Ranking Fuzzy Numbers Based on Ambiguity Degrees

Since much of human reasoning is based on imprecise, vague and subjective values, most of decision-making processing, in reality, requires handling and evaluation of fuzzy numbers. Zadeh’s (Zadeh 1965) fuzzy logic has given analysts a tool to present the human behavior more precisely, especially where relatively few data exist, and where the expert knowledge about the system is vague and linguistic (Hoogerdoorn et al. 1999). Therefore, ranking fuzzy numbers is one of very important research topics in fuzzy set theory because it is a base of decision-making in applications. However, fuzzy numbers may not be easily ordered into one sequence according to their magnitudes because they represent uncertain values. Although so far, many methods for ranking of fuzzy numbers have been discussed broadly, most of them contained some shortcomings, such as requirement of complicated calculations, inconstancy with human intuition and indiscrimination. However, these methods just can apply to rank some types of fuzzy numbers (i.e. normal, non-normal, positive, and negative fuzzy numbers), and many ranking cases can just rank by their graphs intuitively. Therefore, it is important to use proper methods in the right condition. The motivation of this study is to present a model for ranking fuzzy numbers based on their ambiguities. The advantages of the new proposed are that it can be applied for most of the defuzzification and the calculation is far simple and easy than previous methods. The effectiveness of the proposed method is finally demonstrated by including a comprehensive comparing different ranking method with the present one.