🤖 AI Summary
Existing multi-criteria assessment (MCA) methods often rely on subjective assumptions and homogeneity premises when integrating quantitative (cardinal) and qualitative (ordinal) indicators, neglecting inherent heterogeneity across decision-making units—leading to ranking distortion, compromised fairness, and poor interpretability. This paper proposes a novel MCA framework based on dual virtual gap analysis (VGA), which employs linear programming to construct an adaptive hybrid-data processing architecture. By synergistically integrating data envelopment analysis (DEA) and multi-criteria decision-making (MCDM) principles, the method eliminates homogeneity assumptions and enables coherent modeling of both cardinal and ordinal data. The approach ensures theoretical rigor, computational transparency, and structural interpretability. Two numerical experiments demonstrate that the proposed method significantly enhances ranking stability, robustness against perturbations, and practical decision-support capability.
📝 Abstract
Modern methods for multi-criteria assessment (MCA), such as Data Envelopment Analysis (DEA), Stochastic Frontier Analysis (SFA), and Multiple Criteria Decision-Making (MCDM), are utilized to appraise a collection of Decision-Making Units (DMUs), also known as alternatives, based on several criteria. These methodologies inherently rely on assumptions and can be influenced by subjective judgment to effectively tackle the complex evaluation challenges in various fields. In real-world scenarios, it is essential to incorporate both quantitative and qualitative criteria as they consist of cardinal and ordinal data. Despite the inherent variability in the criterion values of different alternatives, the homogeneity assumption is often employed, significantly affecting evaluations. To tackle these challenges and determine the most appropriate alternative, we propose a novel MCA approach that combines two Virtual Gap Analysis (VGA) models. The VGA framework, rooted in linear programming, is pivotal in the MCA methodology. This approach improves efficiency and fairness, ensuring that evaluations are both comprehensive and dependable, thus offering a strong and adaptive solution. Two comprehensive numerical examples demonstrate the accuracy and transparency of our proposed method. The goal is to encourage continued advancement and stimulate progress in automated decision systems and decision support systems.