Decision making with fuzzy-belief-state-based reasoning

An outstanding problem is how to make decisions with uncertain and incomplete data from disparate sources without NP-hard algorithms. Here we introduce a new reasoning methodology, fuzzy-belief-state-based reasoning, to solve this problem. In this methodology, we first create a fuzzy-belief-state base for a system from its historical data. For any component n(n=1,...,N) of the set of empirical state vectors, the values of that component are clustered into Low, Medium and High fuzzy sets. Then each state vector is fuzzified into a fuzzy-belief-state vector of N triples, where the n-th triple contains the fuzzy truths of membership of the variable value in these respective three fuzzy sets. Each such vector of N triples is associated with a decision to form a fuzzy-belief-case and such cases comprise a fuzzy-belief-state base. Then, when given an observed state vector that is incomplete and uncertain, we mine fuzzy association rules from the fuzzy-belief-state base and apply them to infer the missing values and their fuzzy beliefs based on that incomplete observation. The completed observation is used to match fuzzy-belief-state vectors in the fuzzy-belief-state base. Decisions of the best matching cases are retrieved for use as in case-based reasoning.