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{{Bookind2}}

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[[File:Fuzzy1.jpg|left|250px]]

[[File:Fuzzy1.jpg|left|250px]]

In this chapter, we will discuss '''fuzzy logic'''. It is called ''fuzzy'' because it is characterized by a gradualness: an object can be attributed a quality that can have ''various degrees of truth''.

<translate>In this chapter, we will discuss '''fuzzy logic'''. It is called ''fuzzy'' because it is characterized by a gradualness: an object can be attributed a quality that can have ''various degrees of truth''.</translate>

In the first part of this chapter, the meaning of graded truth will be conceptually discussed, while in the second part, we will delve into the mathematical formalism by introducing the membership function <math>\mu_{\displaystyle {\tilde {A}}}(x)</math>: the element that allows us to mathematically synthesize the nuances of this logic of language. It has been possible to show that with ‘fuzzy’ reasoning, unlike the previous logics of language, the diagnoses show less uncertainty. Despite this, however, the need is still felt to further refine the language method and enrich it with further ‘logics’.{{ArtBy|

<translate>In the first part of this chapter, the meaning of graded truth will be conceptually discussed, while in the second part, we will delve into the mathematical formalism by introducing the membership function <math>\mu_{\displaystyle {\tilde {A}}}(x)</math>: the element that allows us to mathematically synthesize the nuances of this logic of language</translate>. <translate>It has been possible to show that with ‘fuzzy’ reasoning, unlike the previous logics of language, the diagnoses show less uncertainty. Despite this, however, the need is still felt to further refine the language method and enrich it with further ‘logics’</translate>.{{ArtBy|

| autore = Gianni Frisardi

| autore = Gianni Frisardi

| autore2 = Riccardo Azzali

| autore2 = Riccardo Azzali

}}

}}

==Introduction==

==<translate>Introduction</translate>==

We have come this far because, as colleagues, are very often faced with responsibilities and decisions that are very difficult to take and issues such as conscience, intelligence and humility come into play. in such a situation, however, we are faced with two equally difficult obstacles to manage that of one <math>KB</math> ( Knowledge Basis), as we discussed in the chapter ‘Logic of probabilistic language’, limited in the time that we codify in <math>KB_t</math> and one <math>KB</math> limited in the specific context (<math>KB_c</math>). These two parameters of epistemology characterize the scientific age in which we live. Also, both <math>KB_t</math> that the <math>KB_c</math> are dependent variables of our phylogeny, and, in particular of our conceptual plasticity and attitude to change.<ref>{{Cite book  

<translate>We have come this far because, as colleagues, are very often faced with responsibilities and decisions that are very difficult to take and issues such as conscience, intelligence and humility come into play</translate>. <translate>In such a situation, however, we are faced with two equally difficult obstacles to manage that of one <math>KB</math> (Knowledge Basis), as we discussed in the chapter ‘[[Logic of probabilistic language]]’, limited in the time that we codify in <math>KB_t</math> and one <math>KB</math> limited in the specific context (<math>KB_c</math>)</translate>. <translate>These two parameters of epistemology characterize the scientific age in which we live. Also, both <math>KB_t</math> that the <math>KB_c</math> are dependent variables of our phylogeny, and, in particular of our conceptual plasticity and attitude to change</translate>.<ref>{{Cite book  

  | autore = Takeuchi S

  | autore = Takeuchi S

  | autore2 = Okuda S

  | autore2 = Okuda S