On a new class of distances between fuzzy numbers

In the course of the studies on fuzzy regression analysis, we encountered the problem of introducing a distance between fuzzy numbers, which replaces the classical (x-y)² on the real line. Our proposal is to compute such a function as a suitable weighted mean of the distances between the \ac s of the fuzzy numbers. The main difficulty is concerned with the definition of the distance between intervals, since the current definitions present some disadvantages which are undesirable in our context. In this paper we describe an approach which removes such drawbacks.