Random Sets and Histograms

A probability density function verifies more demanding properties than a possibility measure. Probabilistic models ensure a predictable asymptotic behaviour. This should not be taken to suggest possibility theory should not be used. In fact, a histogram is a possibility measure and it is generally a better descriptor of a small sample of data than a probability density function regardless of its asymptotic properties. A possibility measure or also called fuzzy restriction is also more flexible or adaptable to different practical problems whereas probability theory try to generalize optimal methods applied to many different stochastic processes. Some people have already exploited the connection between probability theory and possibility theory or fuzzy sets to set up membership functions and to create fuzzy sets models. In this paper, we show that a histogram is the coverage function of a determined random set. This suggests other methods to create more accurate or different featured histograms by using random set theory. One example of a histogram with overlapping classes is provided.