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Insieme sfocato Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tilde{A}} e funzione di appartenenza Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_{\displaystyle {\tilde {A}}}(x)}

Scegliamo - come formalismo - di rappresentare un insieme sfocato con la 'tilde':Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tilde{A}} . Un insieme fuzzy è un insieme in cui gli elementi hanno un 'grado' di appartenenza (coerente con la logica fuzzy): alcuni possono essere inclusi nell'insieme al 100%, altri in percentuali inferiori.

A rappresentare matematicamente questo grado di appartenenza è la funzione Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_{\displaystyle {\tilde {A}}}(x)} chiamata 'Funzione di appartenenza'. La funzione Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_{\displaystyle {\tilde {A}}}(x)} è una funzione continua definita nell'intervallo Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [0;1]} dove:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_ {\tilde {A}}(x) = 1\rightarrow } se Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} è totalmente contenuta in Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} (questi punti sono chiamati 'nucleus', essi indicano i valori plausibili del predicato ).
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_ {\tilde {A}}(x) = 0\rightarrow } se Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} non è contenuto in Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0<\mu_ {\tilde {A}}(x) < 1 \;\rightarrow } se Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} è parzialmente contenuto in Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} (questi punti sono chiamati 'Support' ed indicano i valori possibili del predicato possible predicate values).

La rappresentazione grafica della funzione Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_{\displaystyle {\tilde {A}}}(x)} può essere variato; da quelli con linee lineari (triangolari, trapezoidali) a quelli a forma di campana o 'S' (sigmoidale) come rappresentato in Figura 1, che racchiude l'intero concetto grafico della funzione di appartenenza.^[1]^[2]

Figure 1: Types of graphs for the membership function.

Il support set di un insieme fuzzy è definito come la zona in cui il grado di appartenenza risulta Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0<\mu_ {\tilde {A}}(x) < 1} ; il nucleo o core è invece definito come l'area in cui il grado di appartenenza assume valore Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_ {\tilde {A}}(x) = 1}

Il 'Support set' rappresenta i valori del predicato ritenuti possibili, mentre il 'core' rappresenta quelli ritenuti più plausibili.

Se Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {A}} rappresentasse un insieme nel senso ordinario del termine o nella logica del linguaggio classico precedentemente descritto, la sua funzione di appartenenza potrebbe assumere solo i valori Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1} o Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_{\displaystyle {{A}}}(x)= 1 \; \lor \;\mu_{\displaystyle {{A}}}(x)= 0} a seconda che l'elemento 0 appartenga o meno al tutto, come considerato. La figura 2 mostra una rappresentazione grafica del concetto nitido (rigidamente definito) o sfocato di appartenenza, che richiama chiaramente le considerazioni di Smuts.^[3]

Torniamo al caso specifico della nostra Mary Poppins, in cui vediamo una discrepanza tra le affermazioni del dentista e del neurologo e cerchiamo un confronto tra logica classica e logica fuzzy:

Figure 2: Representation of the comparison between a classical and fuzzy ensemble.

Figura 2: Immaginiamo l'Universo della Scienza Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle U} in cui ci sono due mondi o contesti paralleli Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {A}} e Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tilde{A}}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {A}=} Nel contesto scientifico, il cosiddetto 'ben definito', della logica del linguaggio classico, in cui il medico ha un background scientifico assoluto Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB} con una chiara linea di demarcazione che abbiamo chiamato Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB_c}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tilde{A}=} In un altro contesto scientifico chiamato 'logica fuzzy', in cui esiste un'unione tra il sottoinsieme Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {A}} in Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tilde{A}} tanto da poter dire: unione tra i contesti Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB_c}

Noteremo notevolmente le seguenti deduzionii:

Logica classica nel contesto odontoiatrico Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {A}} in cui sarà possibile solo un processo logico che dia come risultato Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_{\displaystyle {{A}}}(x)= 1 } , ovvero Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_{\displaystyle {{A}}}(x)= 0 } essendo l'intervallo di dati Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle D=\{\delta_1,\dots,\delta_4\}} ridotto alle conoscenze di base Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB} nell'insieme Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {A}} Ciò significa che al di fuori del mondo odontoiatrico c'è un vuoto e che il termine di teoria degli insiemi è scritto esattamente Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_{\displaystyle {{A}}}(x)= 0 } e che è sinonimo di un alto range di:

«Errore nella diagnosi differenziale»

Logica fuzzy in un contesto odontoiatrico Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tilde{A}} in cui sono rappresentati oltre le conoscenze di base Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB} del contesto odontoiatrico anche quelli parzialmente acquisiti dal mondo neurofisiologico Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0<\mu_ {\tilde {A}}(x) < 1} avranno la prerogativa di restituire un risultato Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_\tilde{A}(x)= 1 } e un risultato 0 per via delle conoscenze di base 0 che a questo punto è rappresentato dall'unione di Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0<\mu_ {\tilde {A}}(x) < 1} contesti odontoiatrici e neurologici. Il risultato di questa implementazione scientifico-clinica dell'odontoiatria consentirebbe una
«Riduzione dell'errore diagnostico differenziale»

↑ Zhang W, Yang J, Fang Y, Chen H, Mao Y, Kumar M, «Analytical fuzzy approach to biological data analysis», in Saudi J Biol Sci, 2017».
PMID:28386181 - PMCID:PMC5372457
DOI:10.1016/j.sjbs.2017.01.027
↑ Lazar P, Jayapathy R, Torrents-Barrena J, Mol B, Mohanalin, Puig D, «Fuzzy-entropy threshold based on a complex wavelet denoising technique to diagnose Alzheimer disease», in Healthc Technol Lett, The Institution of Engineering and Technology, 2016».
PMID:30800318 - PMCID:PMC6371778
DOI:10.1049/htl.2016.0022
↑ •SMUTS J.C. 1926, Holism and Evolution, London: Macmillan.

[1] Zhang W, Yang J, Fang Y, Chen H, Mao Y, Kumar M, «Analytical fuzzy approach to biological data analysis», in Saudi J Biol Sci, 2017».
PMID:28386181 - PMCID:PMC5372457
DOI:10.1016/j.sjbs.2017.01.027

[2] Lazar P, Jayapathy R, Torrents-Barrena J, Mol B, Mohanalin, Puig D, «Fuzzy-entropy threshold based on a complex wavelet denoising technique to diagnose Alzheimer disease», in Healthc Technol Lett, The Institution of Engineering and Technology, 2016».
PMID:30800318 - PMCID:PMC6371778
DOI:10.1049/htl.2016.0022

[:0-3] •SMUTS J.C. 1926, Holism and Evolution, London: Macmillan.

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