Imprecision and Vagueness: Interval-valued exploratory data analysis approaches

Uncertainty plays a critical role in the whole human everyday knowledge process. Scholars with different scientific backgrounds, have attempted to consider the uncertainty not only in terms of randomness but an unified view has not yet reached. Formalisation and definitions we will consider are most likely been influenced by the statistical approach in data analysis. In the discrete calculus field Interval Arithmetic appeared in the late 60’s. The first complete formalisation is marked by the appearance of the book entitled Interval Analysis by R.E. Moore in 1966. In 1965 and in another context, L.A. Zadeh, motivated by the same need, published his famous paper entitled Fuzzy Sets. Interval variables and fuzzy sets have been defined to capture two new and different sources of uncertainty that can be referred to the Imprecision and to the Vagueness, respectively. It appears clear that any effort to treat in one paper the practical and theoretical different implications of uncertainty in the statistical analysis will turn out boastful. This paper focuses on the special case of quantitative variables and it considers the uncertainty as imprecision and vagueness. In this framework some exploratory statistical approaches methods will be illustrated.