Fuzzy Knowledge Representation Based on Possibilistic and Necessary Bayesian Networks

Within the framework proposed in this paper, we address the issue of extending the certain networks to a fuzzy certain networks in order to cope with a vagueness and limitations of existing models for decision under imprecise and uncertain knowledge. This paper proposes a framework that combines two disciplines to exploit their own advantages in uncertain and imprecise knowledge representation problems. The framework proposed is a possibilistic logic based one in which Bayesian nodes and their properties are represented by local necessity-valued knowledge base. Data in properties are interpreted as set of valuated formulas. In our contribution possibilistic Bayesian networks have a qualitative part and a quantitative part, represented by local knowledge bases. The general idea is to study how a fusion of these two formalisms would permit representing compact way to solve efficiently problems for knowledge representation. We show how to apply possibility and necessity measures to the problem of knowledge representation with large scale data. On the other hand fuzzification of crisp certainty degrees to fuzzy variables improves the quality of the network and tends to bring smoothness and robustness in the network performance. The general aim is to provide a new approach for decision under uncertainty that combines three methodologies: Bayesian networks certainty distribution and fuzzy logic.