The research results can offer a beneficial reference for decision-making in mining method optimization.

Optimal selection of mining method  /  Game theory  /  CRITIC Method  /  Analytic hierarchy process
任杰, 李角群, 路增祥, 赵宝洋, 刘子阳. 基于博弈论-主客观多属性组合赋权的采矿方法优选. 矿业研究与开发, 2025 , 45 (3) : 24 -30 .
Jie REN, Jiaoqun LI, Zengxiang LU, Baoyang ZHAO, Ziyang LIU. Optimal Selection of the Mining Method Based on Game Theory-Subjective and Objective Multi-Attribute Combined Weighting[J]. Mining Research and Development, 2025 , 45 (3) : 24 -30 .
正文
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0　引言
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选择合适的采矿方法对于地下矿山工程设计来说至关重要，不仅要综合考虑矿山开采对周边环境的潜在影响，而且要确保经济合理、技术可行以及生产安全等多个关键因素[1]。
目前，依赖传统经验类比法进行采矿方案优选仍较普遍。经验类比法带有较强的主观性，存在适用性小、效率低和严谨性差等问题。赋权法综合考虑多个影响因素，并对不同因素赋予不同的权重，从而给出更为系统、合理的决策[3]。针对主观赋权法，李加州等[4]应用AHP-TOPSIS评价模型确定了最优的采矿方案。龚剑等[5]构建了AHP-模糊数学综合评判模型，为某高海拔矿山优选了采矿方法。宋宏元等[6]采用未确知测度理论对4种采矿方法进行优选评价。顾春宏[7]综合运用模糊聚类法与模糊综合评判法，确定了低品位多金属矿体的最优采矿方法。主观赋权法存在主观随意性，不仅会导致问题分析的复杂性，还增大了该方法应用的局限性。客观赋权法克服了主观赋权法的缺陷，段旦等[8]基于CRITIC-VIKOR法，对适宜残矿开采的3种采矿方法进行了选优。胡建华等[9]将FLAC3D与熵权法相结合，确定了琅琊山铜矿的最优采矿方法。陈建宏等[10]将主成分分析法与神经网络结合构建了采矿方法优选模型，既加快了数据处理速度，又提高了预测精度。但客观赋权法受数据质量的影响较大，可能会出现决策结果与工程实际存在偏差的问题。因此，主观赋权法和客观赋权法的组合成为了一种趋势，既可以依靠专家的知识和经验来处理一些难以量化的因素，又可以通过对客观数据的分析来减少主观判断的不确定性。张睿等[11]建立了AHP-均方差法多属性决策模型，以更偏向于主观权重的比例组合主、客观权重，完成了对采矿方法的终选。刘洋等[12]采用AHP-熵权法作为综合评判模型，通过乘法合成法对主、客观权重进行组合，平衡了主、客观权重给各指标造成的影响。马凯等[13]构建了TOPSIS-博弈论组合赋权模型，确定了某磷矿最优采矿方法。张居正等[14]将模糊数学-TOPSIS法与数值模拟相结合，并进行了采矿方法的优选。
综上所述，在采用合适的主客观赋权法基础上，合理分配权重以提高优选结果的准确性，是采矿方法优选的研究方向。司家营铁矿正在处于露天转为地下开采的前期研究，亟需确定转入地下开采的采矿方法。为此，本文建立了博弈论-主客观多属性组合赋权模型。该模型使用改进层次分析法和CRITIC法求得主、客观权重，采用博弈论思想进行权重融合以获得综合指标权重，进而选出最优的采矿方案。
1　博弈论-主客观多属性组合赋权模型
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1.1　应用改进层次分析法确定主观权重
层次分析法是一种多属性决策方法，旨在将复杂问题中的多属性进行拆分，使其分解为多个相关且层次分明的指标，以实现定性与定量相结合的分析。对定性指标进行量化处理时，通常采用九标度法确定不同层次各指标的相对重要性。但专家打分结果的一致性较难保证，会影响到决策结果的合理性。为简化这一过程，以“重要”“同样重要”和“不重要”三标度来判断同一层某一因素的重要性，专家不必提供精确的数字打分结果，便可完成打分[15]。这种改进提高了专家打分和决策分析的效率和准确性。使用改进层次分析法确定权重步骤如下。
（1）构造比较矩阵O。根据三标度法，以上一层各元素为基准，将每一层元素两两比较，用(0, 1，2)表示各指标的相对重要程度，进而构建比较矩阵。设有a个方案，b个指标，建立如下的比较矩阵。
（2）计算各指标排序指数ci。由比较矩阵O计算出指标排序指数。
（3）采用极比法，将比较矩阵O，构造成完全判断矩阵B。
式中：Bt为常量，一般Bt=9;c=cmax/cmin,cmax=max{c1,c2,⋯,cn},cmin=min{c1,c2,⋯,cn}.
