The middle-parametric representation of fuzzy numbers and applications to fuzzy interpolation

•The middle-parametric representation of fuzzy numbers is introduced.•The structure of symmetric fuzzy numbers is investigated.•Applications of middle-parametric representation in fuzzy interpolation are included.

In this paper we introduce the middle-parametric representation of a fuzzy number presenting some of the advantages in the use of this representation. A special attention is focused on the subset of symmetric fuzzy numbers presenting the special properties of their arithmetic. The approach on symmetric fuzzy numbers is sustained by the applications of these kinds of fuzzy numbers in fuzzy linear programming and by the presence of the symmetric Gaussian type fuzzy numbers in the theory of errors. As potential applications of the middle-parametric representation, some fuzzy interpolation problems are considered.