's IEEE International Conference on Fuzzy Systems: March 8-12, PDF

ISBN-10: 0780302370

ISBN-13: 9780780302372

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Extra info for IEEE International Conference on Fuzzy Systems: March 8-12, 1992, Town & Country Hotel, San Diego, California

Example text

The various operations and properties of these sets were also dealt in detail. It was found that the variation of the classical and the fuzzy set was in the excluded middle law. The demorgan’s law discussed helps in determining some tautologies while some operations are performed. Except for the excluded middle law all other operations and properties are common for the crisp set and the fuzzy set. Review Questions 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. Define classical set. How is the power set formed from the existing universe?

2 3 4 5 6 Solution. 6 + + + + 2 3 4 5 6 . Comparing the membership values and writing maximum of the two values determine Union of the fuzzy set. 3 + + + + 2 3 4 5 6 . 3 Fuzzy Sets 25 Comparing the membership values and writing minimum of the two values determine intersection of the fuzzy set. 3 + + + + . 7 + + + + . 5. We want to compare two sensors based upon their detection levels and gain settings. The following table of gain settings and sensor detection levels with a standard item being monitored provides typical membership values to represents the detection levels for each of the sensors.

A ∪φ = A. 2. A ∩φ = A. φ is going to be a null set, hence it is clearly understood, that, A ∪ φ & A ∩ φ will give as the same set A. 3. A ∩ X = A. A ∩ X = {a, d, f}, A = {a, d, f}. Hence, A ∩ X = A. 4. A ∪ X = X, A ∪ X = {a, b, c, d, e, f, g, h}, X = {a, b, c, d, e, f, g, h}. Hence, A ∪ X = X. This identity property is proved. 3 Fuzzy Sets In the classical set, its characteristic function assigns a value of either 1 or 0 to each individual in the universal set, there by discriminating between members and nonmembers of the crisp set under consideration.

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IEEE International Conference on Fuzzy Systems: March 8-12, 1992, Town & Country Hotel, San Diego, California


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