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'''顺序优先法'''（OPA）是一种{{le|多准则决策分析方法|Multiple-criteria decision analysis}}（multi-criteria decision-making ,MCDM），有助于解决具有[[偏好关系]]的[[集體決策]]问题。 == 描述 == 大多数的多准则决策分析方法，如[[层次分析法]]（analytic hierarchy Process, AHP）和{{le|网络分析法|Analytic network process}}（Analytic Network Process, ANP），是以[[成对比较]]矩阵为基础的<ref>{{Cite journal |last=Penadés-Plà |first=Vicent |last2=García-Segura |first2=Tatiana |last3=Martí |first3=José V. |last4=Yepes |first4=Víctor |date=2016-12 |title=A Review of Multi-Criteria Decision-Making Methods Applied to the Sustainable Bridge Design |url=https://www.mdpi.com/2071-1050/8/12/1295 |journal=Sustainability |language=en |volume=8 |issue=12 |doi=10.3390/su8121295 |issn=2071-1050 |access-date=2022-10-31 |archive-date=2022-11-22 |archive-url=https://web.archive.org/web/20221122211902/http://www.mdpi.com/2071-1050/8/12/1295 |dead-url=no }}</ref>。 [[File:决策问题.png|alt=决策问题|thumb|170x170px|决策问题<ref name=":10" />]] 该方法使用[[線性規劃]]方法同时计算专家、评价指标和备选方案的权重<ref name=":10">{{Cite journal |last=Ataei |first=Younes |last2=Mahmoudi |first2=Amin |last3=Feylizadeh |first3=Mohammad Reza |last4=Li |first4=Deng-Feng |date=2020-01-01 |title=Ordinal Priority Approach (OPA) in Multiple Attribute Decision-Making |url=https://www.sciencedirect.com/science/article/pii/S156849461930674X |journal=Applied Soft Computing |language=en |volume=86 |doi=10.1016/j.asoc.2019.105893 |issn=1568-4946 |access-date=2022-10-31 |archive-date=2022-10-18 |archive-url=https://web.archive.org/web/20221018043220/https://www.sciencedirect.com/science/article/pii/S156849461930674X |dead-url=no }}</ref>。在OPA方法中使用{{le|序数数据|Ordinal data}}的主要原因是与涉及人类的群体决策问题中使用的精确比例相比，序数数据的可及性和准确性<ref>{{Cite journal |last=Wang |first=Haomin |last2=Peng |first2=Yi |last3=Kou |first3=Gang |date=2021-07-01 |title=A two-stage ranking method to minimize ordinal violation for pairwise comparisons |url=https://www.sciencedirect.com/science/article/pii/S1568494621002106 |journal=Applied Soft Computing |language=en |volume=106 |doi=10.1016/j.asoc.2021.107287 |issn=1568-4946 |access-date=2022-10-31 |archive-date=2022-10-31 |archive-url=https://web.archive.org/web/20221031054953/https://www.sciencedirect.com/science/article/pii/S1568494621002106 |dead-url=no }}</ref>。 在现实世界中，专家们可能对某一选择或评价指标没有足够的了解。这种情况下，问题的输入数据是不完整的，此时需要在OPA线性规划模型中删除与评价指标或备选方案相关的约束条件<ref name="未命名-20230318201033">{{Cite journal |last=Mahmoudi |first=Amin |last2=Deng |first2=Xiaopeng |last3=Javed |first3=Saad Ahmed |last4=Yuan |first4=Jingfeng |date=2021-10-01 |title=Large-scale multiple criteria decision-making with missing values: project selection through TOPSIS-OPA |url=https://doi.org/10.1007/s12652-020-02649-w |journal=Journal of Ambient Intelligence and Humanized Computing |language=en |volume=12 |issue=10 |doi=10.1007/s12652-020-02649-w |issn=1868-5145 |access-date=2022-10-31 |archive-date=2022-09-23 |archive-url=https://web.archive.org/web/20220923134422/https://link.springer.com/article/10.1007/s12652-020-02649-w |dead-url=no }}</ref>。 近年来，各种类型的数据归一化方法被应用于多准则决策方法 (multi-criteria decision-making ,MCDM) 中。Palczewski和 Satabun表明，使用各种数据归一化方法可以改变多准则决策方法的最终排名<ref>{{Cite journal |last=Palczewski |first=Krzysztof |last2=Sałabun |first2=Wojciech |date=2019-01-01 |title=Influence of various normalization methods in PROMETHEE II: an empirical study on the selection of the airport location |url=https://www.sciencedirect.com/science/article/pii/S1877050919315819 |journal=Procedia Computer Science |series=Knowledge-Based and Intelligent Information & Engineering Systems: Proceedings of the 23rd International Conference KES2019 |language=en |volume=159 |doi=10.1016/j.procs.2019.09.378 |issn=1877-0509 |access-date=2022-10-31 |archive-date=2022-10-31 |archive-url=https://web.archive.org/web/20221031054951/https://www.sciencedirect.com/science/article/pii/S1877050919315819 |dead-url=no }}</ref>。