Refine and Merge: Generating Small Rule Bases from Training Data

The characteristics of a fuzzy model are frequently influenced by the method used to construct the rules. Models produced by a heuristic assessment of the underlying system are generally highly granular with interpretable rules. Generating rules using algorithms that analyse training data has the potential of producing highly precise models defined by rules of small granularity. This paper presents an algorithm designed for constructing models of high granularity within a prescribed precision bound. An initial domain decomposition is produced and a rule base is generated. If the error between the resulting model and training data exceeds the precision bound, the domain decompositions are refined and the process repeated. When a sufficiently precise model is generated, a greedy strategy is used to combine adjacent rules to increase the granularity of the model. A suite of experiments has been run to demonstrate the ability of the algorithm to reduce the number of rules in a fuzzy model.