Possibility mean and variation coefficient based ranking methods for type-1 fuzzy numbers and interval type-2 fuzzy numbers

Abstract

Although there are many ranking methods for type-1 fuzzy numbers, most of which exist some limitations. In this paper, we propose a new concept to rank type-1 fuzzy numbers, which defines the 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 logicality of the ranking with their images'. Some properties of the proposed ranking methods are discussed. Then, we extend the concept to interval type-2 fuzzy numbers environment, and present a new ranking method with possibility mean and variation coefficient forms. Some properties are also discussed. For ranking the type-1 fuzzy numbers and interval type-2 fuzzy numbers, the proposed ranking methods are easy to understand and their computations are simple. Several examples are proposed to illustrate the ranking of type-1 fuzzy numbers and interval type-2 fuzzy numbers, and the results show that it enriches the existing fuzzy ranking methods.