St. Joseph’s College of Arts & Science (Autonomous) Cuddalore – 607001 EPMT915 – FUZZY SUBSETS AND ITS APPLICATIONS
Time : 3 hrs
Max Marks :75
U
SECTION – A (5X2=10) Answer ALL Questions 1. Define union and intersection of two fuzzy sets and give an example. 2. Define support and envelope of a fuzzy relation and give examples. 3. Define fuzzy semipreorder and give an example. 4. What is sheffer operator? 5. What is a schedule coordination problem? SECTION – B (3X5=15) Answer any THREE Questions 6. Explain the concept of index of fuzziness and index of fuzziness for a product giving suitable examples. 7. Explain conditioned fuzzy subsets and given an example. 8. State and prove theorem of decomposition for a similitude relation. 9. Determine the domain of f ( a, b )= a ∧ b knowing that ℘a [ a1 , a2 [ and ℘b [b1 , b2 [ 10. Explain the applications of the theory of fuzzy sets in soft computers.
~1~
U
Q3-13/11 S/13 SECTION – C (5X10=50) Answer ALL Questions 11. a) Define generalized relative Hamming distance and relative Euclidean distance and give an example for each. (or) + b) If pi , mi , n i ∈ R , i = 1, 2,....., k ; then prove that ni, i 1, 2,..., k ) ⇒ ( pi ≤ mi +=
k
∑ pi2 ≤
k
∑ mi2 +
k
∑n
=i 1 =i 1 =i 1
2 i
.
12. a) Explain max-min composition and max-product composition of fuzzy relations. Illustrate with examples. (or) b) Define symmetry, reflexivity and transitivity of fuzzy binary relation and give examples. 13. a) Explain the procedure to construct fuzzy order relation existing between the similitude classes. (or) µ b) If ℜ is the max-min transitive closure of the resemblance µis the max-min transitive closure relation ℜ , then prove that ℜ of the corresponding dissemblance relation. 14. a) Let f ( a, b, c ) =
( a ∧ b ) ∨ ( a ∧ b ∧ c ) .Under what conditions will
(or) b) Let f ( a, b, c ) = ( a ∨ b ) ∧ ( b ∨ c ) .Under what conditions
α k −1 ≤ f ( a, b, c ) < α k . 15. a) Discuss the applications of fuzzy set theory in medicine. (or) b) Discuss the applications of fuzzy set theory in engineering.
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