Strong consistency and rates of convergence for a random estimator of a fuzzy set

Pedro Terán and Miguel López-Díaz

Computational Statistics & Data Analysis, 2014, vol. 77, issue C, 130-145

Abstract: An approximation scheme for estimating a fixed, unknown fuzzy set from random samples taken from the nested random set defined by its α-level sets is presented. Its strong consistency is studied, giving rates of convergence in four metrics. A simulation study suggests that the behaviour for moderately small samples is coherent with the theoretical rate of convergence valid for large samples.

Keywords: Fuzzy set; Random set; Rate of convergence; Set estimation (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:77:y:2014:i:c:p:130-145

DOI: 10.1016/j.csda.2014.02.016

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