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.

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