A distance based ranking methods for type-1 fuzzy numbers and interval type-2 fuzzy numbers

Although there are many methods for ranking type-1 fuzzy numbers, most of which exist some limitations. In this paper, we firstly propose a new distance measure based method to rank type-1 fuzzy numbers, which defines two formats of possibility mean and variation coefficient. It not only clearly discriminates the ranking of the type-1 fuzzy numbers especially for the reasonable ranking of symmetric type-1 fuzzy numbers, but also satisfies the consistence of the ranking with their images. Then, we extend such ranking method to interval type-2 fuzzy numbers. For ranking both the type-1 fuzzy numbers and interval type-2 fuzzy numbers, the proposed methods are easy to understand and their computations are simple. Several typical examples are used to illustrate our new ranking methods for type-1 fuzzy numbers and interval type-2 fuzzy numbers.