1. Exercise 4

2. 4.1
Determine which fuzzy sets defined by the following functions are fuzzy numbers:
(a)
(b)
(c)
(d)
(e)

3. 4.2
Calculate the following:
(a) [-1, 2] + [1, 3];
(b) [-2, 4] – [3, 6];
(c) [-3, 4]˙[-3, 4];
(d) [-4, 6] / [1, 2].

4. 4.5
Let A, B be two fuzzy numbers whose membership functions are given by
Calculate the fuzzy numbers A + B, A - B, B - A, A • B, A/B, MIN(A, B) and MAX(A, B).

5. 4.6
Let A, B be two fuzzy numbers given in Exercise 4.5 and let
Solve the following equations for X:
(a) A + X = B;
(b) B • X = C.

6. 4.9
Consider fuzzy sets A and B whose membership functions are defined by formulas
for all x {0,1, 2 , , 10} = X. Calculate:
(a) Scalar and fuzzy cardinalities of A and B (also plot the fuzzy cardinalities);
(b) degrees of subsethood S(| |, | |) and S(| |, | |).