Taking into Account Interval (and Fuzzy) Uncertainty Can Lead to More Adequate Statistical Estimates
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 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.
This work was performed when Vladik Kreinovich was a visiting researcher within the Research Training Group “Integrity and collaboration in dynamic sensor networks” at the Geodetic Institute of the Leibniz University of Hannover, a visit supported by the German Science Foundation under grant number GRK2159. This work was also supported in part by NSF grant HRD-1242122.
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