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Distinguish between classical logic and fuzzy logic. Your answer should include "membership function", "crisp", "fuzzy" and "set".
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Define with examples, fuzzification, rule evaluation, de-fuzzification
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Write down the three Zadeh operators. Illustrate each with a diagram.
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Here is the truth table for classical logic
A B A and B A or B not A
-- -- ----------- -------- -------
0 0 0 0 1
0 1 0 1 1
1 0 0 1 0
1 1 1 1 0
Reproduce this table using the Zadeh operators for (A B) = (0.3 0.7).
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Define the extension principle and its implications for the connection of classical logic to fuzzy logic. Using the Zadeh operators, demonstrate
the extension principle for row 2 or the above table. Show all calculations
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Draw the following membership function for
- (a b crisp)= ( -50,50,0.1) and
- (a b crisp)= ( -50,50,1)
(defun crisp (x a b crisp)
"Return a point in a sigmoid function centered at (a - b)/2"
(labels ((as100 (x min max)
(+ -50 (* 100 (/ (- x min) (- max min))))))
(/ 1 (+ 1 (exp (* -1 (as100 x a b) crisp))))))
Mark on the x-axis the key points of the function.
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Draw the following membership function for (x a b c) = (x 10 20 30).
(defun fuzzy-fun1 (x a b c)
(max 0 (min (/ (- x a) (- b a))
(/ (- c x) (- c b)))))
Mark on the x-axis the key points of the function.
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Draw the following membership function for (x a b c d) = (x 10 20 30 60).
(defun fuzzy-fun2 (x a b c d)
(max 0 (min (/ (- x a) (- b a))
1
(/ (- d x) (- d c)))))
Mark on the x-axis the key points of the function.
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On one plot, draw the following membership functions for
(dist 'close) (dist 'medium) (dist 'far)
(defun dist (d what)
(case what
(range '(close medium far))
(close (fuzzy-triangle d -30 0 30))
(medium (fuzzy-trapezoid d 10 30 50 70))
(far (fuzzy-grade d 0.3 50 100))
(t (warn "~a not known to dist" what))))
Mark on the x-axis the key points of these functions.