Difference between revisions of "Fuzzy logic language/it"

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 <math>P(D| Deg.TMJ   \cap TMDs)=0.95</math>
-<span lang="en" dir="ltr" class="mw-content-ltr">and which is, that our Mary Poppins is 95% affected by TMDs since she has a degeneration of the temporomandibular joint supported by the positivity of the data <math>D=\{\delta_1,\dots\delta_4\}</math> in a population sample <math>n</math></span>. <span lang="en" dir="ltr" class="mw-content-ltr">However, we also found that in the process of constructing probabilistic logic (Analysandum <math>  = \{P(D),a\}</math>) which allowed us to formulate the aforementioned differential diagnostic conclusions and choose the most plausible one, there is a crucial element to the whole Analysand'''<math>= \{\pi,a,KB\}</math>''' represented by the term <math>KB</math> which indicates, specifically, a 'Knowledge Base' of the context on which the logic of probabilistic language is built</span>.
+e cioè che la nostra Mary Poppins è affetta al 95% da TMD poiché ha una degenerazione dell'articolazione temporomandibolare sostenuta dalla positività dei dati <math>D=\{\delta_1,\dots\delta_4\}</math> in un campione di popolazione <math>n</math>. <span lang="en" dir="ltr" class="mw-content-ltr">However, we also found that in the process of constructing probabilistic logic (Analysandum <math>  = \{P(D),a\}</math>) which allowed us to formulate the aforementioned differential diagnostic conclusions and choose the most plausible one, there is a crucial element to the whole Analysand'''<math>= \{\pi,a,KB\}</math>''' represented by the term <math>KB</math> which indicates, specifically, a 'Knowledge Base' of the context on which the logic of probabilistic language is built</span>.
 <span lang="en" dir="ltr" class="mw-content-ltr">We therefore concluded that perhaps the dentist colleague should have become aware of his own 'Subjective Uncertainty' (affected by TMDs or <sub>n</sub>OP?) and 'Objective Uncertainty' (probably more affected by TMDs or <sub>n</sub>OP?)</span>.
-*<blockquote><big><span lang="en" dir="ltr" class="mw-content-ltr">Why have we come to these critical conclusions?</span></big></blockquote>
+*<blockquote><big>Perché siamo arrivati a queste conclusioni critiche?</big></blockquote>
-<span lang="en" dir="ltr" class="mw-content-ltr">For a widely shared form of the representation of reality, supported by the testimony of authoritative figures who confirm its criticality</span>.  <span lang="en" dir="ltr" class="mw-content-ltr">This has given rise to a vision of reality which, at first glance, would seem unsuitable for medical language; in fact, expressions such as ‘about 2’ or ‘moderately’ can arouse legitimate perplexity and seem an anachronistic return to pre-scientific concepts</span>. <span lang="en" dir="ltr" class="mw-content-ltr">On the contrary, however, the use of fuzzy numbers or assertions allows scientific data to be treated in contexts in which one cannot speak of ‘'''probability'''’ but only of ‘'''possibility’</span>.'''<ref>{{Cite book
+Per una forma ampiamente condivisa di rappresentazione della realtà, sostenuta dalla testimonianza di figure autorevoli che ne confermano la criticità.  Questo ha dato origine a una visione della realtà che, a prima vista, sembrerebbe inadatta al linguaggio medico; infatti, espressioni come "circa 2" o "moderatamente" possono suscitare legittime perplessità e sembrare un anacronistico ritorno a concetti pre-scientifici. Al contrario, però, l'uso dei numeri fuzzy o delle asserzioni permette di trattare i dati scientifici in contesti in cui non si può parlare di ''''probabilità'''' ma solo di ''''possibilità'.'''<ref>{{Cite book
   | autore = Dubois D
   | autore2 = Prade H
@@ Line 80: / Line 80: @@
   }}</ref>
-{{q2|<span lang="en" dir="ltr" class="mw-content-ltr">Probability or Possibility?</span>|}}
+{{q2|Probabilità o possibilità?|}}
-==<span lang="en" dir="ltr" class="mw-content-ltr">Fuzzy truth</span>==
+==Verità fuzzy==
-<span lang="en" dir="ltr" class="mw-content-ltr">In the ambitious attempt to mathematically translate human rationality, it was thought in the mid-twentieth century to expand the concept of classical logic by formulating fuzzy logic. Fuzzy logic concerns the properties that we could call ‘graduality’, i.e., which can be attributed to an object with different degrees. Examples are the properties ‘being sick’, ‘having pain’, ‘being tall’, ‘being young’, and so on.</span>
+Nell'ambizioso tentativo di tradurre in matematica la razionalità umana, si è pensato a metà del XX secolo di espandere il concetto di logica classica formulando la logica fuzzy. La logica fuzzy riguarda le proprietà che potremmo chiamare 'gradualità', cioè che possono essere attribuite a un oggetto con gradi diversi. Esempi sono le proprietà 'essere malato', 'avere dolore', 'essere alto', 'essere giovane', e così via.
