Linear Programming for Multi-Criteria Assessment with Cardinal and Ordinal Data: A Pessimistic Virtual Gap Analysis
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914464546160640 |
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| author | Liu, Fuh-Hwa Franklin Shih, Su-Chuan |
| author_facet | Liu, Fuh-Hwa Franklin Shih, Su-Chuan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09555 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Linear Programming for Multi-Criteria Assessment with Cardinal and Ordinal Data: A Pessimistic Virtual Gap Analysis Liu, Fuh-Hwa Franklin Shih, Su-Chuan Artificial Intelligence Optimization and Control 90B50, 90C29, 90C08, 91A80, 91B06 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. |
| title | Linear Programming for Multi-Criteria Assessment with Cardinal and Ordinal Data: A Pessimistic Virtual Gap Analysis |
| topic | Artificial Intelligence Optimization and Control 90B50, 90C29, 90C08, 91A80, 91B06 |
| url | https://arxiv.org/abs/2604.09555 |