Discrete Math Structures: (1 point) Fuzzy Logic is used in artificial intelligen

Question

Discrete Math Structures:

(1 point) Fuzzy Logic is used in artificial intelligence. In fuzzy logic, a proposition has a truth value that is a number between 0 and 1 inclusive. A proposition with a truth value of 0 is false and one with truth value of 1 is true. Truth values that are between 0 and 1 indicate varying degrees of truth. For instance, the truth value 0.8 can be assigned to the statement "Fred is happy." since Fred is happy most of the time, and the truth value 0.35 can be assigned to the statement "John is happy." since John is happy slightly less than half the time. The truth value of the negation of a proposition in fuzzy logic is 1 minus the truth value of the proposition. The truth value of a conjunction of two propositions in fuzzy logic is the minimum of the truth values of the two propositions What are the truth value of the statements: (a) Fred and John are happy." (b) Neither Fred nor John is happy."

Explanation / Answer

a) Fred and John are happy is a conjunction.

So truth value of Fred is happy is = 0.8 and

truth value of John is happy is = 0.35.

So truth value of Fred and John are happy is = minimum{0.8 , 0.35}

= 0.35

b) Neither Fred nor John is happy is the negation of Fred and John are happy. So the truth value is = 1- truth value of Fred and John are happy

= 1- 0.35 = 0.65

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