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10 10 09 04 0.1. 0.3 0.0
+—+—+—+—+—+
0 1 2 5 7 9 10

Ls (x)= |

0.0 0.1 0.3 0.5 0.3 0.8 1.0
+--+--+--+--+-- +
0 1 2 5 7 9 10

/ (x) = {

where ൭. represents silent and C. represents congestion. Perform algebraic

product, bounded sum and bounded difference over the two fuzzy sets.

10 State the conditions for fuzzy tolerance and fuzzy equivalence relations? (3)
11 The fuzzy relations are given as (3)
201 ‏ولا( ولا‎ டே 22
0.8 0.1
20.1 0.2 0.3 5
= S=y,|0.6 9
- ൧04 0.5 0.6 ~
1 y,;|0.4 1.0

Perform composition over the two given fuzzy relations and obtain a fuzzy
relation T~.
PART D
Answer any two full questions, each carries 9 marks.
12 a) An athletic race was conducted. The following membership functions are defined (6)

based on the speed of athletes:
Low = _0_ + 01 + 03
− 100 200 300
Medium = ‏فنعا + لت‎ + Ze
2 100 200 300

High = (का zat
Find the following:
(a) R.=Low x Medium
(0) S-=Medium x High

(0) 1-1२ ० ७ using max-min composition

b) Explain any two defuzzification methods? (3)
13 a) Explain the features of membership functions? (3)
b) Differentiate between Normal and subnormal fuzzy set. (2)

c) Using intuition and your own definition of the universe of discourse, plot fuzzy (4)
membership functions to the following variables:
(i) Liquid level in the tank
(a) Very small

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