The preference order of fuzzy numbers

Many fuzzy number ranking approaches are developed in the literature for multiattribute decision-making problems. Almost all of the existing approaches focus on quantity measurement of fuzzy numbers for ranking purpose. In this paper, we consider the ranking process to determine a decision-maker's preference order of fuzzy numbers. A new ranking index is proposed to not only take quantity measurement, but incorporate quality factor into consideration for the need of general decision-making problems. For measuring quantity, several α-cuts of fuzzy numbers are used. A signal/noise ratio is defined to evaluate quality of a fuzzy number. This ratio considers the middle-point and spread of each α-cut of fuzzy numbers as the signal and noise, respectively. A fuzzy number with the stronger signal and the weaker noise is considered better. Moreover, the associated α levels are treated as the degree of belief about the α-cut and used as weights in the index for strengthening the influence of α-cut with higher α levels. The membership functions of fuzzy numbers are not necessarily to be known beforehand while applying this index. Only a few left and right boundary values of α-cuts of fuzzy numbers are required. We have proved the feature of the proposed index in a particular case. Several examples are also used to illustrate the feature and applicability in ranking fuzzy numbers.