Select Page

1. Solve the following problems.

a) Define fuzzy set and give the examples.

b) Let A and B be two fuzzy set, π΄ = {(2,1), (3,0.5)}; π΅ = {(3,1), (4,0.5)}, Fine A + B

c) Discuss the procedure for solving fuzzy linear programming problem with right hand size as fuzzy numbers.

2. Consider the fuzzy sets A, B and C defined on π = [0,10] of real numbers by the membership grade function

π₯ 1

π΄ = π₯ + 2 , π΅ = 2, πΆ = 1 + 10(π₯ β 2)2

Calculate π΄ βͺ π΅, π΄ βͺ πΆ πππ π΄ β© πΆΜ.

3. Solve the following fuzzy linear programming problem

πππ₯ π§ = 0.5π₯1 + 0.2π₯2

ππ’πππππ‘ π‘π

π₯1 + π₯2 β€ π΅1 2π₯1 + π₯2 β€ π΅2

π€βπππ

1 πππ π₯ β€ 300.

1 πππ π₯ β€ 400.

π΅1(π₯) = {

400βπ₯

100

πππ 300 < π₯ β€ 400

π΅2

(π₯) = {

500βπ₯

100

πππ 400 < π₯ β€ 500

0 πππ π₯ > 400. 0 πππ π₯ > 500.

4. Solve the following fuzzy linear programming problem

πππ₯ π§ = 5π₯1 + 4π₯2

ππ’πππππ‘ π‘π

(4,2,1)π₯1 + (5,3,1)π₯2 β€ (24,5,8)

(4,1,2)π₯1 + (1,0.5,1)π₯2 β€ (12,6,3)

π₯1, π₯2 β₯ 0