地理学报 ›› 2022, Vol. 77 ›› Issue (9): 2389-2406.doi: 10.11821/dlxb202209017

• 国土资源与空间治理 • 上一篇    下一篇

耦合高维排序权和对偶线性规划的综合指数算法

高培超1,2(), 王昊煜2, 王元慧2, 宋长青1,2(), 叶思菁2   

  1. 1.北京师范大学地表过程与资源生态国家重点实验室,北京 100875
    2.北京师范大学地理科学学部地理数据与应用分析中心,北京 100875
  • 收稿日期:2021-10-27 修回日期:2022-07-25 出版日期:2022-09-25 发布日期:2022-11-03
  • 通讯作者: 宋长青(1961-), 男, 黑龙江人, 教授, 主要从事地理学研究范式、地理区域综合研究方法等方面的研究。E-mail: songcq@bnu.edu.cn
  • 作者简介:高培超(1991-), 男, 河南人, 讲师, 硕导, 中国地理学会会员(S110014357M), 主要从事信息地理学研究。E-mail: gaopc@bnu.edu.cn
  • 基金资助:
    中国科学院战略性先导科技专项(XDA23100303);第二次青藏高原综合考察研究(2019QZKK0608);国家自然科学基金项目(42171088);国家自然科学基金项目(41901316);国家自然科学基金项目(42171250)

A method for constructing a composite index by coupling high-dimensional ranked weights and the duality of linear programming

GAO Peichao1,2(), WANG Haoyu2, WANG Yuanhui2, SONG Changqing1,2(), YE Sijing2   

  1. 1. State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University, Beijing 100875, China
    2. Center for Geodata and Analysis, Faculty of Geographical Science, Beijing Normal University, Beijing 100875, China
  • Received:2021-10-27 Revised:2022-07-25 Published:2022-09-25 Online:2022-11-03
  • Supported by:
    The Strategic Priority Research Program of the Chinese Academy of Sciences(XDA23100303);The Second Tibetan Plateau Scientific Expedition and Research Program(2019QZKK0608);National Natural Science Foundation of China(42171088);National Natural Science Foundation of China(41901316);National Natural Science Foundation of China(42171250)

摘要:

区域可持续与高质量发展需定期监测并科学评估。综合指数评价是应用最为广泛、信息传输效率最高的评估方法。该方法将表征区域发展质量不同侧面的系列指标加权聚合为单个指数,其核心是采用或客观或主观的方式确权。客观确权基于指标的数值统计特性实现,故权重值随指标值而改变,实非“客观”;主观确权能反映决策者智慧,但指标过多时难以实现。学界新提出的基于耦合排序权和熵权法的综合指标法允许决策者确权时仅给出权重排序,但仅支持低维情况(限制为3个指标)。本文在其基础上,借助对偶线性规划推导,使其适用性不再受限于指标数(即实现高维排序权)。同时,对指标的聚合方式进行修改,扩大了算法的适用范围;对熵权法的使用进行修正,增强了算法结果的可解译性。基于推导结果,本文进一步发展出单排序、复排序、全排序3种不同模式下的综合指数计算方法,以满足决策者主观性强、弱、无等不同情况。最后,将算法用于全球可持续发展格局的时空评价分析。本文新发展的算法同时适用于高低不同维度的指数聚合、可兼顾决策者不同层次的主观参与度,具有较强的普适性。

关键词: 排序权, 综合指数, 对偶线性规划, 指标权重, 区域发展

Abstract:

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.

Key words: ranked weights, composite index, duality in linear programming, weights of indicators, regional development