A possibilistic-logic-based approach to integrating imprecise and uncertain information

A reasoning mechanism capable of dealing with imprecise and uncertain information is essential for expert systems. In this paper, we propose the use of truth-qualified fuzzy propositions as the representation of imprecise and uncertain information, where the fuzzy sets embody the intended meaning of imprecise information and the fuzzy truth values serve as the representation of uncertainty for its capability to express the possibility of the degree of truth of a fuzzy proposition. An inference mechanism for fuzzy propositions with fuzzy truth values is developed to serve as a bridge that brings together the possibilistic reasoning and fuzzy reasoning into a hybrid approach to reasoning under uncertainty and imprecision. There are three steps involved. First, the fuzzy rules and fuzzy facts with fuzzy truth values are transformed into a set of uncertain classical propositions with necessity and possibility measures. Second, a possibilistic reasoning called possibilistic entailment is performed on the set of uncertain classical propositions. Third, we reverse the process in the first step to synthesize all the classical sets obtained in the second step into a fuzzy set, and to compose necessity and possibility pairs to form a fuzzy truth value.