用线性规划构建悲观虚拟差距模型，融合定量定性数据做多准则评估
Linear Programming for Multi-Criteria Assessment with Cardinal and Ordinal Data: A Pessimistic Virtual Gap Analysis
- 基于线性规划构建双阶段虚拟差距模型，从保守视角评估各方案
- 支持基数与序数数据混合，提升评估在复杂场景下的适用性
- 适合需要稳健排序的决策支持系统，尤其适用于存在主观偏见的场景
多准则分析（MCA）用于根据多种标准对备选方案进行排序。主流多准则决策方法（MCDM）通过估计准则参数来计算每个方案的表现，但主观评价和偏差常影响结果可靠性，且数据多样性降低参数精度。本文提出一种基于线性规划的新型虚拟差距分析（VGA）模型，采用两步法整合两个新提出的VGA模型，从悲观视角评估每个方案，同时处理定量与定性准则，并融合基数与序数数据。随后对方案进行优先排序，剔除最不利者。该方法具有良好的可靠性与可扩展性，能高效、有效地在决策支持系统中实现全面评估。
原文摘要 · Abstract (English)
Multi-criteria Analysis (MCA) is used to rank alternatives based on various criteria. Key MCA methods, such as Multiple Criteria Decision Making (MCDM) methods, estimate parameters for criteria to compute the performance of each alternative. Nonetheless, subjective evaluations and biases frequently influence the reliability of results, while the diversity of data affects the precision of the parameters. The novel linear programming-based Virtual Gap Analysis (VGA) models tackle these issues. This paper outlines a two-step method that integrates two novel VGA models to assess each alternative from a pessimistic perspective, using both quantitative and qualitative criteria, and employing cardinal and ordinal data. Next, prioritize the alternatives to eliminate the least favorable one. The proposed method is dependable and scalable, enabling thorough assessments efficiently and effectively within decision support systems.
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