（4）计算主观权重Wi，并进行一致性检验。鉴于各层指标数量较多，可能会导致对事物的客观重要程度产生混淆，因此必须进行一致性检验，以确保判断矩阵的有效性。
计算判断矩阵各指标的几何平均值ri。
将ri归一化，求出最大特征值对应的特征向量，即主观权重Wi。
求出判断矩阵的最大特征值λmax。
最后进行一致性检验。只有当一致性指标CR<0.1，才算作为有效判断矩阵，否则需重新进行专家打分，以调整判断矩阵。
式中：CI为一致性指标；RI为平均随机一致性指标；n为指标数量。
1.2　应用CRITIC法确定客观权重
CRITIC作为一种客观赋权法，比常用于采矿方法优选实践中的其他客观赋权法更合理[16]。该赋权法不仅通过计算各指标间的标准差来表示各指标间的差异性，还能通过计算各指标的相关系数来考究指标之间的线性关系，综合分析矛盾性与相关性，从而更深层次地分析指标自身的客观属性，并进行科学的评价。
（1）建立评价矩阵S=(sij)a×b。设有a个方案、b个指标，则：
（2）标准化处理。由于指标层中指标类型不同，处理方式也需相应调整。效益型指标，如矿块生产能力等，作为优选评价指标以越大越好为标准；而成本型指标，如损失率、贫化率和生产成本等，则以小为优，为方便比较计算，需要将各指标同向化。同时，由于指标种类繁多，存在单位不统一的问题，亦需要进行无量纲化处理，以消除不同指标之间的量纲影响。标准化处理方式采用比重法，计算公式见式(9)：
式中：s′ij表示效益型指标标准化处理后的指标值；s″ij为成本型指标处理后的结果；sij表示第j个指标的初始值。
（3）计算标准差σi。标准差可以度量出评价各指标间的差异性大小，标准差的计算见式(10)：
式中，表示第j个指标的均值。
（4）计算指标的信息量ηi。信息量由指标间相关性来表示，当两指标间的相关性越大时，则意味着二者体现的评价内容重复性越高，分配给两指标的权重也越小。
式中，αij为指标i与指标j的相关系数。
（5）计算客观权重W′i。将信息量归一化处理即可获得客观权重。
1.3　应用博弈论法确定综合权重
针对改进层次分析法在主观方面的局限性，以及CRITIC法过分强调客观数据而可能导致主观性较差的问题，可以通过组合二者权重的方式来兼顾决策者的主观经验判断与数据本身所带有的客观属性。博弈论在处理多属性决策问题时，寻求一致性或妥协，使所得出的综合权重与单一权重的偏差极小化。对于多属性决策问题的博弈法处理流程如下[17]。
（1）构造基础权重向量集qm。设对n个指标用M种方法进行赋权。
（2）构造M个权重向量V。
式中：V为综合权重向量；φm为线性组合系数且φm>0。
（3）求线性组合系数φm。
依照博弈论思想，需寻找一组φm使V与每组qm之间离差最小化，即：
依据微分原理求导，对式（15）求导可得出式（16）最优化一阶导数条件解为：
求解后，φm=[φ1,φ2,⋯,φn]即为组合权重最优线性组合系数。
（4）归一化处理，求得各方法权重系数。
（5）计算各指标综合权重V。
1.4　计算综合隶属度
依据式（19）计算各方案综合隶属度，并对各方案综合隶属度按大小排序，综合隶属度最大者为最优方案。
式中，S为指标标准化后矩阵。
2　采矿方法优选实例
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2.1　基于工程类比法的采矿方法初选
司家营铁矿区主要开采的矿体走向近南北，倾向西，倾角40°~50°，为倾斜厚及中厚矿体，呈似层状，主要产出矿石为磁铁矿。矿体围岩与夹石以黑云变粒岩为主，岩层稳定性为较稳定。司家营矿区周边村庄密集，且有天然水系流经矿区东南角。采用崩落法开采会引起地表塌陷，对周边村庄及建筑设施造成不利影响，而在露天转地下的特殊情况下，空场法需要开展较严格的地压管理[14]，因此，充填采矿法是一个更优的选择。基于此，初步选择了分段空场嗣后充填采矿法(M1)和阶段空场嗣后充填采矿法(M2)作为该矿的采矿方法备选方案。
2.2　采矿方法终选
2.2.1　基于改进层次分析法的主观权重计算
（1）构建多属性决策矩阵。构建多属性决策矩阵是采矿方法优选的基础工作，多属性决策矩阵是否合理科学直接影响着优选结果。决策矩阵选取的指标需定性与定量相结合，各指标间相互限制、相互补充，以能够较全面地反映信息。根据层次分析法原理与司家营矿区条件，广泛征求专家意见，并参考同类矿山，建立多属性评价体系，对初选的2种采矿方案进行综合评判[18-20]，如图1所示。
