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

In the last few decades, there has been an increase in the interest of the scientific community for multivariate statistical techniques of data analysis in which the data are affected by uncertainty, imprecision, or vagueness. In this context, following a fuzzy formalization, several contributions and developments have been offered in various fields of the multivariate analysis. In this paper—to show the advantages of the fuzzy approach in providing a deeper and more comprehensive insight into the management of uncertainty in this branch of Statistics—we present an overview of the developments in the exploratory multivariate analysis of imprecise data. In particular, we give an outline of these contributions within an overall framework of the general fuzzy approach to multivariate statistical analysis and review the principal exploratory multivariate methods for imprecise data proposed in the literature, i.e., cluster analysis, self-organizing maps, regression analysis, principal component analysis, multidimensional scaling, and other exploratory statistical approaches. Finally, we point out certain potentially fruitful lines of research that could enrich the future developments in this interesting and promising research area of Statistical Reasoning. All in all, the main purpose of this paper is to involve the Granular Computing scientific community and to stimulate and focus its interest on these statistical fields.