Towards a Possibilistic Processing of Missing Values Under Complex Conditions

To estimate the missing values of an attribute in the records of a dataset, all the information provided by the other attributes and the knowledge databases must be considered. However, the information elements could be imperfect (imprecise, possibilistic, probabilistic, etc.) and could have different measuring scales (quantitative, qualitative, ordinal, etc.) at the same time. Furthermore, the relationships and the correlation between the considered attribute and the others should also be pondered. Unlike the prior works that have separately processed these issues using complex and conditional techniques, our approach, essentially based on the tools provided by the possibility theory, can easily handle these aspects within a unified, robust, and simple frameworks. Several numeric examples and applications have been given to simply illustrate the main steps of our method, and some promising perspectives have been proposed at the end of this paper. Key-Words: Possibility Theory, Missing Data, Information Imperfection (Uncertainty and Ambiguity), Data Mining.