Evaluation of city sustainability using multi-criteria decision-making considering interaction among criteria in Liaoning province China

City sustainability is a complex system affected by economic, social, and environmental dimensions, with the existence of interaction and conflict among factor. However, there is a lack of real methodology on the measurement of interaction. Then, this article presents a method to calculate the interaction among multiple criteria, including static interaction and dynamic trend similarity, and to compute the weigh coefficient of each indicator induced by this interaction. In addition, the applicability of the proposed method is demonstrated by evaluating the sustainability performance of 14 cities in Liaoning province China in the context of the Triple Bottom Line (TBL) framework. Our results show that the sustainable development of 14 cities in Liaoning province experienced dramatically downward and has a crucial condition from 2013 to 2017. Only Dalian, Shenyang, Panjin, Benxi, and Yingkou could be classified as a Good level (Level.), and none of cities was an Excellent level (Level.). From spatial-temporal perspective, regional disparities of sustainability are demonstrated by spatial distributions of city sustainability. In detail, the comprehensive sustainability and subsystem exhibit a "cold-spot in West" feature. The scores for indicators reveal that the shortage of science expenditure, declining investment in fixed asset, lack of economic growth, and lagging public transportation are the main limit factor faced by most cities. Meanwhile, tertiary industry development, energy efficiency improvement, increase green coverage, and reduce pollutant emissions are primary driving factors for improving sustainability. Comparing with other methods, MCDM considering interaction among criteria is an appropriate method to evaluate city sustainability.