Fuzzy Logic And Application Jntu Model Paper{Www.Studentyogi.Com}

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Code No: RR420208
Set No. 1
IV B.Tech II Semester Regular Examinations, Apr/May 2007
FUZZY LOGIC AND APPLICATION
(Electrical & Electronic Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks

1. Explain the operations on crisp sets by using Venn diagrams? [16]

2. In a computer engineering di erent logic families are often compared on the basis
of their power-delay pro duct.
The fuzzy set F is the logic families F={NMOS, CMOS, TTL, ECL, JJ}.
The range of delay time D= {0.1, 1, 10, 100} in Nano seconds.
The power dissipation in micro watts P= {0.01, 0.1, 1, 10, 100}
By using max-min composition to obtain a fuzzy relation between delay time and
Power dissipation. [16]

3. Write a note on futures of the fuzzy membership function? [16]

4. These exercises use Zadeh’s extension principel

(i)01234567
~ 0.0 0.1 0.6 0.8 0.9 0.7 0.1 0.0
~ 0.0 1.0 0.7 0.5 0.2 0.1 0.0 0.0
If x and y are real numbers de ned by sets ~ and ~ respectively.
Calculate the fuzzy set ~ representing the real numbers Z given by

(a) Z = 3x-2
(b) Z = 4x2+3
[16]

5. v3 is not a rational number; i.e., show that it can not be the ratio of two even
integers by contradiction? [16]

6. Write a short notes on aggregation of fuzzy rules and explain about determination
of aggregation strategy. [16]

7. In making a decision to purchase a air plane, air line management will consider the
qualities of an air plains performance with respect to the competitor. The Boeing
737 is the best selling airplane in aviation history and continues to outsell its more
modern competitor the A 320 manufactured by the air bus consortium. The four
factors to be considered are range payload, operating cost, and reliability. The
criteria will be comparison of 737 with respect to A320: superior (sup.) equivalent


Code No: RR420208
Set No. 1
(eq.) and de cient (def.)

073
181
~= 154
721

Air lines weighting factors of the four factors as ~ = {.15, .15, .3, .4} nd the fuzzy
vectors for the evaluation. [16]

8. As a company issuing bank cards. We want to separate individuals holding personal
credit cards into two groups: pro table card holders usually let a nonzero balance
on the card go from month to month, thereby accruing interest: and a eventually
always pay the total balance. Unpro table card holders often do not pay a balance,
and card privileges usually have to be cancelled. Suppose the data for the jth card
holder consist of three features:
Xj = (X11,X21,X31)
where X11 = account balance
X21 = amount paid
X31 = amount purchased
Suppose we want to classify four individuals, each characterized by the following
normalized data:
X1 = (1, .75, 1)
X2 = (0, 0, -.5)
X3 = (.5, .5, .75)
X4 = (1, -.5, -.5)
Note that the values (features) in each vector are normalized Gaussian variables
such that = 0 and = 1, where
Value=(X- c)/ c
Hence, values at zero are at the mean of a class (c), positive values indicate a
variable greater than the mean, and negative values indicate a variable less than
the mean. Use the following 2-partition as the initial guess, and nd the optimum
2-partition.
(0) = 1 1 0 0 [16]
0011


Code No: RR420208
Set No. 2

1. (a) Explain the di erence between randomness and fuzziness.
(b) Describe the concept of a fuzzy set in your own words. [16]

2. In a computer engineering di erent logic families are often compared on the basis
of their power-delay pro duct.
The fuzzy set F is the logic families F={NMOS, CMOS, TTL, ECL, JJ}.
The range of delay time D= {0.1, 1, 10, 100} in Nano seconds.
The power dissipation in micro watts P= {0.01, 0.1, 1, 10, 100}
Develop the fuzzy relation between logic families and power dissipation. [16]

3. How to generate membership function by using Genetic Algorithms? [16]

4. For the function y = 2 2 - 3 1 + 4 , where the membership functions for fuzzy
1+2
variables X1 , X2 shown in Figure 4: nd and plot the membership function for the
fuzzy out put variable , y , using the DSW algorithm. [16]

Figure 4

5. v3 is not a rational number; i.e., show that it can not be the ratio of two even
integers by contradiction? [16]

6. A factory process control operation involves two linguistic (atomic) parameters
consisting of pressure and temperature in a uid delivery system. Nominal pressure
limits range from 400 psi maximum. Nominal temperature limits are 1300F to
1400F. We characterize each parametre in fuzzy linguistic terms as follows:


Code No: RR420208
Set No. 2
“”=1
131 + 0132 + 0133 + 0134 + 0135 + 0136
8 6 4 2

“”=0
134 + 0135 + 0136 + 0137 + 0138 + 1139
2 4 6 8

“”=0
400 + 0600 + 0700 + 0800 + 0900 + 11000
2 4 6 8

“”=1
400 + 0600 + 0700 + 0800 + 0900 + 01000
8 6 4 2
Find the following membership functions

(a) Temperature not very low.
(b) Temperature not very high.

