Difference between revisions of "Fuzzy logic language"

Fuzzy logic language (view source)

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→‎Fuzzy set \tilde{A} and membership function \mu_{\displaystyle {\tilde {A}}}(x)

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 <translate>To mathematically represent this degree of belonging is the function</translate> <math>\mu_{\displaystyle {\tilde {A}}}(x)</math> <translate>called</translate> ''''<translate>Membership Function</translate>''''. <translate>The functio</translate>n <math>\mu_{\displaystyle {\tilde {A}}}(x)</math> <translate>is a continuous function defined in the interval</translate> <math>[0;1]</math><translate>where it is</translate>:
-*<math>\mu_ {\tilde {A}}(x) = 1\rightarrow </math>   if <math>x</math> is totally contained in <math>A</math> (these points are called 'nucleus', they indicate <u>plausible</u> predicate values).
-*<math>\mu_ {\tilde {A}}(x) = 0\rightarrow </math>  if <math>x</math> is not contained in <math>A</math>
-*<math>0<\mu_ {\tilde {A}}(x) < 1 \;\rightarrow </math> if <math>x</math> is partially contained in <math>A</math> (these points are called 'support', they indicate the <u>possible</u> predicate values).
-The graphical representation of the function <math>\mu_{\displaystyle {\tilde {A}}}(x)</math> it can be varied; from those with linear lines (triangular, trapezoidal) to those in the shape of bells or 'S' (sigmoidal) as depicted in Figure 1, which contains the whole graphic concept of the function of belonging.<ref>{{Cite book
+*<math>\mu_ {\tilde {A}}(x) = 1\rightarrow </math> <translate>if</translate> <math>x</math> <translate>is totally contained in</translate> <math>A</math> (<translate>these points are called 'nucleus', they indicate <u>plausible</u> predicate values</translate>).
+*<math>\mu_ {\tilde {A}}(x) = 0\rightarrow </math> <translate>if</translate> <math>x</math> <translate>is not contained in</translate> <math>A</math>
+*<math>0<\mu_ {\tilde {A}}(x) < 1 \;\rightarrow </math> <translate>if</translate> <math>x</math> <translate>is partially contained in</translate> <math>A</math> (<translate>these points are called 'support', they indicate the <u>possible</u> predicate values</translate>).
+<translate>The graphical representation of the function</translate> <math>\mu_{\displaystyle {\tilde {A}}}(x)</math> <translate>can be varied; from those with linear lines (triangular, trapezoidal) to those in the shape of bells or 'S' (sigmoidal) as depicted in Figure 1, which contains the whole graphic concept of the function of belonging</translate>.<ref>{{Cite book
   | autore = Zhang W
   | autore2 = Yang J