1.  The height h(A) of a fuzzy set A is defined as h(A) =sup A(x) where x belongs to A. Then the fuzzy set A is called normal when

A.  h(A)=0 
B.  h(A)<0 
C.  h(A)=1 
D.  h(A)<1

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Correct Answer is C 
Explanation 
The height of a fuzzy set is the highest membership value of the membership function:
Height(A) = max ľA(xi)
A fuzzy set with height 1 is called a normal fuzzy set.
In contrast, a fuzzy set whose height is less than 1 is called a subnormal fuzzy set. So, according to the above rule, the fuzzy set A is called normal when h(A)=1.

2.  Fuzzy logic is a form of

A.  Twovalued logic

B.  Crisp set logic 
C.  Manyvalued logic 
D.  Binary set logic 
View/Hide Ans 
Correct Answer is C 
Explanation 
With fuzzy logic set membership is defined by certain value. Hence it could have many values to be in the set. 
3.  What is the Fuzzy Approximation Theorem(FAT) ?

A.  A fuzzy system can model any continuous system 
B.  The conversion of fuzzy logic to probability.

C.  A continuous system can model any fuzzy system. 
D.  Fuzzy patches covering a series of fuzzy rules.

View/Hide Ans 
Correct Answer is A 
Explanation 
The FAT as stated by Bart Kosko shows a fuzzy can model any continuous system. Each of the rules acts as a fuzzy patch that the system places so as to resemble the response of the continuous system. In option B the Fuzzy logic and probability are two completely different concepts and cannot be converted to one another. In Option C is vice versa of the answer and is clearly wrong. In Option D the fuzzy rules are represented by fuzzy patches, and the patches are suppose to be able to cover any curve in a continuous system. 
4.  Consider a fuzzy set old as defined below
old={(20,0),(30,0.2),(40,0.4),(50,0.6),(60,0.8),(70,1),(80,1)}. Then the alphacut for alpha=0.4 for the set old will be

A.  {(40,0.3)}

B.  {50,60,70,80} 
C.  {(20,0.1),(30,0.2)} 
D.  {(20,0),(30,0),(40,1),(50,1),(60,1),(70,1),(80,1)}

View/Hide Ans 
Correct Answer is D 
Explanation 
alphacut of a fuzzy set A will contain those elements where the membership function value is equal to or greater than alpha.
Here, alpha is given a value 0.4. Starting from (40,0.4) all the members have membership function equal or greater than 0.4. so, except (20,0) and (30,0.2) all the members are included in the alphacut of the fuzzy set. The only option which has 40,50,60,70, and 80 included is option D. It has (20,0) and (30,0) too. But it is already noted that any singleton where the membership function is 0 can be considered not included. So basically these two members are not part of the alphacut of the fuzzy set A. So the correct option is D.

5.  Equilibrium of a fuzzy complement c is a solution of the equation

A.  c(a)a=1 
B.  c(a)a=2 
C.  c(a)=2a 
D.  c(a)a=0

View/Hide Ans 
Correct Answer is D 
Explanation 
Equilibrium of a fuzzy complement c is defined as any value a for which c(a) = a. In other words, the equilibrium of a complement c is that degree of membership in a fuzzy set A which equals the degree of membership in the complement cA.

6.  ______________ is/are the way/s to represent uncertainty.

A.  Fuzzy Logic 
B.  Probability 
C.  Entropy 
D.  All of the mentioned

View/Hide Ans 
Correct Answer is D 
Explanation 
Entropy is amount of uncertainty involved in data. Represented by H(data).

7.  Involutive property of the standard fuzzy complement c, for each a? [ , ] is 

A.  c(c(a))=c(a) 
B.  c(c(a))= 1 
C.  c(c(a))=0 
D.  c(c(a))=a

View/Hide Ans 
Correct Answer is D 
Explanation 
A complement function G is said to satisfy
(i) boundry condition if C(0) = 1 and C(1) = 0
(ii) monotonic condition if x<=y ? C(x) >=C(y) for all x,y ? [0,1]
(iii) involutive condition if c(c(x)) = x for all x ? [0,1]

8.  How is Fuzzy Logic different from conventional control methods?

A.  IF and THEN Approach 
B.  FOR Approach 
C.  WHILE Approach 
D.  DO Approach 
View/Hide Ans 
Correct Answer is A 
Explanation 
FL incorporates a simple, rulebased IF X AND Y THEN Z approach to a solving control problem rather than attempting to model a system mathematically. The FL model is empiricallybased, relying on an operator's experience rather than their technical understanding of the system. For example, rather than dealing with temperature control in terms such as "SP =500F", "T <1000F", or "210C 
9.  If A and B are two fuzzy sets with membership functions ?A(x) = {0.6, 0.5, 0.1, 0.7, 0.8} ?B(x) = {0.9, 0.2, 0.6, 0.8, 0.5} Then the value of ? Complement A?B(x) will be

A.  {0.9, 0.5, 0.6, 0.8, 0.8} 
B.  {0.6, 0.2, 0.1, 0.7, 0.5} 
C.  {0.1, 0.5, 0.4, 0.2, 0.2} 
D.  {0.1,0.5,0.4,0.2,0.3}

View/Hide Ans 
Correct Answer is C 
Explanation 
Union of two fuzzy sets
ľAUB(x) = ľA(x) V ľB(x) = max(ľA(x), ľB(x))
?A(x) = {0.6, 0.5, 0.1, 0.7, 0.8}
?B(x) = {0.9, 0.2, 0.6, 0.8, 0.5}
ľAUB(x) = {0.9,0.5,0.6,0.8,0.8}
Complement of ľAUB(x)={0.1,0.5,0.4,0.2,0.2} So, the correct answer is C.

10.  Given U = {1, 2, 3, 4, 5, 6, 7} A = {(3, 0.7), (5, 1), (6, 0.8)} then
A will be : (where ~ ?complement)

A.  {(4, 0.7), (2, 1), (1, 0.8)}

B.  {(4, 0.3), (5, 0), (6, 0.2) } 
C.  {(1, 1), (2, 1), (3, 0.3), (4, 1), (6, 0.2), (7, 1)}

D.  {(3, 0.3), (6.0.2)}

View/Hide Ans 
Correct Answer is C 
Explanation 
Complement of a fuzzy set
The complement of a fuzzy set A is a new fuzzy set A Complement, containing all the elements which are in the universe of discourse but not in A, with the membership function
Complement of ľA(x) = 1  ľA(x)
Complement of a fuzzy set A is a new fuzzy set A complement. Since it is a fuzzy set, there will be two members in a singleton. The first member will be all the elements which are in the universe of discourse but not in A. The membership function will be 1 ľA(x).
So, the complement of A will be
{(1,1),(2,1),(3,0.3),(4,1),(6,0.2),(7,1)}
The first is (1,1). The first 1 is in U but not in A, so it should be added in the complement. The second 1 is because the membership function is 1 ľA(x). 10=1.
The same reason why you get (2,1).
The third one (3,0.3) because it is (3,10.7)=(3,0.3).
Same reason why you have (4,1) and (7,1).
(6,10.8)=(6,0.2).
The member (5,0) is not included because , a singleton whose membership to a fuzzy set is 0, can be excluded .