Javed 及其同事表明，可以通过避免数据归一化来解决多准则决策问题<ref name=":0">{{Cite journal |last=Javed |first=Saad Ahmed |last2=Gunasekaran |first2=Angappa |last3=Mahmoudi |first3=Amin |date=2022-11-01 |title=DGRA: Multi-sourcing and supplier classification through Dynamic Grey Relational Analysis method |url=https://www.sciencedirect.com/science/article/pii/S0360835222006623 |journal=Computers & Industrial Engineering |language=en |volume=173 |doi=10.1016/j.cie.2022.108674 |issn=0360-8352 |access-date=2022-10-31 |archive-date=2022-10-29 |archive-url=https://web.archive.org/web/20221029082854/https://www.sciencedirect.com/science/article/pii/S0360835222006623 |dead-url=no }}</ref>。不需要对偏好关系进行归一化，因此，OPA方法不需要数据归一化<ref name=":1">{{Cite journal |last=Mahmoudi |first=Amin |last2=Deng |first2=Xiaopeng |last3=Javed |first3=Saad Ahmed |last4=Zhang |first4=Na |date=2021-01 |title=Sustainable Supplier Selection in Megaprojects: Grey Ordinal Priority Approach |url=https://onlinelibrary.wiley.com/doi/10.1002/bse.2623 |journal=Business Strategy and the Environment |language=en |volume=30 |issue=1 |doi=10.1002/bse.2623 |issn=0964-4733 |access-date=2022-10-31 |archive-date=2022-09-26 |archive-url=https://web.archive.org/web/20220926123411/https://onlinelibrary.wiley.com/doi/10.1002/bse.2623 |dead-url=no }}</ref>。 == OPA方法 == OPA模型是一个线性规划模型，可以利用[[单纯形法]]来解决。该方法的步骤如下:<ref name=":5">{{Cite journal |last=Mahmoudi |first=Amin |last2=Javed |first2=Saad Ahmed |date=2022-10 |title=Probabilistic Approach to Multi-Stage Supplier Evaluation: Confidence Level Measurement in Ordinal Priority Approach |url=https://link.springer.com/10.1007/s10726-022-09790-1 |journal=Group Decision and Negotiation |language=en |volume=31 |issue=5 |doi=10.1007/s10726-022-09790-1 |issn=0926-2644 |pmc=9409630 |pmid=36042813}}</ref><ref name=":8" /><ref name=":10" /> '''第一步:''' 确定专家，并根据工作经验、教育资格等确定专家的优先次序。 '''第二步:''' 确定评价指标，并确定每个专家对指标的偏好。 '''第三步:''' 确定备选方案，并由每个专家确定在每一评价指标下备选方案的偏好。 '''第四步:''' 构建以下线性规划模型，并通过适当的优化软件如LINGO、GAMS、MATLAB等进行求解。 <math display="inline">\begin{align} &Max Z \\ &S.t. \\ &Z \leq r_{i}\bigg (r_{j} \big(r_{k} (w_{ijk}^{r_{k}} - w_{ijk}^{{r_{k}}+1}) \big)\bigg) \; \; \; \; \forall i,j \; and \; r_{k} \\ &Z \leq r_{i} r_{j} r_{m} w_{ijk}^{r_{m}} \; \; \; \forall i,j \; and \; r_{m} \\ &\sum_{i=1}^{p}\sum_{j=1}^{n}\sum_{k=1}^{m} w_{ijk} = 1 \\ &w_{ijk}\geq0 \; \; \; \forall i, j \; and \; k \\ &Z: Unrestricted\;in\;sign \\ \end{align} </math> 在上述模型中。<math>r_i(i=1,...,p)</math>代表专家的等级<math>i</math>, <math>r_j(j=1...,n)</math>代表指标的等级<math>j</math>,<math>r_k(k=1...,m)</math>代表备选方案的等级<math>k</math>。而<math>w_{ijk}</math>代表专家i在评价指标j下备选方案k的权重。在解决OPA线性规划模型后，每个备选方案的权重由以下公式计算。 <math>\begin{aligned} &w_k=\sum_{i=1}^{p}\sum_{j=1}^{n} w_{ijk} \; \; \; \; \forall k \\ \end{aligned}</math> 每个评价指标的权重按以下公式计算。 <math>\begin{aligned} &w_j=\sum_{i=1}^{p}\sum_{k=1}^{m} w_{ijk} \; \; \; \; \forall j \\ \end{aligned}</math> 每个专家的权重按以下公式计算。 <math>\begin{aligned} &w_i=\sum_{j=1}^{n}\sum_{k=1}^{m} w_{ijk} \; \; \; \; \forall i \\ \end{aligned}</math> == 例子 == [[File:例子的决策问题.png|alt=例子的决策问题|thumb|411x411px|例子的决策问题]] 假设要调查买房子的问题<ref>{{Cite journal |date=2022-10-23 |title=Ordinal priority approach |url=https://en.wikipedia.org/w/index.php?title=Ordinal_priority_approach&oldid=1117748832 |journal=Wikipedia |language=en}}</ref>。