（2）将图1中列出的元素，通过式(1)进行两两比较，从而建立比较矩阵，并应用式(2)计算各指标排序指数ci，准则层比较矩阵见表1，指标层比较矩阵同理可得。
（3）根据式(3)采用极比法将比较矩阵构造成完全判断矩阵，准则层A−P完全判断矩阵见表2，其余指标层完全判断矩阵同理可得。
（4）应用式(4)和式(5)归一化后，得出各层指标权重，见表3。
（5）应用式(6)和式(7)进行一致性检验，各层均通过一致性检验，因此各层权重均为有效权重，整理可得出主观权重Wi：
2.2.2　基于CRITIC法的客观权重计算
（1）对定性指标按7标度法进行“定量化”。在图1列出的11个指标中，设X1、X2、X8、X9、X10、X11为定性指标；X3、X4、X5、X6、X7则为定量指标。定性指标通常无确定数值，由专家按照个人实际经验以及专业知识进行模糊评价，所得结果为“很低、低、较低、一般、较高、高”，为方便计算，需要依照表4对这些定性指标进行量化[21]。
（2）参考攀枝花铁矿采矿方法优选指标数值[22]，确定采矿方法初选评价指标，经量化处理后，初选各采矿方法评价指标数值见表5。
（3）根据式(9)对表5中的初始数据进行标准化处理，如X1、X2、X3、X4、X5、X7、X8、X9作为成本型指标处理；其余X6、X11、X12则按照效益型指标处理。得到标准化矩阵S：
（4）应用式(10)计算标准差σi:
（5）根据式(11)计算出各指标的信息量ηi:
（6）依据式(12)计算客观权重W′i:
2.2.3　基于博弈论思想求得综合隶属度
（1）基于上述赋权法得出的Wi、W′i由式(16)至式(18)可求得综合权重V:
（2）依据式(19)对标准化矩阵S进行加权，得出综合隶属度U=[0.692,0.711]。分段空场法嗣后充填采矿法的综合隶属度为0.692，阶段空场嗣后充填采矿法综合隶属度为0.711，依据最大隶属度决策原则，阶段空场嗣后充填采矿法(M2)为最优的采矿方法。
3　结论
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（1）针对改进层次分析法判断矩阵不一致性的问题，通过二次构造完全判断矩阵减少了迭代次数，提高了模型的效率和合理性。
（2）构建了基于博弈论-主客观多属性组合赋权评价模型，将定性与定量结合，使评价模型更加合理。
（3）采用基于博弈论-主客观多属性组合评价模型，对司家营铁矿露天转地下开采拟采用的采矿方法进行优选。结果显示，阶段空场嗣后充填采矿法具有更高的综合隶属度，确定该采矿法为最优的采矿方法。本文建立的评价模型为采矿方法优选提供了一种新的手段，在类似采矿工程的决策选择中具有一定的参考价值。
基金
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  • 河钢集团重点科技项目(HG2023215)
文献
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2025年第45卷第3期
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  • 接收时间：2024-04-18
  • 首发时间：2026-10-29
  • 出版时间：2025-03-25
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  • 收稿日期：2024-04-18
基金
河钢集团重点科技项目(HG2023215)
作者信息
    辽宁科技大学 矿业工程学院，辽宁　鞍山市　114051

通讯作者:

李角群（1970—），男，辽宁鞍山人，博士，教授，主要从事矿山数字化技术及矿业软件开发方面的教学与科研工作。E-mail:
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
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