Integration of Interpolation and Inference with Multi-antecedent Rules

Abstract

The efficacious fuzzy rule based systems perform their tasks with either a dense rule base or a sparse rule base. The nature of the rule base decides on whether compositional rule of inference (CRI) or fuzzy rule interpolation (FRI) should be applied. Given a dense rule base where at least one rule exists for every observation, CRI can be effectively and sufficiently employed. For a sparse rule base where rules do not cover all possible observations, FRI is required. Nonetheless, certain observations may be matched partly or completely with any of the existing rules in the sparse rule-base. Such observations can be directly dealt with using CRI and the conclusion can be inferred via firing the matched rule, thereby avoiding extra overheads of interpolation. If no such matching can be found then correct rules should be selected to ensure the accuracy while performing FRI. This paper proposes a generalised approach for the integration of FRI and CRI. It utilises the notion of alpha-cut overlapping to determine the matching degree between rule antecedents and a given observation in order to determine if CRI is to be applied. In the event of no matching rules, the nearest rules will be chosen to derive conclusion using FRI based on the best suitable distance metric among possible alternatives such as the Centre of Gravity, Hausdorff Distance and Earth Mover’s Distance. Comparative results are presented to demonstrate the effectiveness of this integrated approach.