Abstract
In many applications of intuitionistic fuzzy sets, comparing or ranking intuitionistic fuzzy numbers (IFNs) plays an important role. In this paper, the orders of intuitionistic fuzzy numbers are discussed. The orders of IFNs have undesired mathematical properties. By using a special function, a new order of IFNs is proposed. This new type of order has good mathematical properties on algebraic intuitionistic fuzzy numbers (A-IFNs) which is a dense collection of IFNs, and A-IFNs are adequate in most applications.