  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. In addition, we also introduce the concepts of average
function on TFN$'s and studies a generalized structure of the vector spaces. In
particular we consider the case of TFN's.
