Artificial Intelligence - Fuzzy Sets

Let heavy = be a fuzzy set on X where x ∈ X is amount of rainfall received in a city measured in mm and high = be a fuzzy set on Y where y ∈ Y is the amount (in lakhs) spent for damage control in event of floods. Let hvery(a) = a2 for a ∈ [0,1].

86. Find the truth of proposition P1 = 'Heavy rains causes high damage' when rainfall is 300mm and damages worth 10 lakh.

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87. Find the truth value of proposition P2 = 'It is very true that high damage implies that the rainfall was high' when rainfall is 200mm and damages worth 1 crore.

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For Question 77 and 78

Consider a distillation process to separate components of a mixture. Let hot = be a fuzzy set on X where x  ∈ X i the temperature measured in 0C, and , where y ∈ Y is the percentage of separation.
Let p1 be the proposition ‘IF temperature is hot, THEN separation is good, ELSE separation is average’.
Note that: If P and Q else R is translated as (P ⇒ Q) ∧ (∼P ⇒ R)

88. Find the truth value of P1 given that the temperature is 75 0C and the 75% mixture is separated.

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Consider a distillation process to separate components of a mixture. Let hot = be a fuzzy set on X where x  ∈ X i the temperature measured in 0C, and , where y ∈ Y is the percentage of separation.
Let p1 be the proposition ‘IF temperature is hot, THEN separation is good, ELSE separation is average’.
Note that: If P and Q else R is translated as (P ⇒ Q) ∧ (∼P ⇒ R)

89. Find the truth value of P1 given that the temperature is 80 0C and the 75% mixture is separated.

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Let A and B are fuzzy subset of R. Determine if the following are true or false.

90. αA ∪ α(A) = R

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