Springer Backward Fuzzy Rule Interpolation

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.  From the Back Cover 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. About the Author Shangzhu Jin received his B.Sc. degree in Computer Science from Beijing Technology and Business University, China, his M.Sc. degree in Control Theory and Control from Yanshan University, China, and his Ph.D. degree from Aberystwyth University, UK. He is currently an Associate Professor at the School of Electronic Information Engineering, Chongqing University of Science and Technology. His research interests include fuzzy systems, approximate reasoning, and network security. His paper, entitled “Backward Fuzzy Interpolation and Extrapolation with Multiple Multi-antecedent Rules” won the best student paper award at the 21st IEEE International Conference on Fuzzy Systems.  Qiang Shen is a Professor and Director of the Institute of Mathematics, Physics and Computer Science (IMPACS) at Aberystwyth University. His major research interests include computational intelligence, fuzzy and qualitative systems, reasoning and learning under uncertainty, pattern recognition, data mining, and real-world applications of such techniques for decision support (e.g., crime detection, space exploration, consumer profiling, systems monitori