Backward Fuzzy Rule Interpolation

Description

This book chiefly presents a novel approach referred to as backward fuzzy rule interpolation and extrapolation (BFRI). BFRI allows observations that directly relate to the conclusion to be inferred or interpolated from other antecedents and conclusions. Based on the scale and move transformation interpolation, this approach supports both interpolation and extrapolation, which involve multiple hierarchical intertwined fuzzy rules, each with multiple antecedents. As such, it offers a means of broadening the applications of fuzzy rule interpolation and fuzzy inference. The book deals with the general situation, in which there may be more than one antecedent value missing for a given problem. Two techniques, termed the parametric approach and feedback approach, are proposed in an attempt to perform backward interpolation with multiple missing antecedent values. In addition, to further enhance the versatility and potential of BFRI, the backward fuzzy interpolation method is extended to support α-cut based interpolation by employing a fuzzy interpolation mechanism for multi-dimensional input spaces (IMUL). Finally, from an integrated application analysis perspective, experimental studies based upon a real-world scenario of terrorism risk assessment are provided in order to demonstrate the potential and efficacy of the hierarchical fuzzy rule interpolation methodology. Front Matter ....Pages i-xvii Introduction (Shangzhu Jin, Qiang Shen, Jun Peng)....Pages 1-15 Background: Fuzzy Rule Interpolation (Shangzhu Jin, Qiang Shen, Jun Peng)....Pages 17-57 Transformation-Based Backward Fuzzy Rule Interpolation with a Single Missing Antecedent Value (Shangzhu Jin, Qiang Shen, Jun Peng)....Pages 59-73 Transformation Based Backward Fuzzy Rule Interpolation with Multiple Missing Antecedent Values (Shangzhu Jin, Qiang Shen, Jun Peng)....Pages 75-89 An Alternative Backward Fuzzy Rule Interpolation Method (Shangzhu Jin, Qiang Shen, Jun Peng)....Pages 91-106 Hierarchical Bidirectional Fuzzy Rule Interpolation and Rule Base Refinement (Shangzhu Jin, Qiang Shen, Jun Peng)....Pages 107-119 Application: Terrorism Risk Assessment Using BFRI (Shangzhu Jin, Qiang Shen, Jun Peng)....Pages 121-141 Conclusion (Shangzhu Jin, Qiang Shen, Jun Peng)....Pages 143-151 Back Matter ....Pages 153-159