在这个决策问题中，有两位专家，同时有两个评价指标，即成本（c）和建筑质量（q），为房屋的选择提供标准。另一方面，有三所房子(h1，h2，h3）可供购买。第一个专家（x）有三年的工作经验，第二个专家（y）有两年的工作经验。该问题的结构如图所示。 '''第 1 步：'''第一位专家（x）比专家（y）有更多经验，因此 x>y。 '''第 2 步：'''专家对评价指标的偏好总结在下表中。 {| class="wikitable" |+专家对评价指标的意见 !评价指标 !专家（x） !专家（y） |- |c |1 |2 |- |q |2 |1 |} '''第 3 步：'''专家对备选方案的偏好总结在下表中。 {| class="wikitable" |+专家对备选方案的意见 ! rowspan="2" |备选方案 ! colspan="2" |专家（x) ! colspan="2" |专家（y） |- !c !q !c !q |- |h1 |1 |2 |1 |3 |- |h2 |3 |1 |2 |1 |- |h3 |2 |3 |3 |2 |} '''第 4 步：'''根据输入数据形成 OPA 线性规划模型，具体如下。 <math>\begin{align} &Max Z \\ &S.t. \\ &Z \leq 1*1* 1* (w_{xch1} - w_{xch3}) \; \; \; \; \\ &Z \leq 1*1*2* (w_{xch3} - w_{xch2})\; \; \; \; \\ &Z \leq 1* 1 *3* w_{xch2} \; \; \; \\ \\ &Z \leq 1*2* 1* (w_{xqh2} - w_{xqh1}) \; \; \; \; \\ &Z \leq 1*2* 2* (w_{xqh1} - w_{xqh3}) \; \; \; \; \\ &Z \leq 1* 2 *3* w_{xqh3} \; \; \; \\ \\ &Z \leq 2*2* 1* (w_{ych1} - w_{ych2}) \; \; \; \; \\ &Z \leq 2*2*2* (w_{ych2} - w_{ych3})\; \; \; \; \\ &Z \leq 2* 2 *3* w_{ych3} \; \; \; \\ \\ &Z \leq 2*1* 1* (w_{yqh2} - w_{yqh3}) \; \; \; \; \\ &Z \leq 2*1* 2* (w_{yqh3} - w_{yqh1}) \; \; \; \; \\ &Z \leq 2* 1 *3* w_{yqh1} \; \; \; \\ \\ &w_{xch1} + w_{xch2} + w_{xch3} + w_{xqh1} + w_{xqh2} + w_{xqh3}+w_{ych1} + w_{ych2} + w_{ych3} + w_{yqh1} + w_{yqh2} + w_{yqh3}= 1 \\ \\ \end{align} </math> 用优化软件求解上述模型后，得到专家、评价指标和备选方案的权重如下。 <math>\begin{align}&w_{x}=w_{xch1} + w_{xch2} + w_{xch3} + w_{xqh1} + w_{xqh2} + w_{xqh3}=0.666667 \\\\&w_{y}=w_{ych1} + w_{ych2} + w_{ych3} + w_{yqh1} + w_{yqh2} + w_{yqh3}=0.333333 \\\\\\&w_{c}=w_{xch1} + w_{xch2} + w_{xch3} + w_{ych1} + w_{ych2} + w_{ych3}=0.555556 \\\\&w_{q}=w_{xqh1} + w_{xqh2} + w_{xqh3} + w_{yqh1} + w_{yqh2} + w_{yqh3}=0.444444 \\\\\\&w_{h1}=w_{xch1} + w_{xqh1} + w_{ych1} + w_{yqh1} = 0.425926 \\\\&w_{h2}=w_{xch2} + w_{xqh2} + w_{ych2} + w_{yqh2} =0.351852 \\\\&w_{h3}=w_{xch3} + w_{xqh3} + w_{ych3} + w_{yqh3} =0.222222\\\\\end{align} </math> 因此，房子1（h1）被认为是最佳选择。此外，可以认为，评价指标成本（c）比评价指标建筑质量（q）更重要。另外，根据专家的权重，可以认为，与专家（y）相比，专家（x）对最终选择的影响更大。 == 应用 == OPA方法在各个研究领域的应用总结如下。 '''农业、制造业、服务业''' * 制造业供应链<ref name=":6">{{Cite journal |last=Mahmoudi |first=Amin |last2=Abbasi |first2=Mehdi |last3=Deng |first3=Xiaopeng |date=2022-04-01 |title=Evaluating the Performance of the Suppliers Using Hybrid DEA-OPA Model: A Sustainable Development Perspective |url=https://doi.org/10.1007/s10726-021-09770-x |journal=Group Decision and Negotiation |language=en |volume=31 |issue=2 |doi=10.1007/s10726-021-09770-x |issn=1572-9907}}</ref><ref name=":0" /> * 可持续农业<ref>{{Cite journal |last=Shajedul |first=Islam |date=2021-07-28 |title=Evaluation of Low-Carbon Sustainable Technologies in Agriculture Sector through Grey Ordinal Priority Approach {{!}} International Journal of Grey Systems |url=http://publish.thescienceinsight.com/index.php/ijgs/article/view/3 |journal= |language=en-US |doi=10.52812/ijgs.3 |access-date=2022-10-31 |archive-date=2022-10-27 |archive-url=https://web.archive.org/web/20221027110914/http://publish.thescienceinsight.com/index.php/ijgs/article/view/3 |dead-url=no }}</ref> * 生产战略<ref name="未命名_2-20230318201033">{{Cite journal |last=Le |first=Minh-Tai |last2=Nhieu |first2=Nhat-Luong |date=2022-01 |title=A Novel Multi-Criteria Assessment Approach for Post-COVID-19 Production Strategies in Vietnam Manufacturing Industry: OPA–Fuzzy EDAS Model |url=https://www.mdpi.com/2071-1050/14/8/4732 |journal=Sustainability |language=en |volume=14 |issue=8 |doi=10.3390/su14084732 |issn=2071-1050 |access-date=2022-10-31 |archive-date=2022-10-31 |archive-url=https://web.archive.org/web/20221031060934/https://www.mdpi.com/2071-1050/14/8/4732 |dead-url=no }}</ref> * 生产调度<ref>{{Cite journal |last=Tafakkori |first=Keivan |last2=Tavakkoli-Moghaddam |first2=Reza |last3=Siadat |first3=Ali |date=2022-06-01 |title=Sustainable negotiation-based nesting and scheduling in additive manufacturing systems: A case study and multi-objective meta-heuristic algorithms |url=https://www.sciencedirect.com/science/article/pii/S0952197622000975 |journal=Engineering Applications of Artificial Intelligence |language=en |volume=112 |doi=10.1016/j.engappai.2022.104836 |issn=0952-1976}}</ref> * 汽车工业<ref>{{Cite journal |date=2022-07-20 |title=Evaluation of Automotive Parts Suppliers through Ordinal Priority Approach and TOPSIS {{!}} Management Science and Business Decisions |url=https://publish.thescienceinsight.com/index.php/msbd/article/view/37 |language=en-US |doi=10.52812/msbd.37 |access-date=2022-10-31 |archive-date=2022-07-21 |archive-url=https://web.archive.org/web/20220721064058/https://publish.thescienceinsight.com/index.php/msbd/article/view/37 |dead-url=no }}</ref> * 社区服务需求<ref>{{Cite journal |last=Li |first=Jintao |last2=Dai |first2=Yan |last3=Wang |first3=Cynthia Changxin |last4=Sun |first4=Jun |date=2022-07-26 |title=Assessment of Environmental Demands of Age-Friendly Communities from Perspectives of Different Residential Groups: A Case of Wuhan, China |url=https://www.mdpi.com/1660-4601/19/15/9120 |journal=International Journal of Environmental Research and Public Health |language=en |volume=19 |issue=15 |doi=10.3390/ijerph19159120 |issn=1660-4601 |pmc=9368052 |pmid=35897508 |access-date=2022-10-31 |archive-date=2022-08-02 |archive-url=https://web.archive.org/web/20220802111652/https://www.mdpi.com/1660-4601/19/15/9120 |dead-url=no }}</ref> '''建筑行业''' * 建筑分包<ref>{{Cite journal |last=Mahmoudi |first=Amin |last2=Javed |first2=Saad Ahmed |date=2022-04-01 |title=Performance Evaluation of Construction Sub‐contractors using Ordinal Priority Approach |url=https://www.sciencedirect.com/science/article/pii/S0149718921001178 |journal=Evaluation and Program Planning |language=en |volume=91 |doi=10.1016/j.evalprogplan.2021.102022 |issn=0149-7189}}</ref> * 可持续建造<ref name=":1" /><ref name=":2">{{Cite journal |last=Sadeghi |first=Mahsa |last2=Mahmoudi |first2=Amin |last3=Deng |first3=Xiaopeng |date=2022-02-01 |title=Adopting distributed ledger technology for the sustainable construction industry: evaluating the barriers using Ordinal Priority Approach |url=https://doi.org/10.1007/s11356-021-16376-y |journal=Environmental Science and Pollution Research |language=en |volume=29 |issue=7 |doi=10.1007/s11356-021-16376-y |issn=1614-7499 |pmc=8443118 |pmid=34528198}}</ref><ref name=":3">{{Cite journal |last=Sadeghi |first=Mahsa |last2=Mahmoudi |first2=Amin |last3=Deng |first3=Xiaopeng |date=2022-01-01 |title=Blockchain technology in construction organizations: risk assessment using trapezoidal fuzzy ordinal priority approach |url=https://doi.org/10.1108/ECAM-01-2022-0014 |journal=Engineering, Construction and Architectural Management |volume=ahead-of-print |issue=ahead-of-print |doi=10.1108/ECAM-01-2022-0014 |issn=0969-9988}}</ref><ref>{{Cite journal |last=Sadeghi |first=M. |last2=Mahmoudi |first2=A. |last3=Deng |first3=X. |last4=Luo |first4=X. |date=2022-06-27 |title=Prioritizing requirements