+Tradotto con www.DeepL.com/Translator (versione gratuita)
 <span lang="en" dir="ltr" class="mw-content-ltr">Mathematically, fuzzy logic allows us to attribute to each proposition a degree of truth between <math>0</math> and <math>1</math>. The most classic example to explain this concept is that of age: we can say that a new-born has a ‘degree of youth’ equal to <math>1</math>, an eighteen-year-old equal to <math>0,8</math>, a sixty-year-old equal to <math>0,4</math>, and so on</span>
-<span lang="en" dir="ltr" class="mw-content-ltr">In the context of classical logic, on the other hand, the statements</span>:
+Nel contesto della logica classica, invece, le affermazioni:
-**<span lang="en" dir="ltr" class="mw-content-ltr">a ten-year-old is young</span>
+**un bambino di dieci anni è giovane
-**<span lang="en" dir="ltr" class="mw-content-ltr">a thirty-year-old is young</span>
+**un trentenne è giovane
-<span lang="en" dir="ltr" class="mw-content-ltr">are both true</span>. <span lang="en" dir="ltr" class="mw-content-ltr">However, in the case of classical logic (which allows only the two true or false data), this would mean that the infant and the thirty-year-old are equally young. Which is obviously wrong</span>.
+sono entrambe vere. Tuttavia, nel caso della logica classica (che ammette solo i due dati vero o falso), questo significherebbe che il bambino e il trentenne sono ugualmente giovani. Il che è ovviamente sbagliato.
-<span lang="en" dir="ltr" class="mw-content-ltr">The importance and the charm of fuzzy logic arise from the fact that it is able to translate the uncertainty inherent in some data of human language into mathematical formalism, coding ‘elastic’ concepts (such as almost high, fairly good, etc.), in order to make them understandable and manageable by computers</span>.
+L'importanza e il fascino della logica fuzzy derivano dal fatto che è in grado di tradurre l'incertezza insita in alcuni dati del linguaggio umano in un formalismo matematico, codificando concetti 'elastici' (come quasi alto, abbastanza buono, ecc.), al fine di renderli comprensibili e gestibili dai computer.
-==<span lang="en" dir="ltr" class="mw-content-ltr">Set theory</span>==
+==Teoria degli insiemi==
-<span lang="en" dir="ltr" class="mw-content-ltr">As mentioned in the previous chapter, the basic concept of fuzzy logic is that of multivalence, i.e., in terms of set theory, of the possibility that an object can belong to a set even partially and, therefore, also to several sets with different degrees</span>. <span lang="en" dir="ltr" class="mw-content-ltr">Let us recall from the beginning the basic elements of the theory of ordinary sets. As will be seen, in them appear the formal expressions of the principles of Aristotelian logic, recalled in the previous chapter</span>.
+Come accennato nel capitolo precedente, il concetto base della logica fuzzy è quello della multivalenza, cioè, in termini di teoria degli insiemi, della possibilità che un oggetto possa appartenere a un insieme anche solo parzialmente e, quindi, anche a più insiemi con gradi diversi. Ricordiamo fin dall'inizio gli elementi di base della teoria degli insiemi ordinari. Come si vedrà, in essi appaiono le espressioni formali dei principi della logica aristotelica, ricordati nel capitolo precedente.
-===<span lang="en" dir="ltr" class="mw-content-ltr">Quantifiers</span>===
+===Quantificatori===
-*<span lang="en" dir="ltr" class="mw-content-ltr">Membership</span>: <span lang="en" dir="ltr" class="mw-content-ltr">represented by the symbol <math>\in </math> (belongs), - for example the number 13 belongs to the set of odd numbers <math>\in </math> <math>13\in  Odd </math></span>
+*Appartenenza: rappresentato dal simbolo <math>\in </math> (appartiene), - per esempio il numero 13 appartiene all'insieme dei numeri dispari <math>\in </math> <math>13\in Odd </math>
-*<span lang="en" dir="ltr" class="mw-content-ltr">Non-membership</span>: <span lang="en" dir="ltr" class="mw-content-ltr">represented by the symbol <math>\notin </math> (It does not belong)</span>
+*Non appartenenza: rappresentato dal simbolo <math>\notin </math> (Non appartiene)
-*<span lang="en" dir="ltr" class="mw-content-ltr">Inclusion</span>: <span lang="en" dir="ltr" class="mw-content-ltr">Represented by the symbol <math>\subset</math> (is content), - for example the whole <math>A</math> it is contained within the larger set <math>U</math>, <math>A \subset U</math> (in this case it is said that <math>A</math> is a subset of <math>U</math>)</span>
+*Inclusione: <span lang="en" dir="ltr" class="mw-content-ltr">Represented by the symbol <math>\subset</math> (is content), - for example the whole <math>A</math> it is contained within the larger set <math>U</math>, <math>A \subset U</math> (in this case it is said that <math>A</math> is a subset of <math>U</math>)</span>
-*<span lang="en" dir="ltr" class="mw-content-ltr">Universal quantifier</span>, <span lang="en" dir="ltr" class="mw-content-ltr">which is indicated by the symbol <math>\forall</math> (for each)</span>
+*Quantificatore universale, <span lang="en" dir="ltr" class="mw-content-ltr">which is indicated by the symbol <math>\forall</math> (for each)</span>
-*<span lang="en" dir="ltr" class="mw-content-ltr">Demonstration</span>, <span lang="en" dir="ltr" class="mw-content-ltr">which is indicated by the symbol <math>\mid</math> (such that)</span>
+*Dimostrazione, <span lang="en" dir="ltr" class="mw-content-ltr">which is indicated by the symbol <math>\mid</math> (such that)</span>
 ===<span lang="en" dir="ltr" class="mw-content-ltr">Set operators</span>===
-<span lang="en" dir="ltr" class="mw-content-ltr">Given the whole universe</span> <math>U</math> <span lang="en" dir="ltr" class="mw-content-ltr">we indicate with</span> <math>x</math> <span lang="en" dir="ltr" class="mw-content-ltr">its generic element so that</span> <math>x \in U</math>; <span lang="en" dir="ltr" class="mw-content-ltr">then, we consider two subsets</span> <math>A</math> and <math>B</math> <span lang="en" dir="ltr" class="mw-content-ltr">internal to</span> <math>U</math> <span lang="en" dir="ltr" class="mw-content-ltr">so that</span> <math>A \subset U</math> <span lang="en" dir="ltr" class="mw-content-ltr">and</span> <math>B \subset U</math>
+<span lang="en" dir="ltr" class="mw-content-ltr">Given the whole universe</span> <math>U</math> <span lang="en" dir="ltr" class="mw-content-ltr">we indicate with</span> <math>x</math> <span lang="en" dir="ltr" class="mw-content-ltr">its generic element so that</span> <math>x \in U</math>; <span lang="en" dir="ltr" class="mw-content-ltr">then, we consider two subsets</span> <math>A</math> and <math>B</math> <span lang="en" dir="ltr" class="mw-content-ltr">internal to</span> <math>U</math> cosicché <math>A \subset U</math> e <math>B \subset U</math>
 {|
 |[[File:Venn0111.svg|left|80px]]
