Grey hybrid normalization with period based entropy weighting and relational analysis for cities rankings

Researchers have addressed uncertainty in multicriteria decision making from the perspective of the performance values of the alternatives, weighting of the evaluation criteria, and the evaluation methods. Still, they are yet to address the uncertainty caused by the normalization approach. In this paper, we show that different normalization methods, namely sum normalization, min–max normalization, vector normalization, and maximization normalization, can result in different rankings of the alternatives while the performance values and weights are unchanged. We applied the grey system theory to address the problem of uncertainty in this study from three aspects: alternative performance values measurement, criteria weighting, and decision matrix/table normalization within a period. The grey hybrid normalization method is proposed as the main contribution in this paper. Then, we present the rankings of 48 cities under uncertainty to decide the location of a branch office of a Chinese electric vehicle manufacturer as a practical example based on the grey entropy weighting method and grey relational analysis with positive and negative references (GRA-PNR) within the period from the year 2019 to 2021. The research results using this approach ranked New York City the best, with a stock market capitalization of economy validity as the top contributor in terms of weighting. Finally, we used simple additive weighting with grey value and the technique for order of preference by similarity to ideal solution with grey value methods to validate the study results.