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Fuzzy Bayesian networks-a general formalism for representation, inference and learning with hybrid Bayesian networks

The paper proposes a general formalism for representation, inference and learning with general hybrid Bayesian networks. The formalism fuzzifies a hybrid Bayesian network into two alternative forms, which are called fuzzy Bayesian network (FBN) form-I and form-II. The first form replaces each continuous variable in the given directed acyclic graph (DAG) with a partner discrete variable and adding a directed link from the partner discrete variable to the continuous one. The second form only replaces each continuous variable whose descendants include discrete variables with a partner discrete variable and adding a directed link from that partner discrete variable to the continuous one. For the two forms of FBN, general inference algorithms exist which are extensions of the junction tree inference algorithm for discrete Bayesian networks.