Q13,paper3, D12. Consider a fuzzy set A defined on the interval X = [0, 10] of integers by the membership Junction mA(x) = x/(x+ 2). Then the alpha cut corresponding to alpha= 0.5 will be

(A) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

(B) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

(C) {2, 3, 4, 5, 6, 7, 8, 9, 10}

(D) { }

Answer©.

 a alpha cut of  fuzzy set is set whose element member is more than  or equal to .5 as given alpha =.5.

Interval is 0 to 10.

mA(0) = x/(x+ 2).=0

mA(1) = x/(x+ 2).= .33

mA(2) = x/(x+ 2).=2/4=.5

mA(3) = x/(x+ 2).= 3/5=.6

mA(4) = x/(x+ 2).=4/6=.6

mA(5) = x/(x+ 2).=5/7=.55

mA(6) = x/(x+ 2).=6/8=.75

mA(7) = x/(x+ 2).=7/9=.77

mA(8) = x/(x+ 2).=8/10=.8

mA(9) = x/(x+ 2).=9/11=.8

mA(10) = x/(x+ 2).=10/12=.83

Hence all element 2 to 10 qualifies having membership equal or greater than .5