The law of large numbers for fuzzy processes and the estimation problem
type: Item
instance of: scholarly article
title: The law of large numbers for fuzzy processes and the estimation problem
zbMATH Open document ID: 0588.60004
DOI: 10.1016/0020-0255(82)90046-9
author: Robert Badard
published in: Information Sciences
publication date: 1982-01-01T00:00:00Z
review text: We study how the law of large numbers can be extended to the case of fuzzy numbers. We work with L-fuzzy sets, where L is a \(CL_{\infty}\) commutative monoid with an operation *. We define the *-independence of fuzzy numbers. We find, when * is the operation \(\bigwedge\) of the lattice, that the arithmetical mean of \(\bigwedge\)-independent fuzzy numbers does not converge. We think that this case could be a limit one; we show, for particular cases of the *-operation, that generally convergence holds. We build estimators for fuzzy models; we particularly consider the ''minimum fuzziness estimator.'' We study the convergence of these estimators and compare them by way of the fuzzy subsets they induce. We lastly study the case where we have dependent fuzzy numbers and particularly the case of linearly filtered ''*-autoindependent'' fuzzy processes.
Mathematics Subject Classification ID: 60A99
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 62A01
Mathematics Subject Classification ID: 94D05
zbMATH DE Number: 3944930
zbMATH Keywords: law of large numbers
zbMATH Keywords: fuzzy numbers
zbMATH Keywords: fuzzy models
MaRDI profile type: Publication
full work available at URL: 0020-0255(82)90046-9
OpenAlex ID: W1965083204
cites work: Q3925673
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description: scientific article; zbMATH DE number 3944930