Multi-sample test-based clustering for fuzzy random variables

Abstract

A clustering method to group independent fuzzy random variables observed on a sample by focusing on their expected values is developed. The procedure is iterative and based on the p-value of a multi-sample bootstrap test. Thus, it simultaneously takes into account fuzziness and stochastic variability. Moreover, an objective stopping criterion leading to statistically equal groups different from each other is provided. Some simulations to show the performance of this inferential approach are included. The results are illustrated by means of a case study. (C) 2009 Elsevier Inc. All rights reserved

Maximum likelihood estimation from fuzzy data using the EM algorithm

“…This model fits well with a physical interpretation of fuzzy data, in which a fuzzy datum is regarded as an existing object, not necessarily connected to any underlying precise variable [13]. Recent work on applying this approach to estimation and hypothesis testing problems may be found, for example, in [2,19,21].…”

Maximum Likelihood Estimation from Uncertain Data in the Belief Function Framework

“…The uncertain data m is thus not assumed to be produced by a random experiment, which is in sharp contrast with alternative approaches based on random set (see, e.g. [52], [53]) or fuzzy random variables (see, e.g., [54], [55], [24]).…”

Central tendency for symmetric random fuzzy numbers

“…Several problems and techniques are being studied and developed along this century. For instance, testing about means (see Colubi et al [4], González-Rodríguez et al [14] or the recent review by BlancoFernández et al [1]), regression analysis (see, for instance, Ferraro et al [9], Ferraro and Giordani [10]), clustering (see, for instance, González-Rodríguez et al [12]), Bayesian analysis (see Stein et al [26]), actuarial developments, portfolio selection and mathematical programming (see, for instance, Shapiro [22], Li and Xu [16], Sakawa and Matsui [20]), and so on.…”