Ranking of Fuzzy Numbers on the Basis of New Fuzzy Distance

Abstract

Real-world problems often deal with uncertainties related to imprecision and vagueness, for which fuzzy modeling has provided a successful approach. Ranking fuzzy numbers is a necessary and complex task in multiple processes, such as decision making. To facilitate the task of ranking fuzzy numbers, it has been introduced an approach to construct fuzzy distances from classical interval distances because their α-cuts are continuous intervals. Usually, extant interval distances use interval endpoints or midpoints, leading to results that might not reflect the correct distance because of information loss. This paper introduces a new fuzzy distance based on a novel interval distance that considers all points within the intervals by using the concept of integration to calculate the average distance between all points belonging to two intervals, respectively. Subsequently, a series of distances between fuzzy numbers based on the proposed interval distances are defined and proved. A new method for ranking fuzzy numbers using the new fuzzy distances is then presented. Finally, the validity and effectiveness of the proposed distances will be demonstrated by a comparative analysis of numerical examples.