Interval and fuzzy-valued approaches to the statistical management of imprecise data

Abstract

In real-life situations experimental data can arise which do not derive from exact measurements or observations, but they correspond to ranges, judgements, perceptions or ratings often involving imprecision and subjectivity. These data are usually formalized with (and treated as) grouped or categorical/qualitative data for which the statistical analysis techniques to be applied are rather limited. However, many of these data could be alternatively and suitably identified with either interval-or fuzzy number-valued data. This approach offers in fact mathematical languages/scales allowing us to express many imprecise data related either to ranges/fluctuations or to judgements/perceptions/ratings, and to capture the underlying imprecision, subjectivity and variability. Besides capturing the information surrounding the imprecision, subjectivity and variability (which is frequently ignored in dealing with grouped or categorical data), the use of the rich interval and fuzzy scales enables to state distances between data with a meaning similar to that for numerical ones. Moreover, it will possible to develop statistical methods based on these distances and exploiting the added information. This paper aims to review the key ideas in this approach as well as some of the existing techniques for the statistical analysis. © 2011 Springer-Verlag Berlin Heidelberg.