Backward Fuzzy Rule Interpolation with Multiple Missing Values

Fuzzy rule interpolation offers a useful means for reducing the complexity of fuzzy models, more importantly, it makes inference possible in sparse rule-based systems. Backward fuzzy rule interpolation is a recently proposed technique which extends the potential existing methods, allowing interpolation to be carried out when a certain antecedent of observation is absent. However, only one missing antecedent may be inferred or interpolated using the other given antecedents and the consequent. In this paper, two approaches are proposed in an attempt to perform backward interpolation with multiple missing antecedent values. Both approaches assume a restricted model with multiple inputs and a single output, where every rule has the same number of antecedents. Experimental comparative studies are carried out to demonstrate the efficacy of the proposed work.