The Empirical Variance of a Set of Fuzzy Intervals

The profile method gives a tool to perform fuzzy interval computation under a condition of local monotony of considered functions. This is a plain extension of interval analysis to fuzzy intervals, viewed as pairs of fuzzy bounds. This method yields exact results without applying interval analysis to alpha-cuts. After a refresher on the notion of profile and its use in fuzzy interval analysis, we adapt the profile method to the computation of the empirical variance of a tuple of fuzzy intervals. To this end, we first reconsider results obtained by Ferson et al. on computation of the empirical variance of a set of intervals. Finally we apply our results to the definition of the variance of a single fuzzy interval, viewed as a family of its alpha-cuts, and compare this definition to previous ones