Qualitative possibility theory and its applications to reasoning and decision under uncertainty

Possibility theory was coined by L.A. Zadeh in the late seventies as an approach to model imprecision and flexibility stemming from vague pieces of information, described by means of fuzzy sets. To-date, it stands as an approach to the modelling of partial belief that is the only simple alternative to probability theory. At the same time, it can be viewed as a calculus of preference. Possibility theory can be either qualitative or quantitative. This brief introduction emphasizes the basic elements of the theory in both settings: possibility and necessity measures (as well as their comparative counterparts), the minimal specificity principle which underlies the whole theory, the combination, and conditioning of possibility distributions, as well as the evaluation of fuzzy events. In the numerical case interpretive frameworks of possibility theory are pointed out. Then the main applications of qualitative possibility theory are pointed out in the fields of automated reasoning and problem-solving. In the field of reasoning, the stress is put on exception-tolerant reasoning. In problem-solving, the fuzzy constraint satisfaction paradigm is described. Putting together possibility distributions expressing uncertainty with fuzzy constraints expressing preference leads to qualitative utility theory.