Averaging Functions on Triangular Fuzzy Numbers and an Application in Graphs

Admissible orders on fuzzy numbers are total orders, which refine a basic and well-known partial order on fuzzy numbers. In this work, we define an admissible order on triangular fuzzy numbers (i.e., $\operatorname{TFN}$’s) and study some fundamental properties with its arithmetic and their relation with this admissible order. We also propose a new hyperstructure for ordered vector spaces and, in particular, consider the case of $\operatorname{TFN}$. In addition, we also introduce the concepts of averaging functions on $\operatorname{TFN}$, with emphasis on ordered weighted averaging functions on $\operatorname{TFN}$ equipped with an admissible order. Finally, the problem of joining central vertices is presented with an illustrative example where the previous concept is used.