Fuzzy statistics provides useful techniques for handling real situations which are affected by vagueness and imprecision. Several fuzzy statistical techniques (e.g., fuzzy regression, fuzzy principal component analysis, fuzzy clustering) have been developed over the years. Among these, fuzzy regression can be considered an important tool for modeling the relation between a dependent variable and a set of inde- pendent variables in order to evaluate how the independent variables explain the empirical data which are modeled through the regression system. In general, the standard fuzzy least squares method has been used in these situations. However, several applicative contexts, such as for example, analysis with small samples and short and fat matrices, violation of distributional assumptions, matrices affected by multicollinearity (ill-posed problems), may show more complex situations which cannot successfully be solved by the fuzzy least squares. In all these cases, different estimation methods should instead be preferred. In this paper we address the problem of estimating fuzzy regression models characterized by ill-posed features. We introduce a novel fuzzy regression framework based on the Generalized Maxi- mum Entropy (GME) estimation method. Finally, in order to better highlight some characteristics of the proposed method, we perform two Monte Carlo experiments and we analyze a real case study.

### A Generalized Maximum Entropy (GME) estimation approach to fuzzy regression model

#### Abstract

Fuzzy statistics provides useful techniques for handling real situations which are affected by vagueness and imprecision. Several fuzzy statistical techniques (e.g., fuzzy regression, fuzzy principal component analysis, fuzzy clustering) have been developed over the years. Among these, fuzzy regression can be considered an important tool for modeling the relation between a dependent variable and a set of inde- pendent variables in order to evaluate how the independent variables explain the empirical data which are modeled through the regression system. In general, the standard fuzzy least squares method has been used in these situations. However, several applicative contexts, such as for example, analysis with small samples and short and fat matrices, violation of distributional assumptions, matrices affected by multicollinearity (ill-posed problems), may show more complex situations which cannot successfully be solved by the fuzzy least squares. In all these cases, different estimation methods should instead be preferred. In this paper we address the problem of estimating fuzzy regression models characterized by ill-posed features. We introduce a novel fuzzy regression framework based on the Generalized Maxi- mum Entropy (GME) estimation method. Finally, in order to better highlight some characteristics of the proposed method, we perform two Monte Carlo experiments and we analyze a real case study.
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2016
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11587/406197`
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