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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 -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.
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 -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.
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