Sparse Data and Rule Base Completion

Several techniques have been proposed for making inferences using the information contained in an incomplete rule base. These fall into three major categories; interpolative reasoning, analogical inference, and rule base completion. Interpolation uses the relative locations and shapes of the fuzzy sets in a pair of bounding rules to construct an output when an input occurs between the antecedents of the bounding rules. Analogical inference employs similarity to a single proximate example to produce the output. Completion generates a set of rules whose antecedents link the antecedents of the bounding rules. In this paper we compare the underlying principles of interpolation, analogical inference, and rule base completion. In addition, we propose a completion technique that partitions the domain between the antecedents of the bounding rules. The size of the partition is determined by the variation between fuzzy regions specified by the bounding rules.