Using Two-layer Minimax Optimization and DEA to Determine Attribute Weights

Abstract

This study aims to explore a novel method for determining attribute weights, which is a key issue in constructing and analyzing multiple-attribute decision-making (MADM) problems. To this end, a hybrid approach combining the data envelopment analysis (DEA) model without explicit inputs (DEA-WEI) and a two-layer minimax optimization scheme is developed. It is demonstrated that in this approach, the most favorable set of weights is first considered for each alternative or decision-making unit (DMU) and these weight sets are then aggregated to determine the best compromise weights for attributes, with the interests of all DMUs simultaneously considered in a fair manner. This approach is particularly suitable for situations where the preferences of decision-makers (DMs) are either unclear or difficult to acquire. Two case studies are conducted to illustrate the proposed approach and its use for determining weights for attributes in practice. The first case concerns the assessment of research strengths of 24 selected countries using certain measures, and the second concerns the analysis of the performance of 64 selected Chinese universities, where the preferences of DMs are either unknown or ambiguous, but the weights of the attributes should be assigned in a fair and unbiased manner.