Measurement of possibility distributions

The problem of assessing numerical values of possibility distributions is considered in the paper. Particularly, we are interested in estimating the possibility values from a data set. The proposed estimation methods are based on the idea of transforming a probability distribution (obtained from the data set) into a possibility one. They also take into account that smaller data base size involve a greater uncertainty about the model and therefore, less precise assessments should be obtained in such cases. Moreover, in order to validate the estimated joint possibility distribution, a set of properties which guarantee that we obtain reasonable results will be studied. Finally, we are interested in analyzing the feasibility of the decisions or the conclusions that can be obtained by manipulating the estimated possibility distribution, so that some of the properties of this distribution, after applying to it the marginalization and conditioning operators, are also studied.