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Difference between revisions of "Fuzzy logic language"
→Fuzzy set \tilde{A} and membership function \mu_{\displaystyle {\tilde {A}}}(x)
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[[File:Fuzzy_crisp.svg|alt=|left|thumb|400px|'''Figure 1:''' Types of graphs for the membership function.]] | [[File:Fuzzy_crisp.svg|alt=|left|thumb|400px|'''<translate>Figure</translate> 1:''' <translate>Types of graphs for the membership function</translate>.]] | ||
The '''support set''' of a fuzzy set is defined as the zone in which the degree of membership results <math>0<\mu_ {\tilde {A}}(x) < 1</math>; on the other hand, the '''core''' is defined as the area in which the degree of belonging assumes value <math>\mu_ {\tilde {A}}(x) = 1</math> | <translate>The '''support set''' of a fuzzy set is defined as the zone in which the degree of membership results</translate> <math>0<\mu_ {\tilde {A}}(x) < 1</math>; <translate>on the other hand, the '''core''' is defined as the area in which the degree of belonging assumes value</translate> <math>\mu_ {\tilde {A}}(x) = 1</math> | ||
The 'Support set' represents the values of the predicate deemed '''possible''', while the 'core' represents those deemed more '''plausible'''. | <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> | 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> | ||