A compact fuzzy extension of the Naive Bayesian classification algorithm

We introduce a conservative fuzzy logic extension of the Naive Bayesian classification algorithm. The extension generalizes the algorithm such that the examples are described by a fuzzy set of attributes, instead of a classical set. Thus, an example possesses each attribute to a degree in [0, 1]. We present a new classification algorithm usable with fuzzy sets that is (a) fast, (b) is able to work with few training examples, (c) uses a compact representation of the internal model, (d) is able to deal with missing attributes, and (e) can be used for incremental learning, such that a rapid alternation of learning of new examples and classification of examples is possible. Our extension to Naive Bayesian classification is conservative in the sense that in the classical limit, when every fuzzy membership degree of the attributes is 0 or 1, our algorithm behaves exactly as the Naive Bayesian classification algorithm.