Maximum Entropy-Minimum Residual Model: An Optimum Solution to Comprehensive Evaluation and Multiple Attribute Decision Making

To assess a subject with multiple factors or attributes, a comprehensive evaluation index, or say a composite indicator, is often constructed to make a holistic judgement. The key problem is to assign weights to the factors. There are various weighting methods in the literature, but a gold standard is in lack. Some weighting methods may lead to a trivial weight assignment that is one factor having a weight equal to 1 and the others all zero, while some methods generate a solution contradicting with intuitive judgement, or even infeasible to calculate. This paper proposes a new model to generate weights based on the maximum entropy-minimum residual (MEMR) principle, directly estimating the relationship between factor weights and the composite indicator. The MEMR composite indicator extracts the common feature of multiple factors with preserving their diversity. This paper compares the MEMR model with other commonly used weighting methods in various case studies. The MEMR model has more robust, consistent, interpretable results than others, and is suitable for all comprehensive evaluation cases involving quantitative factors. The optimization technique of the proposed MEMR model and the related statistical tests are included as a package in the DPS (data processing system) software, for the convenience of application in all fields.