Integration of interpolation and inference

The design of effective rule based systems is a main goal of development in fuzzy logic and systems. If this design is based on a sparse rule-base where many rules are missing or unknown, then an appropriate solution is to use fuzzy rule interpolation. Fuzzy interpolation is helpful when no rule observation matches the given observation. However, observation may sometimes match partially or even exactly with at least one of the rules in the rule-base. In these situations, it is natural to avoid the computational overheads of interpolation by firing the best matching rule directly. If no such matching is found then it should be ensured that correct rules are selected for interpolation. This paper proposes a simple approach which integrates fuzzy interpolation and inference. In particular, the work answers two research questions: (1) When an exact or partial matching exists in the rule-base with a given observation, how should reasoning be performed. (2) When no overlapping rule is found which matches the observation, how should the best rules for interpolation be selected. For efficiency, the first issue is addressed using the concept of α-cut overlapping between fuzzy sets that represent the observation and rule antecedents. The second is dealt with by exploiting the Hausdorff distance metric to identify the closest rules for interpolation or extrapolation. Experimental results are provided to demonstrate the performance of these methods, including comparison between the use of the centre of gravity based distance metric whilst addressing the second issue. Future work is also described in an effort to illustrate that the proposed work may support the development of a generic dynamic fuzzy interpolation framework.