A Method Based on Extended Fuzzy Transforms to Approximate Fuzzy Numbers in Mamdani Fuzzy Rule-Based System

<table class="fixed-width table-group sidewaystable" id="tab5"><tr><td><table class="table"><colgroup><col style="width:54.27em"/><col style="width:4.49em"/></colgroup><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td class="align_left"><b>Comparison parameter</b></td><td class="align_center"><b>Value</b></td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td class="align_left"><b>Mean RMSE index for the fuzzy sets approximation with trapezoidal FNs</b></td><td class="align_center">6.3×10<sup>-2</sup></td></tr><tr><td class="align_left"><b>Mean difference of the final crisp livability values compared with the ones obtained by using the extended iF-transform method</b></td><td class="align_center">5.58%</td></tr><tr><td class="align_left"><b>Number of municipalities classified with different linguistic labels</b></td><td class="align_center">7</td></tr><tr><td class="align_left"><b>Percentage of municipalities classified with different linguistic labels</b></td><td class="align_center">7.61%</td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Comparisons obtained approximating input and output FN with trapezoidal FN.</div>

Advances in Fuzzy Systems

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Table 5

Table 5: A Method Based on Extended Fuzzy Transforms to Approximate Fuzzy Numbers in Mamdani Fuzzy Rule-Based System 