M. Asunción Lubiano

Estimation of a simple linear regression model for fuzzy random variables

A generalized simple linear regression statistical/probabilistic model in which both input and output data can be fuzzy subsets of R^p is dealt with. The regression model is based on a fuzzy-arithmetic approach and it considers the possibility of fuzzy-valued random errors. Specifically, the least-squares estimation problem in terms of a versatile metric is addressed. The solutions are established in terms of the moments of the involved random elements by employing the concept of support function of a fuzzy set. Some considerations concerning the applicability of the model are made.

Soft Methods for Handling Variability and Imprecision

Probability theory has been the only well-founded theory of uncertainty for a long time. It was viewed either as a powerful tool for modelling random phenomena, or as a rational approach to the notion of degree of belief. During the last thirty years, in areas centered around decision theory, artificial intelligence and information processing, numerous approaches extending or orthogonal to the existing theory of probability and mathematical statistics have come to the front. The common feature of those attempts is to allow for softer or wider frameworks for taking into account the incompleteness or imprecision of information. Many of these approaches come down to blending interval or fuzzy interval analysis with probabilistic methods. This book gathers contributions to the 4th International Conference on Soft methods in Probability and Statistics. Its aim is to present recent results illustrating such new trends that enlarge the statistical and uncertainty modeling traditions, towards the handling of incomplete or subjective information. It covers a broad scope ranging from philosophical and mathematical underpinnings of new uncertainty theories, with a stress on their impact in the area of statistics and data analysis, to numerical methods and applications to environmental risk analysis and mechanical engineering. A unique feature of this collection is to establish a dialogue between fuzzy random variables and imprecise probability theories.

Estimating the expected value of fuzzy random variables in random samplings from finite populations

AbstractIn this paper we consider the problem of estimating the expected value of a fuzzy-valued random element in random samplings from finite populations. To this purpose, we quantify the associated sampling error by means of a parameterized measure we have introduced in a previous paper.Keywords: Aumanns integral, expected value of a fuzzy random variable, fuzzy random variable,

A generalized real-valued measure of the inequality associated with a fuzzy random variable

\bar \lambda

Two-Way Analysis of Variance for Interval-Valued Data

-mean squared dispersion, random samplings, random set.

Some Properties of the dK-Variance for Interval-Valued Random Sets

Abstract In this paper, we consider the problem of estimating the expected value of a fuzzy-valued random element in the stratified random sampling from finite populations. To this purpose, we quantify the associated sampling error by means of a generalized measure introduced in a previous paper. We also suggest a way to compare different variates for stratification, as well as to test the adequacy of a certain one.

Empirical Results Concerning a Fuzzy-Based Measure of Symmetry of Real Random Variables

Abstract Fuzzy random variables have been introduced by Puri and Ralescu as an extension of random sets. In this paper, we first introduce a real-valued generalized measure of the “relative variation” (or inequality) associated with a fuzzy random variable. This measure is inspired in Csiszars f-divergence, and extends to fuzzy random variables many well-known inequality indices. To guarantee certain relevant properties of this measure, we have to distinguish two main families of measures which will be characterized. Then, the fundamental properties are derived, and an outstanding measure in each family is separately examined on the basis of an additive decomposition property and an additive decomposability one. Finally, two examples illustrate the application of the study in this paper.

Enhanced QTL Linkage Analysis with DNA Pooling by Means of Monte Carlo EM

Due to the important role as central summary measure of a fuzzy random variable (FRV), statistical inference procedures about the mean of FRVs have been developed during the last years. The R package SAFD (Statistical Analysis of Fuzzy Data) provides basic tools for elementary statistics with one dimensional Fuzzy Data (in the form of polygonal fuzzy numbers). In particular, the package contains functions for doing a bootstrap test for the equality of means of two or more FRVs. The corresponding algorithm will be described and applied to both real-life and simulated data.