改进一致性分类:AHP的一种创新的基于基准的方法

IF 1.9 Q3 MANAGEMENT
Amarnath Bose
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引用次数: 0

摘要

层次分析法(AHP)是多标准决策分析的基石,可以在不同的背景下做出明智的选择。本文介绍了一个原始的基于基准的框架,旨在提高AHP方法中成对比较矩阵(PCMs)一致性分类的精度。这种创新的方法量化给定PCM与其基准矩阵之间的差异,包括忠实地反映主特征向量值中封装的相对偏好的比较比率,从而捕获真实的一致性程度。为了确保基准与人类感知一致,基准PCM的元素进一步四舍五入到基本尺度上最接近的值。我们框架的效力源于两个关键因素:主特征向量内固有的优先级偏好范围和PCM的顺序。一致性的统计阈值是使用Bose[2022]提出的基于模拟逻辑pcm的技术建立的。这种严格的方法确保了对一致性的公正、客观和实用的评估,消除了基于随机pcm的任意阈值所固有的主观性。我们的方法纠正了传统CR方法中的不一致性,该方法对3阶和4阶pcm产生假阳性,对更高阶pcm产生假阴性。通过利用定制基准和避免随机矩阵,我们的框架系统地面对AHP内部固有的一致性挑战,从而增强其决策能力。AHPtools是一个基于R的库包,旨在展示我们新颖的一致性评估方法。附录B中的软件包演示将有助于读者轻松地将我们的方法应用于AHP中的现实世界PCM分类场景。总之,我们基于基准的框架预示着AHP内部一致性分类的变革时代,使现实世界的多标准决策具有前所未有的准确性和可靠性,并开创了一种新的知情和精明结果范式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Improving consistency classification: An innovative benchmark-based approach for the AHP

The analytic hierarchy process (AHP) is a cornerstone of multi-criteria decision analysis, enabling well-informed choices across diverse contexts. This paper introduces an original benchmark-based framework designed to enhance the precision of consistency classification for pairwise comparison matrices (PCMs) within the AHP methodology. This innovative approach quantifies the discrepancy between a given PCM and its benchmark matrix, comprising comparison ratios that faithfully reflect the relative preferences encapsulated within principal eigenvector values, thereby capturing the true degree of coherence. To ensure benchmark alignment with human perception, elements of the benchmark PCM are further rounded to the nearest values on the Fundamental Scale. The potency of our framework derives from two pivotal factors: the inherent Priority Preference Range within the principal eigenvector and the order of the PCM. Statistical thresholds for consistency are established using a technique based on simulated, logical PCMs, proposed by Bose [2022]. This rigorous method ensures an unbiased, objective and pragmatic evaluation of consistency, eliminating the subjectivity inherent in arbitrary thresholds based on random PCMs. Our approach rectifies the inconsistencies in the conventional CR method that yields false positives for PCMs of orders 3 and 4, and false negatives for higher orders. By harnessing customized benchmarks and eschewing random matrices, our framework systematically confronts the inherent consistency challenges within AHP, thus enhancing its decision-making capability. The practical utility of our approach is aptly demonstrated through AHPtools, an R-based library package designed to showcase our novel consistency evaluation method. The demonstration of the package in Appendix B will facilitate readers to easily apply our methodology to real-world PCM classification scenarios within the AHP. In conclusion, our benchmark-based framework heralds a transformative era in consistency classification within the AHP, empowering real-world multi-criteria decision-making with unprecedented precision and reliability, and ushering in a new paradigm of informed and astute outcomes.

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来源期刊
CiteScore
4.70
自引率
10.00%
发文量
14
期刊介绍: The Journal of Multi-Criteria Decision Analysis was launched in 1992, and from the outset has aimed to be the repository of choice for papers covering all aspects of MCDA/MCDM. The journal provides an international forum for the presentation and discussion of all aspects of research, application and evaluation of multi-criteria decision analysis, and publishes material from a variety of disciplines and all schools of thought. Papers addressing mathematical, theoretical, and behavioural aspects are welcome, as are case studies, applications and evaluation of techniques and methodologies.
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