Taking Into Account Interval (and Fuzzy) Uncertainty Can Lead to More Adequate Statistical Estimates

Authors

Ligang Sun, Leibniz University HannoverFollow
Hani Dbouk, Leibniz University HannoverFollow
Steffen Schön, Leibniz University HannoverFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

6-2017

Comments

Technical Report: UTEP-CS-17-57a

To appear in: Proceedings of the 2017 Annual Conference of the North American Fuzzy Information Processing Society NAFIPS'2017, Cancun, Mexico, October 16-18, 2017

Abstract

Traditional statistical data processing techniques (such as Least Squares) assume that we know the probability distributions of measurement errors. Often, we do not have full information about these distributions. In some cases, all we know is the bound of the measurement error; in such cases, we can use known interval data processing techniques. Sometimes, this bound is fuzzy; in such cases, we can use known fuzzy data processing techniques.

However, in many practical situations, we know the probability distribution of the random component of the measurement error and we know the upper bound -- numerical or fuzzy -- on the measurement error's systematic component. For such situations, no general data processing technique is currently known. In this paper, we describe general data processing techniques for such situations, and we show that taking into account interval and fuzzy uncertainty can lead to more adequate statistical estimates.