(c) Temperature not very low & not very high. [16]

7. Write a notes on decision making under fuzzy states and fuzzy actions? [16]

8. A fuzzy tolerance relation. R. is re exive and symmetric. Find the equivalence
relation R and then classify it according to -cut levels ={0.9,0.8,0.5}.
10800201
08109004
= 0091003 [16]
0200105
010403051


Code No: RR420208
Set No. 3

1. Propose membership functions to describe ‘a fuzzy resister’ with a nominal value
of 1M and another one of 5.6k . [16]

2. In DC motor speed control under no load condition, generally the external series
resistance in armature Rse should be kept in cut in position. For example in ar-
mature controlled method the ux maintained at some constant value; then motor
speed is proportional to back e.m.f.

(a) What should be the minimum and maximum level of Rse ?
(b) What should be the minimum and maximum level of Ia?

Rse= Rs1, Rs2, Rs3 Rsn
Ia= I1, I2, I3 Im
N= N1,N2,N3NV
Where Rse, Ia, N, are fuzzy sets of armature series resistance, armature current,
Speed respectively. The membership functions for above for given in terms of
Percentage of respective rated values.
Rse = 0.3
30 + 0.7 60 + 1.0100 + 0.2120
Ia = 0.2
20 + 0.4 40 + 0.6 60 + 0.8 80 + 1.0 100 + 0.1120
= 0.33
500 + 0.67
1000 + 1.01500 + 0.15 1800
R=Rse Ia; S=N Ia
Find max-min composition for T=R S. [16]

3. Using your own institution, develop fuzzy membership functions on the real line
for the fuzzy numbers 3, using the following function shapes;

(a) Symmetric triangle
(b) Trapezio d

(c) Gaussian function. [16]

4. Explain Center of Sums, Center of Largest Area Defuzzifying Methods? [16]

5. Show that the dual of equivalence ( ) is also true? [16]

6. Using the image processing techniques, suppose you are trying to locate object or
shapes within an image eld. An object is big or small according to whether it has
a value above or below a prede ned threshold based on the number of consecutive
pixel elds in a row - column image matrix. De ne a universe of discourse of the
number of adjacent pixels above a certain threshold on the interval [50, 300], then,


Code No: RR420208
Set No. 3
for the membership function for “big” and “small,”
“”=0
50 + 0100 + 0150 + 0200 + 0250 + 1300
2 3 8 9

“”=1
50 + 0100 + 0150 + 0200 + 0250 + 0300
5 1
De ne the membership function for the following three linguistic expression:

(a) Not big and very small
(b) Very, very big or not small

(c) Not very, very big. [16]

7. Write a short note on multi stage decision making? [16]

8. Write step by step procedure C - Means Algorithm? [16]


Code No: RR420208
Set No. 4

1. Let the fuzzy sets A, B and C be the sub sets of the universe {1,2,3??., 199,200}.
Let A= {1/0.1, 2/0.3,3/0.3, 4/0.4, 5/0.5, 6/0.7, 7/0.8, 8/0.9, 9/1, 10/1} and
B= {1/0.1, 2/0.3, 3/0.5, 4/0.7, 5/0.9, 6/1,7/0.8, 8/0.5, 9/0.2, 10/0}. Find out the
fuzzy sets C= A*(A+B); C= A2; C= 1/B. [16]

2. The matrix expression for the crisp relation by using max-min composition opera-
tion The relation matrices for R & S would be expressed as

1 0 1 0
1 2 3 4 1 0 21
1

=1 2 00 Find max-min composition?
2
3
0 0 0 1 And = 3
01
0 0 0 0 4
00 [16]

3. Classify all possible hedges? And Explain with suitable meaning? [16]

4. For the function y = 2 2 - 3 1 + 4 , where the membership functions for fuzzy
1+2
variables X1 , X2 shown in Figure 4: nd and plot the membership function for the
fuzzy out put variable , y , using A discretized form of the extension principle. [16]

Figure 4
5. Explain about classical predicate logic connectives? [16]

6. What are the di erent linguistic hedges and how the linguistic hedges have the
e ect of modifying the membership function basic atomic term ? [16]

7. When evaluating expert system to ols, four evaluation criteria are used:

(a) Excellent
(b) good


Code No: RR420208
Set No. 4
(c) Fair and
(d) Mediocre.

There are four aspects: I / O facilities, debugging aids, knowledge based editors,
and explanation facilities. The following table shows relationship matrix.

Excellent good fair mediocre
I/O 0.3 0.4 0.2 0.1
Debug 0.2 0.5 0.3 0
Editors 0.5 0.2 0.2 0.1
Explain 0.1 0.6 0.2 0.1

Suppose we have weight factor ~ = {0.2, 0.4, 0.3, 0.1}, Evaluate the expert system
tool. [16]

8. A customer evaluates ve banks by their mortgage policy, loan interest, and div-
idend bene ts. She has developed a fuzzy tolerance relation R according to these
three criteria for banks. If she uses a -cut level of 0.8, then how many classes can
she make from these banks?
102050907
021060408
= 050610403 [16]
090404105
070803051

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Fuzzy Logic And Application Jntu Model Paper{Www.Studentyogi.Com}