Fuzzy Logic is used in artificial intelligence. In fuzzy logic, a proposition ha
ID: 3009594 • Letter: F
Question
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 0.75 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: Fred and John are happy." Neither Fred nor John is happy."Explanation / Answer
The truth value of "Fred is happy" is 0.75
Truth value of "John is happy" is 0.35
a) Fred and John are happy
The above statement is equivalent to:
'Fred is happy' and 'John is happy' i.e. A conjuction of the two statements.
Now, as per the Fuzzy Logic, the truth value of a Conjuction is the minimum of the two propositions. So, the truth value of "Fred and John are happy" will be min{0.35,0.75} = 0.35
b) Neither Fred nor John is happy
The above statement is equivalent to, Fred is not happy and John is not happy. i.e.
(~Fred is happy) and (~John is happy)
[where, ~ means negation ]
So, as per fuzzy logic , the truth value will be
min{ (1-0.75) , (1-0.35) } = min{0.25 , 0.65} = 0.25
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