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> <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>).
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 <translate>The 'Support set' represents the values of the predicate deemed '''possible''', while the 'core' represents those deemed more '''plausible'''</translate>.
-If <math>{A}</math> represented a set in the ordinary sense of the term or classical language logic previously described, its membership function could assume only the values <math>1</math> or <math>0</math>, <math>\mu_{\displaystyle {{A}}}(x)= 1 \; \lor \;\mu_{\displaystyle {{A}}}(x)= 0</math> depending on whether the element <math>x</math> whether or not it belongs to the whole, as considered. Figure 2 shows a graphic representation of the crisp (rigidly defined) or fuzzy concept of membership, which clearly recalls Smuts's considerations.<ref name=":0">•SMUTS J.C. 1926, [[wikipedia:Holism_and_Evolution|Holism and Evolution]], London: Macmillan.</ref>
+<translate>If</translate> <math>{A}</math> <translate>represented a set in the ordinary sense of the term or classical language logic previously described, its membership function could assume only the values</translate> <math>1</math> <translate>or</translate> <math>0</math>, <math>\mu_{\displaystyle {{A}}}(x)= 1 \; \lor \;\mu_{\displaystyle {{A}}}(x)= 0</math> <translate>depending on whether the element</translate> <math>x</math> <translate>belongs to the whole or not, as considered</translate>. <translate>Figure 2 shows a graphic representation of the crisp (rigidly defined) or fuzzy concept of membership, which clearly recalls Smuts's considerations</translate>.<ref name=":0">•SMUTS J.C. 1926, [[wikipedia:Holism_and_Evolution|<translate>Holism and Evolution</translate>]], London: Macmillan.</ref>
-Let us go back to the specific case of our Mary Poppins, in which we see a discrepancy between the assertions of the dentist and the neurologist and we look for a comparison between classical logic and fuzzy logic:
+<translate>Let us go back to the specific case of our Mary Poppins, in which we see a discrepancy between the assertions of the dentist and the neurologist and we look for a comparison between classical logic and fuzzy logic</translate>:
-[[File:Fuzzy1.jpg|thumb|400x400px|'''Figure 2:''' Representation of the comparison between a classical and fuzzy ensemble.]]
+[[File:Fuzzy1.jpg|thumb|400x400px|'''<translate>Figure 2</translate>:''' <translate>Representation of the comparison between a classical and fuzzy ensemble</translate>.]]
-'''Figure 2:''' Let us imagine the Science Universe <math>U</math> in which there are two parallel worlds or contexts, <math>{A}</math> and <math>\tilde{A}</math>.
+'''<translate>Figure</translate> 2:'''<translate> Let us imagine the Science Universe</translate> <math>U</math> <translate>in which there are two parallel worlds or contexts</translate>, <math>{A}</math> <translate>and</translate> <math>\tilde{A}</math>.
-<math>{A}=</math>  In the scientific context, the so-called ‘crisp’, and we have converted into ''the logic'' of ''Classic Language'', in which the physician has an absolute scientific background information <math>KB</math>  with a clear dividing line that we have named <math>KB_c</math>.
+<math>{A}=</math>  <translate>In the scientific context, the so-called ‘crisp’, and we have converted into ''the logic'' of ''Classic Language'', in which the physician has an absolute scientific background information</translate> <math>KB</math>  <translate>with a clear dividing line that we have named</translate> <math>KB_c</math>.
-<math>\tilde{A}=</math> In another scientific context called  ‘fuzzy logic’, and in which there is a union between the subset <math>{A}</math> in <math>\tilde{A}</math> that we can go so far as to say: union between <math>KB_c</math>.
+<math>\tilde{A}=</math> <translate>In another scientific context called  ‘fuzzy logic’, and in which there is a union between the subset</translate> <math>{A}</math> <translate>in</translate> <math>\tilde{A}</math> <translate>that we can go so far as to say: union between</translate> <math>KB_c</math>.
-We will remarkably notice the following deductions:
+<translate>We will remarkably notice the following deductions</translate>:
 *'''Classical Logic''' in the Dental Context <math>{A}</math> in which only a logical process that gives as results <math>\mu_{\displaystyle {{A}}}(x)= 1 </math> it will be possible, or <math>\mu_{\displaystyle {{A}}}(x)= 0 </math> being the range of data <math>D=\{\delta_1,\dots,\delta_4\}</math>reduced to basic knowledge <math>KB</math> in the set <math>{A}</math>. This means that outside the dental world there is a void and that term of set theory, it is written precisely <math>\mu_{\displaystyle {{A}}}(x)= 0 </math> and which is synonymous with a high range of: