Zadanie 1 Graduation of fuzzy sets. First Determine the membership values of individuals, whose age is given, the set of "old." Apply the following criterion for membership function:

Zadanie 1

Graduation of fuzzy sets. First Determine the membership values of individuals, whose age is given, the set of "old."

Apply the following criterion for membership function:

name age(x) µage(x)

Ewa 33

Ola 43

Waldek 44 Marek 51

Anna 55

Mirela 57 Grzegorz 61 Marcin 67 Karol 85 Kasia 88

Then, knowing that fuzzy sets can be graded calculate the value of membership function for each person to set a "very old" based on the value of membership function of the "old":

Zadanie 2

Please suggest a function of belonging, which for a given hour will give the appropriate time of day. Use the following illustration of the solution:

Zadanie 3

Suppose we have rules:

And that the functions belonging to different classes of data are as follows:

0 0,5 1 1,5

33 43 44 51 55 57 61 67 85 88

"stary"

"bardzo stary"

Determine the risk of an insurance company for the customer:

a) Wiek = 35 AND moc samochodu = 150 KM b) Wiek = 55 AND moc samochodu = 150 KM c) Wiek = 35 AND moc samochodu = 190 KM

Zadanie 4

Assume that the system knowledge base contains the following rules:

RULE1: IF temperature is hot or warm, THEN the swimming pool is crowded.

RULE2: IF temperature is cold, THEN the swimming pool is quiet.

Membership functions for the individual sets may be as follows:

1. What is the linguistic variable here and what is the value of linguistic?

2. Construct the membership functions for temperature and number of vendors in the pool.

Additional tasks:

Report of the solution of the following two tasks will be an opportunity to increase the assessment of the subject.

1. Suppose we have a system within a simple controller that uses an error signal e and the error signal de change as input and questions are 4 rules based on fuzzy model that works:

RULE 1: IF e = P AND de = P THEN x = N RULE 2: IF e = P AND de = N THEN x = 0 RULE 3: IF e = N AND de = P THEN x = 0 RULE 4: IF e = N AND de = N THEN x = P

Suppose that the data are two fuzzy sets as the fuzzy input variables e and de: P (positive) and N (negative).

Fuzzy output variable has three values: P (positive), 0 (zero), N (negative) as shown in the figure above.

Assuming that the input variables have the following values in the collection of membership function of input:

µN(e) = 0.4; µP(e) = 0.6 i µN(de) = 0.2; i µP(de) = 0.8

a. using a Mamdani-type inference Prove that the total value of the output fuzzy set is as shown below (red line). Construct appropriate graphs.

b. Sharpen the output values using the method centroid.

c. Using the method of "zero-order Sugeno" calculate the value of output. Draw graphically.

d. Compare the results for both methods of inference.

2. Design a Mamdani-type fuzzy system, which will assess the likelihood of an accident while driving.

Input variables:

• speed (10 - 200km / h): {small, medium, fast, very fast}

• visibility (0.05 - 4km): {very poor, average, good}

The output of the system:

• The probability of an accident (0 - 1): {very small, small, medium, large}