Estimation of fuzzy memberships from histograms
type: Item
instance of: scholarly article
title: Estimation of fuzzy memberships from histograms
zbMATH Open document ID: 0566.68069
DOI: 10.1016/0020-0255(85)90040-4
author: B. Bharathi Devi
author: V. V. S. Sarma
published in: Information Sciences
publication date: 1985-01-01T00:00:00Z
review text: The values of membership of a fuzzy set are either obtained subjectively or as the values of a function for patterns. Desirable characteristics of the membership function are: The chosen form should reflect the real fuzziness. The number of parameters in the membership function should be small. The parameters should be infered from the elements of the training set. It should be computationally manageable in the estimation and decision making operations involved. Based on relationships between probability and possibility functions the authors recommend the histograms of the experimental data for estimation of the membership function in each class. A rational function approximation to the histogram is proposed and the estimated parameters of the approximation are normalized to derive the fuzzy membership function. The parameters representing the rational function are used for classifying the pattern samples based on max-min decision rule. The method is illustrated with the well-known Iris data and an example for vowel recognition.
Mathematics Subject Classification ID: 68T10
Mathematics Subject Classification ID: 94D05
zbMATH DE Number: 3903995
zbMATH Keywords: fuzzy sets
zbMATH Keywords: pattern recognition
zbMATH Keywords: speech recognition
zbMATH Keywords: fuzziness
zbMATH Keywords: training set
zbMATH Keywords: probability
zbMATH Keywords: possibility
zbMATH Keywords: fuzzy membership function
zbMATH Keywords: max-min decision rule
zbMATH Keywords: Iris data
zbMATH Keywords: vowel recognition
MaRDI profile type: Publication
full work available at URL: 0020-0255(85)90040-4
OpenAlex ID: W2138553938
cites work: Abstraction and pattern classification
cites work: Fuzzy sets and systems. Theory and applications
cites work: Q3657935
cites work: Unfair coins and necessity measures: Towards a possibilistic interpretation of histograms
cites work: Q3874122
cites work: Q3214234
cites work: Fuzzy Sets and Decisionmaking Approaches in Vowel and Speaker Recognition
cites work: Bibliography on estimation of misclassification
cites work: Fuzzy sets as a basis for a theory of possibility
description: scientific article; zbMATH DE number 3903995