Alpha-Cut-Based Backward Fuzzy Interpolation

Fuzzy rule interpolation offers a useful means for enhancing the robustness of fuzzy models by making inference possible in sparse rule-based systems. However, in real-world applications of inter-connected 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 issue, an approach named backward fuzzy rule interpolation and extrapolation has been proposed recently, allowing the observations which directly relate to the conclusion to be inferred or interpolated from the known antecedents and conclusion. As such, it significantly extends the existing fuzzy rule interpolation techniques. However, the current idea has only been implemented via the use of the scale and move transformation-based fuzzy interpolation method, which utilise analogical reasoning mechanisms. In order to strengthen the versatility and feasibility of backward fuzzy interpolative reasoning, in this paper, an alternative alpha-cut-based interpolation method is proposed. Two numerical examples and comparative studies are provided in order to demonstrate the efficacy of the proposed work.