Ranking of Z-numbers based on value and ambiguity at levels of decision making

The concept of Z-number, is very new in the literature, proposed by Zadeh in 2011. The Z-numberZ=(A,B)is a pair of fuzzy numbers where the first component represents the restriction and the second component represents the certainty of the first component. Further, its application is evident in decision-making problems, risk assessment, linear programming problems, and so forth. Hence, under such circumstances ranking of Z-numbers need an utmost attention, as such, a few methods of ranking Z-numbers are proposed by various researcher. However, in many situations the existing methods depict drawbacks and limitations as discussed in this paper. Hence, a new method of ranking Z-numbers is essential for an appropriate decision-making. In this paper, a new method of ranking Z-numbers based on the concept of value and ambiguity at levels of decision-making have been proposed. The method seems to deliver a reasonable decision and proper ranking of Z-numbers of various types. A few numerical examples are discussed which show the out-performance of the proposed method.