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Since Bertoluzza et al.’s metric between fuzzy numbers has been introduced, several studies involving it have been developed. Some of these studies concern equivalent expressions for the metric which are useful for either theoretical, practical or simulation purposes. Other studies refer to the potentiality of Bertoluzza et al.’s metric to establish statistical methods for the analysis of fuzzy data...
This article presents preliminary observations from a study that investigates and models the fuzziness inherent in post-retirement financial concepts. The focus is on how fuzzy post-retirement concepts can be conceptualized and represented, and the goal is to give the reader a sense of the issues involved. The study begins with a brief overview of the conceptual aspects of fuzzy logic that are used...
In standard Bayesian inference, a-priori distributions are assumed to be classical probability distributions. This is a topic of critical discussions because, in reality, a-priori information is usually more or less non-precise, i.e. fuzzy. Hence, a more general form of a-priori distributions (so-called fuzzy a-priori densities) is more suitable to model such a-priori information. Moreover, data from...
We describe the concepts of fuzzy probability measure and the expected value (integral) of a random vector in this framework. The main result presented here is a strong law of large numbers with respect to a fuzzy probability measure. This framework is useful in Bayesian inference with a prior containing a mixture of probabilistic-fuzzy information.
In this paper, we discuss the problem of regression analysis in a fuzzy domain. By considering an iterative Weighted Least Squares estimation approach, we propose a general linear regression model for studying the dependence of a general class of fuzzy response variable, i.e., $$LR_2$$ L R 2 fuzzy variable or trapezoidal fuzzy variable,on a set of crisp or $$LR_2$$ L R 2 ...
We propose a robust fuzzy clustering model for classifying time series, considering the autoregressive metric based. In particular, we suggest a clustering procedure which: 1) considers an autoregressive parameterization of the time series, capable of representing a large class of time series; 2) inherits the benefits of the partitioning around medoids approach, classifying time series in classes...
The so-called fuzzy representations of real-valued random variables are reviewed. They are used to visualize or/and characterize distributions through fuzzy sets. Various fuzzy representations useful to explore or test about different characteristics of real distributions are described. The main developments concerning the representation, goodness-of-fit, equality of distribution and asymmetry are...
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