  The aim of this paper is to show the interest in fitting features with an
$\alpha$-stable distribution to classify imperfect data. The supervised pattern
recognition is thus based on the theory of continuous belief functions, which
is a way to consider imprecision and uncertainty of data. The distributions of
features are supposed to be unimodal and estimated by a single Gaussian and
$\alpha$-stable model. Experimental results are first obtained from synthetic
data by combining two features of one dimension and by considering a vector of
two features. Mass functions are calculated from plausibility functions by
using the generalized Bayes theorem. The same study is applied to the automatic
classification of three types of sea floor (rock, silt and sand) with features
acquired by a mono-beam echo-sounder. We evaluate the quality of the
$\alpha$-stable model and the Gaussian model by analyzing qualitative results,
using a Kolmogorov-Smirnov test (K-S test), and quantitative results with
classification rates. The performances of the belief classifier are compared
with a Bayesian approach.
