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In the 1960s Cargo and Shisha introduced a metric in a family of quasi-arithmetic means defined on a common interval as the maximal possible difference between these means taken over all admissible vectors with corresponding weights. During the years 2013–2016 we proved that, having two quasi-arithmetic means, we can majorize the distance between them in terms of the Arrow–Pratt index. In this paper...
This paper presents a new validation index for the Fuzzy C-Means algorithm, which is composed of two metrics, the modified partition entropy index and the sum of the distances between the means of the fuzzy partitions. The modified partition entropy represents the variation of the data in clusters of the dataset, and the sum of the distances between the means of the fuzzy partition represents the...
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