Ranking fuzzy numbers by their left and right wingspans

Based on the area between the curve of the membership function and the horizontal real axis, concepts of left and right wingspans are introduced. By them, a new index, called the w-center for fuzzy numbers is proposed. It is continuous with respect to the convergence of fuzzy number sequence. An intuitive and reasonable ranking method for fuzzy numbers based on their w-center is also established. This new ranking method is useful in fuzzy decision making and fuzzy data mining. The paper also points out that, in literature, some ranking methods based on the centroid of fuzzy numbers are not reasonable.