Reference no: EM132847215

Question 1:

The direction of the wind was in a North-South direction from morning until noon. Then it changed direction to East-West, The time noon is considered a transition period for changing the wind direction from North-South to East-West as seen in Figure P2.1, Find the intersection, union, and difference for the two directions of wind flow.

Question 2:

Two types of steel are tested four times each for their tensile strength, Let us consider fuzzy sets 'A_~' and `B_~' to be the two types of steel on the universe of strengths (no dimensional unit) where four tests X = {1, 2, 3, 4} were conducted on each of the two steel types, The following given sets represent the tensile strengths of each steel. Compare the tensile strength of these two steels by finding the following.

A_~ = {0.4/1 + 0.35/2 + 0.5/3 + 0.6/4} B_~ = {0.7/1 + 0.75/2 + 0.65/3 + 0.8/4}

a. A_~ ∩ B_~

b. A_~ ∪ B_~

c. ‾A_~, ‾B_~

d. A_~ - B_~

Question 3: In determining corporate profitability, many construction companies must make decisions based on the particular client's spending habits, such as the amount the client spends and their capacity for spending. Many of these attributes are fuzzy. A client which spends a "large amount' is considered to be "profitable" to the construction company. A "large" amount of spending is a fuzzy variable, as is a "profitable' return. These two fuzzy sets should have some overlap, but they should not he defined on an identical range.
A_~= {"large" spenders},
B_~ = ("profitable" clients}.

For the two fuzzy sets shown in Figure P23, find the following properties graphically:

a. A_~ ∪ B_~: all clients deemed profitable or who are large spenders.
b. A_~ ∩ B_~: all clients deemed profitable and large spenders
c. ‾A_~ and ‾B_~: Those clierit s (i) deemed not profitable and (ii) deemed not large spenders (separately).
d. ‾A_~|‾B_~: Entities deemed profitable clients but not large spenders.

c. ‾(A_~∪B_~) = ‾A_~ ∩ ‾B_~  (De Morgan's principle).

Question 4:

A Moto hike (M_~), Car (C_~), and Truck (T_~) are tested for their speed. Speed is directly influenced by the Horsepower (HP) of the engine,. Let *X' denotes speeds HP, then X = {10, 30. 100, 200. 500}. Their membership function values are given in the table:

Find the following:
a. M_~ ∪ C_~
b. C_~ ∩ T_~
c. ‾M_~

d. ‾T_~

e. M_~|T_~

f. C_~ ∩ T_~

g. M_~U(C_~ ∩ T_~)

Question 5:

A company is thinking to organize a weeklong event during the month of February in two different cities,. The event will take place outside. and the company wants to avoid the rain_ The weather department released a prediction of "'chances of not having rainfall' for three cities during the four wceks of the month of February. The fuzzy sets given show the assessment of rain in each city for each of the four weeks of February

The company wants to find the best two cities and the best week to hold the event. What are the cities and the week for the best time to try to hold the event?

Question 6:

A survey was conducted to study the demand for electricity and water in five parts of a city. lt was found that peak demand for hoth water and electricity was not same in all parts in the city,. The membership functions for these two sets is shown in Figure P2.6. For these two fuzzy sets. compute the union, intersection, and difference. The rive parts of ihe city are denoted as X { 1. 2, 3, 4, 5}.