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Difference between revisions of "Fuzzy logic language"
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Gianfranco (talk | contribs) (Marked this version for translation) |
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==<translate><!--T:108--> Fuzzy set</translate> <math>\tilde{A}</math> <translate><!--T:109--> and membership function</translate> <math>\mu_{\displaystyle {\tilde {A}}}(x)</math>== | ==<translate><!--T:108--> Fuzzy set</translate> <math>\tilde{A}</math> <translate><!--T:109--> and membership function</translate> <math>\mu_{\displaystyle {\tilde {A}}}(x)</math>== | ||
We choose - as a formalism - to represent a fuzzy set with the 'tilde':<math>\tilde{A}</math>. A fuzzy set is a set where the elements have a 'degree' of belonging (consistent with fuzzy logic): some can be included in the set at 100%, others in lower percentages. | <translate>We choose - as a formalism - to represent a fuzzy set with the 'tilde'</translate>:<math>\tilde{A}</math>. <translate>A fuzzy set is a set where the elements have a 'degree' of belonging (consistent with fuzzy logic): some can be included in the set at 100%, others in lower percentages</translate>. | ||
To mathematically represent this degree of belonging is the function <math>\mu_{\displaystyle {\tilde {A}}}(x)</math> called | <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) = 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). | ||