## 1 Introduction  
As we know, the real world is imperfect, imprecise, and uncertain. Hence, many theories and approaches, e.g., fuzzy sets, rough sets, and interval sets, have been proposed to reflect the vagueness of the real world. To reflect the human's subjective uncertainty of linguistics, Professor [PERSON] used fuzzy numbers to capture the uncertainty and the membership function to be the corresponding weights [1]. Usually, a fuzzy number is represented by a triangular fuzzy number (\(a_{1},a_{2},a_{3}\)), where \(a_{1},a_{2}\), and \(a_{3}\) are the left, center, and right values of a fuzzy number, respectively. Indeed, we can use alternative forms, e.g., trapezoidal or Gaussian, to present fuzzy numbers.  
However, in most practical situations, we still hope the information for decision-making is clear and crisp. Therefore, many defuzzification methods are proposed and used to transform imprecise values, e.g., interval or fuzzy numbers, into crisp values for decision-making. Note that defuzzifying imprecise data means using some functions to transform fuzzy or interval numbers into crisp values. Since imprecise data analysis, no matter interval or fuzzy numbers, is popular in many fields, e.g., multiobjective programming [2; 3; 4], data envelopment analysis (DEA) [5; 6; 7], and decision sciences [8; 9; 10], the defuzzification of imprecise numbers is a critical topic.  
The problem of defuzzifying interval numbers is similar to that of defuzzifying fuzzy numbers. The main difference is that the y-axis of fuzzy numbers denotes the membership function, but the y-axis of interval numbers is the probability density function (pdf). The authors of [11] first proposed the concept of ranking fuzzy numbers using the mean and spread. However, it is inefficient to determine the better fuzzy number or interval data when one has a higher mean and a higher spread. Although the concept of coefficient of variance (\(CV\)) was provided in [12] to cope with the problem of inconsistency, it failswhen there are crisp values, and it is hard to apply to follow-up multiple attribute decision-making (MADM) applications, such as simple additive weighting (SAW) or weight product method (WPM), due to the fact the original unit is changed. Hence, an easy and efficient algorithm to defuzzify imprecise numbers is a critical issue for practical applications.  
In this paper, we first find the mean and spread of imprecise numbers via the Mellin transformation. Then, we derive the trade-off coefficient between the mean and spread. Finally, we develop the preference relation of imprecise numbers to rank them. In addition, we use four examples to demonstrate our concepts and extend our method to choose the best alternative using the SAW method. Based on the numerical results, our method can handle the problem of the inconsistency between the mean and the spread with respect to the center of area (CoA) and the bisector of area (BoA), and can be easily used in further applications.  
The rest of this paper is organized as follows. Section 2 states the problem of the inconsistency between the mean and the spread. Section 3 derives the relation between the mean and the spread according to the utility theory. The detail of the Mellin transform is presented in Section 4. Four numerical examples are used in Section 5 to demonstrate our concept. Discussion is presented in Section 6, and the final section presents conclusions.