A Practical Approach to Nonlinear Fuzzy Regression

Support vector fuzzy regression machines

“…This model-free method turned out to be a promising method which 1 has been attempted to treat fuzzy nonlinear regression model with numerical inputs and fuzzy output. The main di erence between our SVM approach and the nonlinear approaches by Buckley et al 3 [2,3] and Celmins [5] is not crisp input-fuzzy output versus fuzzy input-fuzzy output, but model-free versus model-dependent. 5 Here we use kernel parameter and control parameter C determined in a heuristic way.…”

“…This explains why SVM can have good performance 17 even in high dimensional problem. The main di erence between our SVM approach and the nonlinear approaches by Buckley et al 19 [2,3] and Celmins [5] is not crisp input-fuzzy output versus fuzzy input-fuzzy output, but model-free versus model-dependent. 21…”

“…What researchers in fuzzy nonlinear regression were concerned with was data of the form with crisp inputs and fuzzy output. However, some papers, for example [2,3,5], were concerned 3 with the data set with fuzzy inputs and fuzzy output. By the way, in this paper we will treat fuzzy nonlinear regression for data of the form with crisp inputs and fuzzy output.…”

“…What researchers in fuzzy nonlinear regression were concerned with was data of the form with crisp inputs and fuzzy output. 3 Some papers, for example [1,2,5], were concerned with the data set with fuzzy inputs and fuzzy output. However, we think those fuzzy nonlinear regression methods look somewhat unrealistic and 5 treat the estimation procedures of some particular models such as linear, polynomial, exponential and logarithmic.…”

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.…”