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Some properties of operations on the fuzzy sets Let A, B, C be fuzzy sets in X, then 1. AnA = A and AUA = A 2. AnB = Bn A and AUB = BUA 3. Anø = ¢ and AUØ = A 4. AnX = A and AUX = X 5. AU (BUC) = (A U B) U C 6. An (Bn C) = (An B) n C 7. AU (Bn C) = (A U B) N (A U C) 8. An (BUC) = (An B) U (An C) 9. (A°) = A 10. (An B)° = A° U B° 11. (AUB)C = A°n B° It is not required that it be AUA° = X_and An A° = ¢ 12.

Some properties of operations on the fuzzy sets Let A, B, C be fuzzy sets in X, then 1. AnA = A and AUA = A 2. AnB = Bn A and AUB = BUA 3. Anø = ¢ and AUØ = A 4. AnX = A and AUX = X 5. AU (BUC) = (A U B) U C 6. An (Bn C) = (An B) n C 7. AU (Bn C) = (A U B) N (A U C) 8. An (BUC) = (An B) U (An C) 9. (A°) = A 10. (An B)° = A° U B° 11. (AUB)C = A°n B° It is not required that it be AUA° = X_and An A° = ¢ 12.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Some properties of operations on the fuzzy sets Let A, B,C be fuzzy sets in X, then 1. AnA = A and AUA = A 2. AnB = BNA and AUB = BUA 3. Anø = 6 and AUØ = A 4. AnX = A and AUX = X 5. AU (BU C) = (A U B) U C 6. An (Bn C) = (An B) n C 7. AU (Bn C) = (A U B) N (A U C) 8. An (BUC) = (An B) U (A n C) 9. (A°) = A 10. (An B)° = A° U BC 11. (AUB)C = A° n BC It is not required that it be AU AC = X_ and An A° = ¢ 12. %3D
Transcribed Image Text:Some properties of operations on the fuzzy sets Let A, B,C be fuzzy sets in X, then 1. AnA = A and AUA = A 2. AnB = BNA and AUB = BUA 3. Anø = 6 and AUØ = A 4. AnX = A and AUX = X 5. AU (BU C) = (A U B) U C 6. An (Bn C) = (An B) n C 7. AU (Bn C) = (A U B) N (A U C) 8. An (BUC) = (An B) U (A n C) 9. (A°) = A 10. (An B)° = A° U BC 11. (AUB)C = A° n BC It is not required that it be AU AC = X_ and An A° = ¢ 12. %3D
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