Logarithmic OWA Operators in Weighted Averages: Theoretical Advances and Decision-Making Applications

Abstract

Aggregation operators are essential in multi-attribute decision-making, particularly for managing uncertainty and risk. Traditional methods, such as the Ordered Weighted Averaging (OWA) operator, typically address either probability-based weighting or uncertainty-based reordering, but rarely combine both within a unified framework. This paper proposes the Ordered Weighted Logarithmic Averaging Weighted Average (OWLAWA) operator, a novel approach that merges the benefits of weighted averaging and ordered reordering with a logarithmic transformation to better reflect decision-maker preferences under uncertainty. The theoretical properties of this operator including monotonicity, boundedness, and commutativity are formally established. A multi-attribute decision-making framework is then presented, integrating recognized expert weighting methods, including an entropy-based approach, to enhance decision robustness. Through comparative analysis and a sustainability-focused case study involving 20 companies, results demonstrate that the proposed approach yields a controlled sub valuation effect, particularly beneficial in risk-sensitive or compliance-driven environments. These findings indicate a more adaptive and structured decision-making process relative to conventional operators, accommodating both structured probabilities and uncertain preferences. By unifying risk-based and uncertainty-based weighting within a logarithmic formulation, this operator offers a versatile and structured tool for applications in financial risk management, policy evaluation, and supply chain optimization. Future research may explore its integration with fuzzy systems and machine learning methods, further expanding its adaptability in complex decision scenarios.