A new method of ranking parametric form of fuzzy numbers using value and ambiguity

Most of the real-life, medical and engineering problem may often involve decision-making under uncertain circumstances. These problems may be interpreted in terms of fuzzy numbers. Hence, a propermethod of comparing and ranking these fuzzy numbers is very essential. In recent years, numerous way of ranking fuzzy numbers have been proposed. Most of the existing approaches have shortcomings and limitations under certain circumstances. In particular symmetric fuzzy numbers having same core and different supports, fuzzy numbers having same support and different cores, crisp valued fuzzy numbers, crisp valued fuzzy numbers having same support and different heights and fuzzy numbers having compensation of areas are not properly ranked in most of the studies. Hence, a new method of ranking fuzzy number using the value and the ambiguity, which are ill-defined magnitude and amount of vagueness present in the ill-defined magnitude respectively, at different decision level has been proposed. The proposed method has been discussed on the concept of parametric form of fuzzy number with the defuzzifiers are at different heights and the concept of decision levels. This concept of parametric form of fuzzy number with the defuzzifiers are at different heights has been discussed for the first time. The proposed method has been compared with other existing methods through numerical examples and found to outperform in all situations. The results demonstrate that the proposed method can clearly overcome the addressed limitations and shortcomings. As a possible application, a problem on fuzzy linear programming has been addressed. (C) 2016 Elsevier B.V. All rights reserved.