Ranking of fuzzy numbers based on alpha-distance

Abstract

This paper presents a new approach to compare fuzzy numbers using α-distance. Initially, the metric distance on the interval numbers based on the convex hull of the endpoints is proposed and it is extended to fuzzy numbers. All the properties of the α-distance are proved in details. Finally, the ranking of fuzzy numbers by the α-distance is discussed. In addition, the proposed method is compared with some known ones, the validity of the new method is illustrated by applying its to several group of fuzzy numbers.