Towards and Integration of Vague and Uncertain Information

Abstract

In this paper, we have proposed truth-qualified fuzzy propositions as the representation of uncertain vague information where the fuzzy sets embody the intended meaning of imprecise information and the fuzzy truth values serve as the representation of uncertainty. We have developed an inference values. There are three step 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 by mean of λ-cut. Second, our proposed inference called possibilistic entailment is performed on the set of uncertain classical propositions. Third, we reverse the process in the first step to synthesize all theλ-level-sets obtained in the second step into a fuzzy set, and to compose necessity and possibility pairs to form a fuzzy truth values. Compared with the existing work, our approach does not impose any restriction on the inference mechanism, that is , the intended meaning is not required to be unchanged；meanwhile, the confidence level can be partially certain. The proposed approach is not only a generalization of Zadeh’s generalized modus poens but also an uncertain reasoning for classical propositions with necessity and possibility pairs.