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Chapter 1: Q47E (page 16)

The truth value of the disjunction of two propositions in fuzzy logic is the maximum of the truth values of the two propositions. What are the truth values of the statements “Fred is happy, or John is happy” and “Fred is not happy, or John is not happy?”

Short Answer

Expert verified

Truth value of “Fred is happy or John are happy “is 0.8 and truth value of “Fred is not happy, or John is not happy?” is 0.6.

Step by step solution

01

Definition of Fuzzy logic

Fuzzy logic is a mathematical logic which solves problems with an open, imprecise data spectrum.

02

Calculate truth values

The truth value of Fred is happy, is0.8.

Also, the truth value of John is happy, is0.4.

Disjunction of two propositions in fuzzy logic is the maximum of the truth values of the two propositions.

Hence truth value of “Fred is happy, or John is happy” is max(0.8,0.4) = 0.8.

The truth value of “Fred is not happy, or John is not happy” is max(0.2,0.6) = 0.6.

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