European Countries Ranking and Clustering Solution by Children’s Physical Activity and Human Development Index Using Entropy-Based Methods

Abstract

The aim of the present study is to propose a new approach for evaluating and comparing European countries using indicators of the children physical activity and the human development index. The Global Matrix 3.0 on physical activity for children and youth and human development index data on the 18 European countries were used. MADM (multi-attribute decision making) approach was applied for this task. The criteria weights calculated by applying the weight balancing method—weight balancing indicator ranks accordance (WEBIRA). New methodology of interval entropy is proposed for determining the priority of criteria separately in each group. The novel approach of α-cuts for recursive procedure of ranking the alternatives was used. For comparison, three alternative entropy-based methods—entropy method for determining the criterion weight (EMDCW), method of criteria impact LOSs and determination of objective weights (CILOS) and integrated determination of objective criteria weights (IDOCRIW) were applied to address this MADM problem. Cluster analysis of European countries carried out using results obtained by all above methods. Comparison of the MADM methods revealed that three alternative methods assigned negligible values to whole group of criteria. Meanwhile, WEBIRA family methods performed the ranking of European countries according to the interrelation of the two groups of criteria in a balanced way. Thus, when addressing MADM tasks with two or more naturally related sets of criteria, it is appropriate to apply criteria adapted for that purpose, such as WEBIRA.