-|'''<span lang="en" dir="ltr" class="mw-content-ltr">Union</span>:''' <span lang="en" dir="ltr" class="mw-content-ltr">represented by the symbol</span> <math>\cup</math>, <span lang="en" dir="ltr" class="mw-content-ltr">indicates the union of the two sets</span> <math>A</math> <span lang="en" dir="ltr" class="mw-content-ltr">and</span> <math>B</math> <math>(A\cup B)</math>. <span lang="en" dir="ltr" class="mw-content-ltr">It is defined by all the elements that belong to</span> <math>A</math> <span lang="en" dir="ltr" class="mw-content-ltr">and</span> <math>B</math> <span lang="en" dir="ltr" class="mw-content-ltr">or both</span>:
+|'''Unione:''' <span lang="en" dir="ltr" class="mw-content-ltr">represented by the symbol</span> <math>\cup</math>, <span lang="en" dir="ltr" class="mw-content-ltr">indicates the union of the two sets</span> <math>A</math> e <math>B</math> <math>(A\cup B)</math>. <span lang="en" dir="ltr" class="mw-content-ltr">It is defined by all the elements that belong to</span> <math>A</math> e <math>B</math> <span lang="en" dir="ltr" class="mw-content-ltr">or both</span>:
 <math>(A\cup B)=\{\forall x\in U \mid x\in A \land x\in B\}</math>
 |-
 |[[File:Venn0001.svg|sinistra|80px]]
-|'''<span lang="en" dir="ltr" class="mw-content-ltr">Intersection</span>:''' <span lang="en" dir="ltr" class="mw-content-ltr">represented by the symbol</span> <math>\cap</math>, <span lang="en" dir="ltr" class="mw-content-ltr">indicates the elements belonging to both sets</span>:
+|'''Intersezione:''' <span lang="en" dir="ltr" class="mw-content-ltr">represented by the symbol</span> <math>\cap</math>, <span lang="en" dir="ltr" class="mw-content-ltr">indicates the elements belonging to both sets</span>:
 <math>(A\cap B)=\{\forall x\in U \mid x\in A \lor x\in B\}</math>
 |-
 |[[File:Venn0010.svg|left|80px]]
-|'''<span lang="en" dir="ltr" class="mw-content-ltr">Difference</span>:''' <span lang="en" dir="ltr" class="mw-content-ltr">represented by the symbol</span> <math>-</math>, <span lang="en" dir="ltr" class="mw-content-ltr">for example</span> <math>A-B</math> <span lang="en" dir="ltr" class="mw-content-ltr">shows all elements of</span> <math>A</math> <span lang="en" dir="ltr" class="mw-content-ltr">except those shared with</span> <math>B</math>
+|'''Differenza:''' <span lang="en" dir="ltr" class="mw-content-ltr">represented by the symbol</span> <math>-</math>, per esempio <math>A-B</math> <span lang="en" dir="ltr" class="mw-content-ltr">shows all elements of</span> <math>A</math> <span lang="en" dir="ltr" class="mw-content-ltr">except those shared with</span> <math>B</math>
 |-
 |[[File:Venn1000.svg|left|80px]]
-|'''<span lang="en" dir="ltr" class="mw-content-ltr">Complementary</span>:''' <span lang="en" dir="ltr" class="mw-content-ltr">represented by a bar above the name of the collection, it indicates by</span> <math>\bar{A}</math> <span lang="en" dir="ltr" class="mw-content-ltr">the complementary of</span> <math>A</math>, <span lang="en" dir="ltr" class="mw-content-ltr">that is</span>, <span lang="en" dir="ltr" class="mw-content-ltr">the set of elements that belong to the whole universe except those of</span> <math>A</math>, <span lang="en" dir="ltr" class="mw-content-ltr">in formulas</span>: <math>\bar{A}=U-A</math><br />
+|'''<span lang="en" dir="ltr" class="mw-content-ltr">Complementary</span>:''' <span lang="en" dir="ltr" class="mw-content-ltr">represented by a bar above the name of the collection, it indicates by</span> <math>\bar{A}</math> <span lang="en" dir="ltr" class="mw-content-ltr">the complementary of</span> <math>A</math>, cioè, <span lang="en" dir="ltr" class="mw-content-ltr">the set of elements that belong to the whole universe except those of</span> <math>A</math>, in formule: <math>\bar{A}=U-A</math><br />
 |}