Multidimensional least-squares fitting of fuzzy models

Fuzzy linear regression model based on fuzzy scalar product

“…It may not be possible to review all the articles in this topic within this paper. The other interesting articles are also given in Alex (2004), Celminš (1987Celminš ( , 1991, Chang and Lee (1996), Dunyak and Wunsch (2000), D'Urso (2003), D' Urso and Gastaldi (2000), Jajuga (1986), Kacprzyk and Fedrizzi (1992), Kim et al (1996), Kim and Bishu (1998), Moskowitz and Kim (1993), Nasrabadi and Nasrabadi (2004), Sakawa and Yano (1992), Tanaka and Lee (1998), Toyoura et al (2004), Wang and Tsaur (2000), Yager (1982).…”

Exploratory multivariate analysis for empirical information affected by uncertainty and modeled in a fuzzy manner: a review

“…Instead, our interest focuses upon the set of the p "juxtaposed" variables, observed as a whole in the group of n objects. In this case, we have p membership functions and the investigation of the links among the p fuzzy variables is carried out directly on the matrix of fuzzy data concerning the npvariate observations (Coppi 2003;D'Urso 2007 For an analytical formalization of a conical fuzzy variable with conical membership function (conjunctive approach), see Celminš (1987Celminš ( , 1991.…”

“…In particular, in the literature, different approaches to regression analysis for fuzzy data have been developed, starting from the pioneering works by Tanaka et al (1982), Celminš (1987), Diamond (1988), based respectively on possibilistic principles (Tanaka et al 1993) and least squares principles. In this connection, two main approaches are available: --The possibilistic approach In this framework, given a regression model involving fuzzy regression coefficients, these are estimated by minimizing the fuzziness of the estimated response variable, conditionally on obtaining fuzzy response values which contain (to a certain possibility degree) the observed fuzzy responses.…”

“…The least squares criterion is then utilized with respect to the chosen metric. This approach has been followed by many researchers in the last two decades (for instance , Celminš 1987;Diamond 1988;Chang and Lee 1996;Ma et al 1997 (Coppi et al 2006a, b, c, d). …”

Fuzzy data analysis and classification

“…Körner (2000), Montenegro et al (2001), Gil et al (2006), González-Rodríguez et al (2012), Ramos-Guajardo et al (2010), Ramos-Guajardo and Lubiano (2012) and Lubiano et al (2016b) Fuzzy estimates of location of random fuzzy numbers; robustness Lubiano and Gil (1999) and Sinova et al (2016) Statistical comparison of fuzzy scale with other imprecise-valued scales De la Rosa de Sáa et al (2016), Gil et al (2015) and Lubiano et al (2016aLubiano et al ( , 2017 Fuzzy inequality Gil et al (1998) Discriminant analysis Colubi et al (2011) Cluster analysis Hathaway et al (1996), Pedrycz et al (1998), Auephanwiriyakul and Keller (2002), D'Urso (2007) and Coppi et al (2012) Regression analysis Celminš (1987), Diamond (1988), Näther and Albrecht (1990) …”