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Fuzzy truth

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.

Mathematically, fuzzy logic allows us to attribute to each proposition a degree of truth between $0$ and $1$. 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 $1$, an eighteen-year-old equal to $0,8$, a sixty-year-old equal to $0,4$, and so on

In the context of classical logic, on the other hand, the statements:

• • a ten-year-old is young
  • a thirty-year-old is young

are both true. 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.

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.