Stability of random membership frequency and fuzzy statistics
type: Item
instance of: scholarly article
title: Stability of random membership frequency and fuzzy statistics
zbMATH Open document ID: 0666.62052
DOI: 10.1016/0165-0114(89)90138-3
author: Xihe Li
published in: Fuzzy Sets and Systems
publication date: 1989-01-01T00:00:00Z
review text: The aim of the paper is to estimate a membership function of a fuzzy set by statistical methods. Let X be a totally ordered set. A mapping \(\Gamma\) from a probability space into a set of intervals in X is called a random interval if it satisfies a measurability condition. The author shows that, given a random sample from \(\Gamma\), for all \(x\in X\) the random frequency of x converges to P(x\(\in \Gamma)\) with probability one. A [0,1]-valued random variable \(\lambda\) is a \(\Gamma\)-random degree of membership of a fuzzy set A if \(\Gamma\) (\(\omega)\) is the \(\lambda\) (\(\omega)\)-level set of A for all \(\omega\). Using a random sample from \(\Gamma\) and one of \(\lambda\) the author gives a method for estimating a membership function of a holomorphic fuzzy set.
Mathematics Subject Classification ID: 62G99
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 4090602
zbMATH Keywords: random interval
zbMATH Keywords: random degree of membership
zbMATH Keywords: holomorphic fuzzy set.
reviewed by: Osmo Kaleva
MaRDI profile type: Publication
full work available at URL: 0165-0114(89)90138-3
OpenAlex ID: W1992557469
cites work: Fuzzy sets
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description: scientific article; zbMATH DE number 4090602