On Ranking of Continuous Z-Numbers with Generalized Centroids and Optimization Problems Based on Z-Numbers.

In this paper, we introduce the addition and g-difference of continuous Z-numbers at first. Then, we define a new partial order to rank the Z-numbers with generalized centroids. The g-derivative of Z-number function based on g-difference is proposed. It is well known that convexity plays a vital role in optimization problems; consequently, we present the convexity of Z-number function. Furthermore, we provide the optimality conditions for optimization problems based on Z-numbers. Finally, the validity of the discussion is illustrated by an example. [ABSTRACT FROM AUTHOR]