On Aggregation Functions on Discrete Z-Numbers Based on Total Orders

The study of aggregation functions, either from a theoretical point of view or for their interesting applications, is a hot topic. In this paper we propose a new method for constructing aggregation functions on the set of Zadeh's discrete Z-numbers based on total orders. This method is characterised by using aggregation functions defined on the set of discrete fuzzy numbers whose support is a closed interval of the finite chain $L_{n}=\{0,1, \cdots, n\}$. Furthermore, it is shown that this construction method preserves important properties of the chosen initial aggregation functions.