Exploratory Analysis of Random Variables Based on Fuzzifications

Abstract

In this paper we propose a new way of representing the distribution of a real random variable by means of the expected value of certain kinds of fuzzifications of the original variable. We will analyze the usefulness of this representation from a descriptive point of view. We will show that the graphical representation of the fuzzy expected value displays in a visible way relevant features of the original distribution, like the central tendency, the dispersion and the symmetry. The fuzzy representation is valuable for representing continuous or discrete distributions, thus, it can be employed both for representing population distributions and for exploratory data analysis.