Nonlinear comprehensive evaluation method based on information entropy and discrimination optimization

Abstract In the comprehensive evaluation of multiple indicators, the existence of nonlinear relationships often makes the discrimination of traditional evaluation methods unstable or difficult to accurately reflect the complex relationship between indicators. The outcome of a comprehensive evaluation is to assign a quantitative value to each evaluation object for selection or ranking. The discriminability in the evaluation results is an important measure of the effectiveness of the comprehensive evaluation. In response to the issues of uncertain discriminability or poor stability in commonly used comprehensive evaluation methods, a comprehensive evaluation method prioritizing discriminability is proposed. Based on the principle that information entropy can reflect the degree of variation in the evaluation dataset, a model for quantitatively analyzing the discriminability of evaluation indicators is provided, and the conclusion that low-discriminability indicators will reduce the overall discriminability of the comprehensive evaluation is proven. Accordingly, weighted indicators, qualification indicators, and invalid indicators are defined. By identifying and eliminating low-discriminability qualification indicators and invalid indicators, and retaining weighted indicators, the evaluation results ensure good discriminability while maintaining the comprehensiveness of the evaluation. Through empirical analysis, the scientificity and effectiveness of this method in processing multi-dimensional and nonlinear data are verified.