What is the difference between Fuzzy logic and boolean logic?

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Was reading regarding Fuzzy logic and I realized that it has relations with boolean logic. However, I was very confused at the point that defines the relation of the logic of Fuzzy with the boolean, besides, other doubts also appeared to me.

Doubts

  1. What is the difference between Fuzzy logic and boolean logic and what defines the relationship between the two?
  2. We can use the logic of Fuzzy in programming or it is restricted only for other fields of mathematics?
logic

  • I have answered this (or pincelei) in some answer. Basically it is the traditional Boolean logic with the change of the deleted third axiom

  • @Jeffersonquesado "change the axiom of the excluded third" ? I was more confused now kkkk

  • Here I speak of the 3 axioms: https://answall.com/a/274114/64969; axiom of identity, axiom of non-contradiction and axiom of the excluded middle. But I don’t mean Fuzzy/fuzzy in two of the 3 answers I mention axiom...

  • 1

    Possible duplicate of What is fuzzy logic?; Let me know if it’s not duplicate

  • How about this answer? I explain minimally what is the change in the axiom of the excluded third

  • @Jeffersonquesado the relationship is the scale of values between 1 and 0 that in the fuzzy logic would be 0.001 and 0.11 or 1, would be this? Or would it be a value that represents 1 and 0, as a third value?

  • Fuzzy logic is not quantum, it does not represent both 0 and 1. The axiom of "excluded third" Boolean logic says the following: there are two values, and only two, any third value is identical to one of the two preceding values, or does not belong to Boolean logic. Therefore, the "third value" was "excluded" from Boolean logic. Hence, axiom of the excluded third. All the rest of Boolean logic is only valid because of this axiom.

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To Fuzzy logic is the form of multivariate logic, in which the truth values of the variables can be any real number amid 0 (false) and 1 (true). Already the boolean logic variables and functions can only have values 0 and 1, in this logic we also have the logical gates: and: you have to have all the values for the sentence to be true. or: it is necessary only one of the values for the sentence to be true. xor: returns true only when the input values are different, otherwise false.

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Just to complement @maria-Gabi’s response to logica Fuzzy can support values that are not necessarily true or false.

For example for some condition or method.

  • True = 1
  • Partially True = 0.75
  • Indifferent = 0.50
  • Partially False = 0.25
  • False = 0

You can determine how many values you want for each alternative as long as it is a value within the range of 0 to 1;

In Boolean logic the values must be explicitly true or false for some condition.

I’ll go to the movies if have money and (and) if the cinema is open. that is if the two variables are true the condition to go to the cinema will be performed.

you can exchange logical operators as for example in place of and (e) put a or (or);

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