**3. Ranking fuzzy numbers**

In many applications, ranking of fuzzy numbers is an important component of the decision process. Since fuzzy numbers do not form a natural linear order, like real numbers, a key issue in operationalzing fuzzy set theory is how to compare fuzzy numbers. Various approaches have been developed for ranking fuzzy numbers. In the existing research, the commonly used technique is to construct proper maps to transform fuzzy numbers into real numbers so called defuzzification. These real numbers are then compared. Herein, in approaches (; Abbasbandy & Asady, 2006; Abbasbandy & Hajjari, 2009, 2011; Asady, 2010; S. J. Chen & S. M. Chen, 2003, 2007, 2009; Deng & Liu, 2005; Deng et al., 2006; Hajjari, 2011a; Hajjari, 2011b; Z.-X. Wang et al. 2009) a fuzzy number is mapped to a real number based on the area measurement. In approaches (L. H. Chen & Lu, 2001, 2002; Liu & Han, 2005), cut set and decision-maker's preference are used to construct ranking function. On the other hand, another commonly used technique is the centroid-based fuzzy number ranking approach (Cheng, 1998; Chu, & Tsao, 2002; Y.J. Wang et al. 2008). It should be noted that with the development of intelligent technologies, some adaptive and parameterized defuzzification methods that can include human knowledge have been proposed. Halgamuge et al. (Halgamuge et al. 1996) used neural networks for defuzzification. Song and Leland (Song & Leland, 1996) proposed an adaptive learning defuzzification technique. Yager (1996) proposed knowledge based on defuzzification process, which becomes more intelligent. Similar to methods of Filve and Yager (Filev & Yager, 1991), Jiang and Li (Jiang & Li, 1996) also proposed a parameterized defuzzification method with Gaussian based distribution transformation and polynomial transformation, but in fact, no method gives a right effective defuzzification output. The computational results of these methods are often conflict.

We often face difficultly in selecting appropriate defuzzification, which is mainly based on intuition and there is no explicit decision making for these parameters. For more comparison details on most of these methods, in this chapter we review some of ranking methods.
