Backward Fuzzy Rule Interpolation

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Abstract
Fuzzy rule interpolation offers a useful means to enhancing the robustness of fuzzy models by making inference possible in sparse rule-based systems. However, in real-world applications of interconnected rule bases, situations may arise when certain crucial antecedents are absent from given observations. If such missing antecedents were involved in the subsequent interpolation process, the final conclusion would not be deducible using conventional means. To address this important issue, a new approach named backward fuzzy rule interpolation and extrapolation (BFRIE) is proposed in this paper, allowing the observations, which directly relate to the conclusion to be inferred or interpolated from the known antecedents and conclusion. This approach supports both backward interpolation and extrapolation which involve multiple fuzzy rules, with each having multiple antecedents. As such, it significantly extends the existing fuzzy rule interpolation techniques. In particular, considering that there may be more than one antecedent value missing in an application problem, two methods are proposed in an attempt to perform backward interpolation with multiple missing antecedent values. Algorithms are given to implement the approaches via the use of the scale and move transformation-based fuzzy interpolation. Experimental studies that are based on a real-world scenario are provided to demonstrate the potential and efficacy of the proposed work.

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