for implementing blockchain technology in construction supply chain based on circular economy: Fuzzy Ordinal Priority Approach |url=https://doi.org/10.1007/s13762-022-04298-2 |journal=International Journal of Environmental Science and Technology |language=en |doi=10.1007/s13762-022-04298-2 |issn=1735-2630}}</ref><ref name=":7">{{Cite journal |last=Mahmoudi |first=Amin |last2=Sadeghi |first2=Mahsa |last3=Deng |first3=Xiaopeng |date=2022-04-12 |title=Performance measurement of construction suppliers under localization, agility, and digitalization criteria: Fuzzy Ordinal Priority Approach |url=https://doi.org/10.1007/s10668-022-02301-x |journal=Environment, Development and Sustainability |language=en |doi=10.1007/s10668-022-02301-x |issn=1573-2975 |pmc=9001166 |pmid=35431618}}</ref> * [[项目管理]]<ref name=":8">{{Cite journal |last=Mahmoudi |first=Amin |last2=Abbasi |first2=Mehdi |last3=Deng |first3=Xiaopeng |date=2022-02-01 |title=A novel project portfolio selection framework towards organizational resilience: Robust Ordinal Priority Approach |url=https://www.sciencedirect.com/science/article/pii/S0957417421014068 |journal=Expert Systems with Applications |language=en |volume=188 |doi=10.1016/j.eswa.2021.116067 |issn=0957-4174}}</ref><ref>{{Cite journal |last=Faisal |first=Mohd. Nishat |last2=Al Subaie |first2=Abdulla Abdulaziz |last3=Sabir |first3=Lamay Bin |last4=Sharif |first4=Khurram Jahangir |date=2022-01-01 |title=PMBOK, IPMA and fuzzy-AHP based novel framework for leadership competencies development in megaprojects |url=https://doi.org/10.1108/BIJ-10-2021-0583 |journal=Benchmarking: An International Journal |volume=ahead-of-print |issue=ahead-of-print |doi=10.1108/BIJ-10-2021-0583 |issn=1463-5771 |access-date=2022-10-31 |archive-date=2022-09-23 |archive-url=https://web.archive.org/web/20220923134423/https://www.emerald.com/insight/content/doi/10.1108/BIJ-10-2021-0583/full/html |dead-url=no }}</ref><ref name="未命名-20230318201033"/> '''能源与环境''' * 太阳能和风能<ref>{{Cite journal |last=Elkadeem |first=Mohamed R. |last2=Younes |first2=Ali |last3=Mazzeo |first3=Domenico |last4=Jurasz |first4=Jakub |last5=Elia Campana |first5=Pietro |last6=Sharshir |first6=Swellam W. |last7=Alaam |first7=Mohamed A. |date=2022-09-15 |title=Geospatial-assisted multi-criterion analysis of solar and wind power geographical-technical-economic potential assessment |url=https://www.sciencedirect.com/science/article/pii/S0306261922008492 |journal=Applied Energy |language=en |volume=322 |doi=10.1016/j.apenergy.2022.119532 |issn=0306-2619}}</ref> * 低碳技术<ref>{{Cite journal |date=2021-07-28 |title=Evaluation of Low-Carbon Sustainable Technologies in Agriculture Sector through Grey Ordinal Priority Approach {{!}} International Journal of Grey Systems |url=http://publish.thescienceinsight.com/index.php/ijgs/article/view/3 |language=en-US |doi=10.52812/ijgs.3 |access-date=2022-10-31 |archive-date=2022-10-27 |archive-url=https://web.archive.org/web/20221027110914/http://publish.thescienceinsight.com/index.php/ijgs/article/view/3 |dead-url=no }}</ref> * 电气化和排放<ref>{{Cite journal |date=2022-07-29 |title=Evaluation of Barriers to Electric Vehicle Adoption in Indonesia through Grey Ordinal Priority Approach {{!