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., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\operatorname{TFN}$</tex-math></inline-formula>’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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\operatorname{TFN}$</tex-math></inline-formula>. In addition, we also introduce the concepts of averaging functions on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\operatorname{TFN}$</tex-math></inline-formula>, with emphasis on ordered weighted averaging functions on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\operatorname{TFN}$</tex-math></inline-formula> equipped with an admissible order. Finally, the problem of joining central vertices is presented with an illustrative example where the previous concept is used.