Similarity of Country Rankings on Sustainability Performance

In this paper‎, ‎we extend the fuzzy similarity measure of‎ ‎two rankings to any finite number of rankings‎. ‎We provide a method to‎ ‎convert a measure for a finite number of rankings to a number that‎ ‎represents the number for two rankings‎. ‎We apply our results to the‎ ‎sustainability ranking of countries by the Environmental Performance Index‎ ‎(EPI)‎. ‎The $2020$ EPI provides a summary of the state of sustainability‎ ‎around the world‎. ‎It uses $32$ performance indicators across $11$‎ ‎categories‎. ‎These indicators provide a way to determine problems‎, ‎set‎ ‎targets‎, ‎track trends‎, ‎understand outcomes‎, ‎and identify best policy‎ ‎practices‎. ‎The EPI ranks $180$ countries on environmental health and‎ ‎ecosystem vitality‎. ‎The EPI provides a method in support of efforts to meet‎ ‎the targets of the UN Sustainable Development Goals‎. ‎The EPI determined‎ ‎that the Global West region ranked the highest‎. ‎The purpose of our project‎ ‎is to find the similarity of the $11$ rankings of the countries for eight‎ ‎different regions‎.