}} International Journal of Grey Systems |url=http://publish.thescienceinsight.com/index.php/ijgs/article/view/46 |language=en-US |doi=10.52812/ijgs.46 |access-date=2022-10-31 |archive-date=2022-11-18 |archive-url=https://web.archive.org/web/20221118230222/http://publish.thescienceinsight.com/index.php/ijgs/article/view/46 |dead-url=no }}</ref> * [[循環經濟]]<ref name=":4">{{Cite journal |last=Sadeghi |first=M. |last2=Mahmoudi |first2=A. |last3=Deng |first3=X. |last4=Luo |first4=X. |date=2022-06-27 |title=Prioritizing requirements for implementing blockchain technology in construction supply chain based on circular economy: Fuzzy Ordinal Priority Approach |url=https://doi.org/10.1007/s13762-022-04298-2 |journal=International Journal of Environmental Science and Technology |language=en |doi=10.1007/s13762-022-04298-2 |issn=1735-2630}}</ref> '''医疗保健''' * [[2019冠状病毒病]]<ref>{{Cite journal |last=Sotoudeh-Anvari |first=Alireza |date=2022-09-01 |title=The applications of MCDM methods in COVID-19 pandemic: A state of the art review |url=https://www.sciencedirect.com/science/article/pii/S1568494622004562 |journal=Applied Soft Computing |language=en |volume=126 |doi=10.1016/j.asoc.2022.109238 |issn=1568-4946 |pmc=9245376 |pmid=35795407 |access-date=2022-10-31 |archive-date=2022-10-31 |archive-url=https://web.archive.org/web/20221031063405/https://www.sciencedirect.com/science/article/pii/S1568494622004562 |dead-url=no }}</ref><ref name=":9">{{Cite journal |last=Mahmoudi |first=Amin |last2=Javed |first2=Saad Ahmed |last3=Mardani |first3=Abbas |date=2022-06-01 |title=Gresilient supplier selection through Fuzzy Ordinal Priority Approach: decision-making in post-COVID era |url=https://doi.org/10.1007/s12063-021-00178-z |journal=Operations Management Research |language=en |volume=15 |issue=1 |doi=10.1007/s12063-021-00178-z |issn=1936-9743 |pmc=7960884}}</ref> * 医疗保健供应链<ref>{{Cite journal |date=2021-07-25 |title=Evaluating Suppliers for Healthcare Centre using Ordinal Priority Approach {{!}} Management Science and Business Decisions |url=http://publish.thescienceinsight.com/index.php/msbd/article/view/12 |language=en-US |doi=10.52812/msbd.12 |access-date=2022-10-31 |archive-date=2021-08-04 |archive-url=https://web.archive.org/web/20210804002122/http://publish.thescienceinsight.com/index.php/msbd/article/view/12 |dead-url=no }}</ref> * 社区服务<ref>{{Cite journal |last=Dorado Chaparro |first=Javier |last2=Fernández-Bermejo Ruiz |first2=Jesús |last3=Santofimia Romero |first3=María José |last4=del Toro García |first4=Xavier |last5=Cantarero Navarro |first5=Rubén |last6=Bolaños Peño |first6=Cristina |last7=Llumiguano Solano |first7=Henry |last8=Villanueva Molina |first8=Félix Jesús |last9=Gonçalves Silva |first9=Anabela |last10=López |first10=Juan Carlos |date=2022-01 |title=Phyx.io: Expert-Based Decision Making for the Selection of At-Home Rehabilitation Solutions for Active and Healthy Aging |url=https://www.mdpi.com/1660-4601/19/9/5490 |journal=International Journal of Environmental Research and Public Health |language=en |volume=19 |issue=9 |doi=10.3390/ijerph19095490 |issn=1660-4601 |pmc=9103419 |pmid=35564884 |access-date=2022-10-31 |archive-date=2022-07-18 |archive-url=https://web.archive.org/web/20220718040326/https://www.mdpi.com/1660-4601/19/9/5490 |dead-url=no }}</ref> '''信息技术''' * 元宇宙<ref>{{Cite journal |last=Deveci |first=Muhammet |last2=Pamucar |first2=Dragan |last3=Gokasar |first3=Ilgin |last4=Koppen |first4=Mario |last5=Gupta |first5=Brij B. |date=2022 |title=Personal Mobility in Metaverse With Autonomous Vehicles Using Q-Rung Orthopair Fuzzy Sets Based OPA-RAFSI Model |url=https://ieeexplore.ieee.org/document/9827997/ |journal=IEEE Transactions on Intelligent Transportation Systems |doi=10.1109/TITS.2022.3186294 |issn=1524-9050 |access-date=2022-10-31 |archive-date=2022-11-18 |archive-url=https://web.archive.org/web/20221118230158/https://ieeexplore.ieee.org/document/9827997/ |dead-url=no }}</ref><ref>{{Cite journal |last=Pamucar |first=Dragan |last2=Deveci |first2=Muhammet |last3=Gokasar |first3=Ilgin |last4=Tavana |first4=Madjid |last5=Köppen |first5=Mario |date=2022-09-01 |title=A metaverse assessment model for sustainable transportation using ordinal priority approach and Aczel-Alsina norms |url=https://www.sciencedirect.com/science/article/pii/S004016252200302X |journal=Technological Forecasting and Social Change |language=en |volume=182 |doi=10.1016/j.techfore.2022.121778 |issn=0040-1625}}</ref> * 自动驾驶汽车<ref>{{Cite journal |last=Deveci |first=Muhammet |last2=Pamucar |first2=Dragan |last3=Gokasar |first3=Ilgin |last4=Pedrycz |first4=Witold |last5=Wen |first5=Xin |date=2022 |title=Autonomous Bus Operation Alternatives in Urban Areas Using Fuzzy Dombi-Bonferroni Operator Based Decision Making Model |url=https://ieeexplore.ieee.org/document/9894368/ |journal=IEEE Transactions on Intelligent Transportation Systems |doi=10.1109/TITS.2022.3202111 |issn=1524-9050 |access-date=2022-10-31 |archive-date=2022-09-23 |archive-url=https://web.archive.org/web/20220923134404/https://ieeexplore.ieee.org/document/9894368/ |dead-url=no }}</ref> * 过程控制<ref>{{Cite journal |last=Su |first=Chong |last2=Ma |first2=Xuri |last3=Lv |first3=Jing |last4=Tu |first4=Tao |last5=Li |first5=Hongguang |date=2022-09-01 |title=A multilayer affective computing model with evolutionary strategies reflecting decision-makers’ preferences in process control |url=https://www.sciencedirect.com/science/article/pii/S0019057821006133 |journal=ISA Transactions |language=en |volume=128 |doi=10.1016/j.isatra.2021.11.038 |issn=0019-0578}}</ref> * [[区块链]]<ref name=":2" /><ref name=":3" /><ref name=":4" /> * 技术需求<ref>{{Cite journal |last=Amirghodsi |first=Sirous |last2=Naeini |first2=Ali Bonyadi |last3=Makui |first3=Ahmad |date=2022-08 |title=An Integrated Delphi-DEMATEL-ELECTRE Method on Gray Numbers to Rank Technology Providers |url=https://ieeexplore.ieee.org/document/9083974/ |journal=IEEE Transactions on Engineering Management |volume=69 |issue=4 |doi=10.1109/TEM.2020.2980127 |issn=0018-9391 |access-date=2022-10-31 |archive-date=2022-10-31 |archive-url=https://web.archive.org/web/20221031064506/https://ieeexplore.ieee.org/document/9083974/ |dead-url=no }}</ref> '''交通运输''' * [[供应链管理]]<ref name=":5" /><ref name=":7" /><ref name=":9" /><ref name=":1" /> * 交通管制<ref>{{Cite journal |last=Bouraima |first=Mouhamed Bayane |last2=Kiptum |first2=Clement Kiprotich |last3=Ndiema |first3=Kevin Maraka |last4=Qiu |first4=Yanjun |last5=Tanackov |first5=Ilija |date=2022-08-19 |title=Prioritization Road Safety Strategies Towards Zero Road Traffic Injury Using Ordinal Priority Approach |url=https://oresta.rabek.org/index.php/oresta/article/view/291 |journal=Operational Research in Engineering Sciences: Theory and Applications |language=en |volume=5 |issue=2 |doi=10.31181/oresta190822150b |issn=2620-1747 |access-date=2022-10-31 |archive-date=2022-08-21 |archive-url=https://web.archive.org/web/20220821152434/https://oresta.rabek.org/index.php/oresta/article/view/291 |dead-url=no }}</ref> * 道路维护<ref>{{Cite journal |last=Bouraima |first=Mouhamed Bayane |last2=Qiu |first2=Yanjun |last3=Kiptum |first3=Clement Kiprotich |last4=Ndiema |first4=Kevin Maraka |date=2022-08-17 |title=Evaluation of Factors Affecting Road Maintenance in Kenyan Counties Using the Ordinal Priority Approach |url=https://ojs.bonviewpress.com/index.php/JCCE/article/view/272 |journal=Journal of Computational and Cognitive Engineering |language=en |doi=10.47852/bonviewJCCE2202272 |issn=2810-9503 |access-date=2022-10-31 |archive-date=2022-09-23 |archive-url=https://web.archive.org/web/20220923134408/https://ojs.bonviewpress.com/index.php/JCCE/article/view/272 |dead-url=no }}</ref> == 延伸 == 以下是 OPA 方法的几个扩展。 * 灰色顺序优先法 (OPA-G)<ref name=":1" /> * [[模糊集|模糊]]顺序优先法 (OPA-F)<ref name=":9" /> * OPA 中的置信度测量<ref name=":5" /> * [[鲁棒性|鲁棒]]顺序优先法 (OPA-R)<ref name=":8" /> * 混合 OPA-模糊 EDAS<ref name="未命名_2-20230318201033"/> * 混合 DEA-OPA 模型<ref name=":6" /> * 混合型 MULTIMOORA-OPA<ref>{{Cite journal |last=Irvanizam |first=Irvanizam |last2=Zulfan |first2=Zulfan |last3=Nasir |first3=Puti F. |last4=Marzuki |first4=Marzuki |last5=Rusdiana |first5=Siti |last6=Salwa |first6=Nany |date=2022 |title=An Extended MULTIMOORA Based on Trapezoidal Fuzzy Neutrosophic Sets and Objective Weighting Method in Group Decision-Making |url=https://ieeexplore.ieee.org/document/9763528/ |journal=IEEE Access |volume=10 |doi=10.1109/ACCESS.2022.3170565 |issn=2169-3536 |access-date=2022-10-31 |archive-date=2022-11-18 |archive-url=https://web.archive.org/web/20221118230311/https://ieeexplore.ieee.org/document/9763528/ |dead-url=no }}</ref> * 团体加权顺序优先法 (GWOPA)<ref>{{Cite journal |last=Mahmoudi |first=Amin |last2=Abbasi |first2=Mehdi |last3=Yuan |first3=Jingfeng |last4=Li |first4=Lingzhi |date=2022-09-01 |title=Large-scale group decision-making (LSGDM) for performance measurement of healthcare construction projects: Ordinal Priority Approach |url=https://doi.org/10.1007/s10489-022-04094-y |journal=Applied Intelligence |language=en |volume=52 |issue=12 |doi=10.1007/s10489-022-04094-y |issn=1573-7497 |pmc=9449288 |pmid=36091930}}</ref> == 软件 == 以下非盈利工具可用于解决使用 OPA 方法的 MCDM 问题。 * 基于网络的解算器<ref>{{Cite web |title= |script-title=Web-based solver |url=https://ordinalpriorityapproach.com/opasolver.html |access-date=2022-10-31 |website=ordinalpriorityapproach.com |archive-date=2022-10-19 |archive-url=https://web.archive.org/web/20221019043803/https://ordinalpriorityapproach.com/opasolver.html |dead-url=no }}</ref> * 基于 Excel 的解算器<ref>{{Citation|title=Excel-based solver|url=https://zenodo.org/record/4453887|publisher=Zenodo|date=2021-01-21|accessdate=2022-10-31|first=|last=|archive-date=2022-10-16|archive-url=https://web.archive.org/web/20221016034758/https://zenodo.org/record/4453887|dead-url=no}}</ref> * 基于林格的解算器<ref>{{Citation|title=Lingo-based solver|url=https://github.com/Amin-Mhd/Multiple-Criteria-Decision-Analysis-Software|date=2022-07-07|accessdate=2022-10-31|first=|last=|archive-date=2022-10-21|archive-url=https://web.archive.org/web/20221021011957/https://github.com/Amin-Mhd/Multiple-Criteria-Decision-Analysis-Software|dead-url=no}}</ref> * 基于 Matlab 的求解器<ref>{{Cite web |title=Matlab-based solver |script-title= |url=https://www.mathworks.com/matlabcentral/fileexchange/106890-opa-solver-a-solver-for-multiple-criteria-decision-analysis |access-date=2022-10-31 |website=www.mathworks.com |language=en |archive-date=2022-10-17 |archive-url=https://web.archive.org/web/20221017023158/https://www.mathworks.com/matlabcentral/fileexchange/106890-opa-solver-a-solver-for-multiple-criteria-decision-analysis |dead-url=no }}</ref> == 参考文献 == {{Reflist|2}} [[Category:多准则决策分析|Multiple-criteria decision analysis]] [[Category:决策分析]] [[Category:管理系統]] [[Category:數學最佳化]]
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