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Created July 2021 and modified August 2024 by Marco de Angelis.
Posted here for the first time on 1st November 2023.
https://github.com/marcodeangelis/variance_upper_bound/ (now public)
The code computes a sharp (best-possible) upper bound on the population (sample) variance of a finite interval data set. The upper bound coincides with the maximum (exact) for some classes of interval data. In fully nested interval data (fuzzy structures), the upper bound is never exact, i.e. is always larger than the maximum, which is obtained with Kreinovich's real-valued algorithms.
More details about the algorithm that computes the sharp upper bound are given in the SMPS paper appended to this page.
D1 = [[3.5,6.4], [6.9,8.8], [6.1,8.4], [2.8,6.7], [3.5,9.7], [6.5,9.9], [0.15,3.8], [4.5,4.9], [7.1,7.9]]
D2 = [[1.0, 9.0], [1.125, 8.25], [1.25, 7.5], [1.375, 6.75], [1.5, 6.0], [1.625, 5.25], [1.75, 4.5], [1.875, 3.75], [2.0, 3.0]]
D3 = [[-0.75, 10.75], [-0.5, 10.5], [-0.25, 10.25], [-0.05, 10.05], [0. , 10.], [0.05 , 9.95], [0.25 , 9.75], [0.5 , 9.5], [0.75 , 9.25], [1. , 9.], [1.125, 8.25], [1.25 , 7.5], [1.375, 6.75], [1.5 , 6.], [1.625, 5.25], [1.75 , 4.5], [1.875, 3.75], [2. , 3.], [2.25 , 2.75], [2.495, 2.505]]
author_SMPS2024_revised.pdfpresentation_variance_ub.pdfPage updated
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