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., 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 TFN. In addition, we also introduce the concepts of averaging functions on TFN, with emphasis on ordered weighted averaging functions on 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.