Linear Programming for Multi-Criteria Assessment with Cardinal and Ordinal Data: A Pessimistic Virtual Gap Analysis
Summary: arXiv:2604.09555v1 Announce Type: new
Abstract
Multi-criteria Analysis (MCA) serves as a vital tool for ranking alternatives based on a variety of criteria. Prominent methods within MCA, including Multiple Criteria Decision Making (MCDM) techniques, focus on estimating parameters for each criterion to assess the performance of alternatives. However, the reliability of these evaluations is often compromised by subjective judgments and inherent biases, while the diversity of data types can impact the precision of parameter estimation. To address these challenges, novel linear programming-based Virtual Gap Analysis (VGA) models have been proposed. This article outlines a comprehensive two-step methodology that leverages two innovative VGA models to evaluate each alternative through a pessimistic lens, utilizing both quantitative and qualitative criteria, and incorporating both cardinal and ordinal data. In conclusion, the method prioritizes alternatives to systematically eliminate the least favorable options. The proposed approach is both reliable and scalable, facilitating thorough assessments in an efficient and effective manner within decision support systems.
Introduction
In the realm of decision-making, Multi-Criteria Analysis (MCA) is pivotal for evaluating different options based on multiple factors. The challenge lies in the subjective nature of evaluations, which can lead to biases affecting the outcome. Moreover, the complexity stemming from diverse data types complicates the analytical process.
Methodology
The approach introduced in this study consists of two main components:
- Step One: Integration of Cardinal and Ordinal Data
- Step Two: Application of Pessimistic Virtual Gap Analysis
By combining these steps, the model effectively addresses the limitations of traditional MCA methodologies. The utilization of both cardinal and ordinal data allows for a more holistic view of each alternative’s performance.
Results
The implementation of the proposed VGA models demonstrated significant improvements in decision-making processes. The prioritization of alternatives based on a pessimistic perspective ensures that the least favorable options are systematically identified and eliminated, thereby enhancing overall decision quality.
Conclusion
The introduction of linear programming-based Virtual Gap Analysis models presents a robust framework for conducting Multi-Criteria Analysis. By effectively integrating both quantitative and qualitative criteria, this approach mitigates the common pitfalls associated with subjective evaluations and data diversity. Overall, the proposed method not only enhances the reliability of assessments but also ensures scalability and efficiency in decision support systems.
Future Work
Further research is encouraged to refine the models and explore their application across various domains. Enhancements in algorithm efficiency and the incorporation of real-time data could lead to even more effective decision-making tools.