Fuzzy clusterwise linear regression analysis with symmetrical fuzzy output variable

A revisited approach to linear fuzzy regression using trapezoidal fuzzy intervals

“…Further works concern the comparison of our method with regard to other existing techniques, for example the granular clustering proposed by Pedrycz and Bargiela [28] or the fuzzy clusterwise linear regression analysis from [17]. For being able to fairly compare different identified models, further works on the aggregation of various quality indicators, including measurements of goodness of fit for a fuzzy regression model [2,10,40], would be also useful.…”

“…(19)) under the inclusion constraints given by Eq. (17). The obtained results are illustrated in Fig.…”

“…In this example, according to available data the model definition domain D is equal to [5,17] and two different segments can be distinguished where the change-point is x = 11, that is: D = D 1 [ D 2 with D 1 = [5,11] and D 2 = [11,17]. The observed outputs on the first segment present a globally decreasing spread.…”

Regularized fuzzy clusterwise ridge regression

“…Clusterwise regression has been a useful method for investigating cluster-level heterogeneity of observations, which involves distinct linear relationships between predictor and dependent variables across different groups of observations (DeSarbo and Cron 1988;DeSarbo et al 1989;DeVeaux 1989;D'Urso 2003;D'Urso and Santoro 2006;Hathaway and Bezdek 1993;Hosmer 1974;Quandt 1958Quandt , 1972Quandt and Ramsey 1978;Späth 1979Späth , 1981Späth , 1982Späth , 1985Wedel and DeSarbo 1995;Yang and Ko 1997). This method enables one to classify observations into clusters and to estimate regression coefficients for each cluster at the same time.…”

Book review

“…Various kinds of uncertainty are dealt with, in this methodology: the vagueness of the response, the imprecision of model parameters, and the ignorance about the specific regression model in a given class of models.• P. D'Urso and A. Santoro, Fuzzy clusterwise linear regression analysis with symmetrical fuzzy output variable. This work[9] is devoted to the development of a regression model for studying the dependence of a fuzzy symmetric LR response on a set of crisp explanatory variables, when the observations may be clustered in different groups showing different regression patterns (clusterwise regression). A least-squares approach is proposed, based on the joint optimization of cluster partition and regression patterns' estimation.…”