Defuzzify Imprecise Numbers Using the Mellin Transform and the Trade-Off between the Mean and Spread

Abstract

Uncertainty or vagueness is usually used to reflect the limitations of human subjective judgment on practical problems. Conventionally, imprecise numbers, e.g., fuzzy and interval numbers, are used to cope with such issues. However, these imprecise numbers are hard for decision-makers to make decisions, and, therefore, many defuzzification methods have been proposed. In this paper, the information of the mean and spread/variance of imprecise data are used to defuzzify imprecise data via Mellin transform. We illustrate four numerical examples to demonstrate the proposed methods, and extend the method to the simple additive weighting (SAW) method. According to the results, our method can solve the problem of the inconsistency between the mean and spread, compared with the center of area (CoA) and bisector of area (BoA), and is easy and efficient for further applications.