Improved entropy weight methods and their comparisons in evaluating the high-quality development of Qinghai, China

“High-quality development” is an important objective for China’s current development projects. For the betterment of the current situation of the underdeveloped regions, high-quality development is necessary. The comprehensive index method is one of the most widely used methods for evaluating high-quality development works, and indicator weighting is its key and at the same time the most controversial step. Among many weighting methods, the entropy weighting method is widely applied due to its easier understandability and use. This article focuses on the problem of weight distortion when the entropy values of indicators are close to 1 and the improvements to this problem. To verify these improvements, this article deduces with mathematical analysis, the underlying assumptions of the problem and evaluates the level of high-quality development in Qinghai Province, which is assumed to be an appropriate example of the underdeveloped regions in western China. Our mathematical deductions demonstrate that these underlying assumptions do not theoretically exist. In addition, both the improved and the original methods have similar performances in practice or, more specifically, have shown an overall upward trend in the level of high-quality development in Qinghai Province. Because the “problem” is extremely stringent and difficult to reproduce, we conclude that further improvements on the entropy weighting method should not be a focus of future research. To address the subjectivity or objectivity issues of weighting, weightless methods may be of use and should be developed.