Linear Programming for Multi-Criteria Assessment with Cardinal and Ordinal Data: A Pessimistic Virtual Gap Analysis

Computer Science > Artificial Intelligence [Submitted on 5 Feb 2026] Linear Programming for Multi-Criteria Assessment with Cardinal and Ordinal Data: A Pessimistic Virtual Gap Analysis Fuh-Hwa Franklin Liu, Su-Chuan Shih 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. Comments: 36 pages, 6 figure, 3 tables Subjects: Artificial Intelligence (cs.AI); Optimization and Control (math.OC) MSC classes: 90B50, 90C29, 90C08, 91A80, 91B06 Cite as: arXiv:2604.09555 [cs.AI]   (or arXiv:2604.09555v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2604.09555 Focus to learn more Submission history From: Fuh-Hwa Liu [view email] [v1] Thu, 5 Feb 2026 05:56:57 UTC (586 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-04 Change to browse by: cs math math.OC References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)