Fuzzy causal probabilistic networks - A new ideal and practical inference engine

Fuzziness and randomness are two distinct components of uncertainty. While fuzzy sets are a rigorous softening of random sets, many of the operations defined in fuzzy logic lack a complete formalism, and are not strongly supported by experimental evidence. Causal Probabilistic Networks (CPN) or Bayesian networks provide an ultimately flexible inference mechanism based on Bayesian probability principles. However, CPNs suffer from the overwhelmingly large conditional probability tables with discrete variables. Fuzzification of continuous or crisp variables reduces the size of conditional probability tables to practically acceptable levels and these tables exhaustively encompass all the intuitive and fuzzy rules for inference problems. In this way, we reach a new inference engine, called fuzzy causal probabilistic networks, which provides a rigorous formalism for inference under fuzziness and randomness.