Transformation of variance to possibilistic variance and vice versa

Abstract

We introduce a new transformation of the variance function to possibilistic variance and vice versa. We show that the transformation of the center-of-gravity-based formulation of variance gives exactly the possibilistic variance introduced by Carlsson and Fullér and that the corresponding inverse transformation gives the original variance formula from the possibilistic variance. We also provide fast-computation formulas for both variances for triangular and trapezoidal fuzzy numbers.