Towards Backward Fuzzy Rule Interpolation

Fuzzy rule interpolation (FRI) is well known for reducing the complexity of fuzzy models and making inference possible in sparse rule-based systems. However, in practical fuzzy applications with inter-connected rule bases, situations may arise when a crucial antecedent of observation is absent, either due to human error or difficulty in obtaining data, while the associated conclusion may be derived according to different rules or even observed directly. To address such issues, a concept termed Backward Fuzzy Rule Interpolation (B-FRI) is proposed, allowing the observations which directly relate to the conclusion be inferred or interpolated from the known antecedents and conclusion. B-FRI offers a way to broaden the fields of research and application of fuzzy rule interpolation and fuzzy inference. The steps of B-FRI implemented using the scale and move transformation-based fuzzy interpolation are given, along with two numerical examples to demonstrate the correctness and accuracy of the approach. Finally, a practical example is presented to show the applicability and potential of B-FRI.