Statistical inference about the means of fuzzy random variables: Applications to the analysis of fuzzy- and real-valued data

Authors:
Ana Colubi
Affiliations:
Dpto. de Estadística e I.O. y D.M., Universidad de Oviedo, 33007 Oviedo, Spain
Venue:
Fuzzy Sets and Systems
Year:
2009

Citing 6
Cited 8

The l&ar; -mean squared dispersion associated with a fuzzy random variable

Fuzzy Sets and Systems
Two-sample hypothesis tests of means of a fuzzy random variable

Information Sciences: an International Journal - Fuzzy random variables
Triangular fuzzification of random variables and power of distribution tests: Empirical discussion

Computational Statistics & Data Analysis
The fuzzy approach to statistical analysis

Computational Statistics & Data Analysis
Bootstrap approach to the multi-sample test of means with imprecise data

Computational Statistics & Data Analysis
A fuzzy representation of random variables: An operational tool in exploratory analysis and hypothesis testing

Computational Statistics & Data Analysis

Simulation of fuzzy random variables

Information Sciences: an International Journal
Multi-sample test-based clustering for fuzzy random variables

International Journal of Approximate Reasoning
A new family of metrics for compact, convex (fuzzy) sets based on a generalized concept of mid and spread

Information Sciences: an International Journal
A linear regression model for imprecise response

International Journal of Approximate Reasoning
An application of fuzzy random variables to control charts

Fuzzy Sets and Systems
Maximum likelihood estimation from fuzzy data using the EM algorithm

Fuzzy Sets and Systems
Nonparametric criteria for supervised classification of fuzzy data

International Journal of Approximate Reasoning
Fuzzy data treated as functional data: A one-way ANOVA test approach

Computational Statistics & Data Analysis

Quantified Score

Hi-index	0.20

Visualization

Abstract

The expected value of a fuzzy random variable plays an important role as central summary measure, and for this reason, in the last years valuable statistical inferences about the means of the fuzzy random variables have been developed. Some of the main contributions in this topic are gathered and discussed. Concerning the hypothesis testing, the bootstrap techniques have empirically shown to be efficient and powerful. Algorithms to apply these techniques in practice and some illustrative real-life examples are included. On the other hand, it has been recently shown that the distribution of any real-valued random variable can be represented by means of a fuzzy set. The characterizing fuzzy sets correspond to the expected value of a certain fuzzy random variable based on a family of fuzzy-valued transformations of the original real-valued ones. They can be used for descriptive/exploratory or inferential purposes. This fact adds an extra-value to the fuzzy expected value and the preceding statistical procedures, that can be used in statistics about real distributions.