Territory Resources and Spatial Governance
GAO Peichao, WANG Haoyu, WANG Yuanhui, SONG Changqing, YE Sijing
To achieve regional sustainable development and high-quality development, regular monitoring and scientific assessment are needed. The most widespread and informative method for such an assessment is to employ a composite index. To generate a composite index, various indicators that reflect regional development quality in different aspects are weighted and then aggregated to an index. The core idea of the composite index is weighting, which can be achieved objectively or subjectively. Objective weighting is usually conducted using statistical characteristics of indicator values; thus, the resultant weights change with the values of indicators. This change questions the objectivity of the weighting. In contrast, subjective weighting well reflects the willingness of decision-makers, who feel it is difficult to determine the weights of each indicator if there are too many. Fortunately, a recently developed method eliminated this difficulty. It requires only the rank (also ranked weights) instead of the accurate weights of different indicators, but the number of indicators is restricted to only three. In this study, we improved this method by relaxing such a restriction. We employed the duality of linear programming to generalize the method for calculating a composite index based on any number of indicators. The aggregation is adjusted to expand the scope of the application, and the use of entropy weights is adjusted to improve the interpretability of results. Furthermore, we developed three different calculation modes: single, multiple, and full ranks, corresponding to three conditions of decision-makers' subjectivity: strong, weak, and non-subjective, respectively. Finally, we employed this method to examine global sustainable development patterns temporally and spatially. Since this method is suitable for high- and low-dimensional cases and can consider decision-makers' subjectivity, it has strong universality.