1. BIS2218 – DECISION SUPPORT SYSTEMS
Coursework, 2013/14
© Middlesex University, 2013/14
BIS2218 – DECISION SUPPORT
SYSTEMS
Coursework, Part B – Exercises 4-6
Mateusz Brzoska
Middlesex University 2014

2. BIS2218 – DECISION SUPPORT SYSTEMS
Coursework, 2013/14
© Middlesex University, 2013/14
Exercise 4 – Association Rule Mining
Data mining is also known as drill data, knowledge acquisition, extracting data, data
extraction. It is one of the steps in the process of knowledge discovery in databases. The idea
of data mining involves the use of computer speed for finding hidden patterns in data stored
in data warehouses.
One of the methods in the field of data mining is association rule mining. This method is used
to finding in a large data set hidden depending in the simple adjust form. It is very often
method used in the analysis of transaction data in supermarkets. The association rule mining
can answer questions such as:
What are the most frequently purchased products?
What is the probability that customers who bought product A, they also will buy product B?
So the main goal is to find the "hidden" rules that are not obvious and enrich knowledge of
specialists [1].
A simple TDB is given below.
Let the minimum support be 2, please mine all the association rules.
The table is located a sample data set. It consists of three sets of items, where each of them
was presented in a separate line. A single set of elements called the transaction. In the sample
data set are presented in rows, while the columns are respectively defined identifier and
elements, which are both included in its composition.
Support is very often defined as the number of transactions containing the set of the item.
In our example, the minimum support is 2.
Sup(X) ≥ 2
sup {A} = 3 sup {A, B} = 2
sup {B} = 2 sup {A, C} = 2
sup {C} = 2

3. BIS2218 – DECISION SUPPORT SYSTEMS
Coursework, 2013/14
© Middlesex University, 2013/14
Association rules:
Sup (Rule) =
𝐴
𝐵
A – A number of transaction consist rule
B – A number of all transactions
Conf (Rule) =
𝐴
𝐵
A – The number of transaction consist the rule
B – The number of groups containing the rule body
The confidence of an association rule is a percentage value that shows how often the rule
head occurs among all the groups containing the rule body. The confidence value says how
reliable this rule is. The higher the value, the more often this set of items is associated
together.
Thus, the confidence of a rule is the percentage equivalent of A/B, where the values.
 Rule #1: {A} => {B}
Sup (rule) = 2/4 50%
Conf (rule) = 2/3 66%
 Rule #2: {A} => {C}
Sup (rule) = 2/4 50%
Conf (rule) = 2/3 66%
 Rule #3: {B} => {A}
Sup (rule) = 2/4 50%
Conf (rule) = 2/3 66%
 Rule #4: {C} => {A}
Sup (rule) = 2/4 50%
Conf (rule) = 2/2 100%

4. BIS2218 – DECISION SUPPORT SYSTEMS
Coursework, 2013/14
© Middlesex University, 2013/14
Exercise 5 – Artificial Neural Networks
Artificial Neural Networks (ANN) is computational models inspired by animals' central
nervous systems (in particular the brain). ANN is capable of machine learning and pattern
recognition. Such systems can retrieve vast amounts of data quickly, and by using the
knowledge represented by the massive parallel-processing. They have the ability to match
patterns based on previous experience. This pattern matching is clearly a technique that is
often used in human reasoning.
One of the form Neutral Networks is Perceptron. It is a single neuron with a number of
weights, which is able to classify data into two classes.
A simple perceptron design is based upon:
 A single neuron divides input into two classifications or categories;
 The weight vector, W, is orthogonal to the decision boundary;
 The weight vector, W, points towards the classification corresponding to the “1”
output.
Design step-by-step solution to train the classifier by the basic perceptron learning rule.
I. Presentation of the above pattern in the table.
Inputs Outputs
2 0 1
1 2 1
-1 2.5 0
0 -1 0
II. Graphical Description
𝑥1
𝑥2
=one output
=zero output
One possible decision
boundary

5. BIS2218 – DECISION SUPPORT SYSTEMS
Coursework, 2013/14
© Middlesex University, 2013/14
III. One possible corresponding value of W is [3 0].
Output: a = hardlim [3 0] |
𝑥1
𝑥2
| + b = hardlim {3𝑥1 + 0𝑥2 +b} – decision boundary
Decision boundary passes through point (0.5; 0): 3(0.5) + 0(0) + b = 0 b = - 1.5
IV. Final Design
a = hardlim [3 0] |
𝑥1
𝑥2
| – 1.5
Test:
a = hardlim [3 0] |
2
0
| – 1.5 = 1  6 + 0 – 1.5 = 4.5 > 0 so 1
a = hardlim [3 0] |
1
2
| – 1.5 = 1  3 + 0 – 1.5 = 1.5 > 0 so 1
a = hardlim [3 0] |
−1
2.5
| – 1.5 = 0  -3 + 0 – 1.5 = - 4.5 <= 0 so 0
a = hardlim [3 0] |
0
−1
| – 1.5 = 0  0 + 0 – 1.5 = - 1.5 <= 0 so 0
*hardlim - The hard limit transfer function forces a neuron to output a 1 if its net input reaches a
threshold, otherwise it outputs 0. This allows a neuron to make a decision or classification. It can say
yes or no. This kind of neuron is often trained with the perceptron learning rule.

6. BIS2218 – DECISION SUPPORT SYSTEMS
Coursework, 2013/14
© Middlesex University, 2013/14
Exercise 6 – DSS Case Study
Design a DSS to help decision-makers run the 2012 London Olympics.
Sixty four years on, this is the time when the Games are back with London 2012. There will
be more than 14 500 athletes from over 200 countries participating in nearly 700 events at
venues throughout the country – watched live worldwide by around four billion people.
London Olympics has prepared for this event 4500 medals. Each of the winners of their
competition will receive one of the heaviest and biggest medals ever taken. Weight the
golden and silver medal is 412g. Competitors from its lowest podium will receive medals
bronze weighing 357g. Producing a golden medal takes six hours, the silver five hours and
bronze four hours. All medals are produced by the Mint. There, each of them undergoes
further production, such as 22-step pressing and cleaning. After every 5 strikes, the medals
were re-heated - to avoid cracking and the ensure uniformity. Finally, the metals are
engraved - sport and discipline - ribbon attached and packed into boxes [2].
Below is a table showing the various stages of the production time’s medals.
Mint operates 24 hours a day in case of bigger orders. Production costs medals respectively
£ 600, £ 500 and £ 400 for gold, silver and bronze medal.
A case study is provided to show how to find the right mix of these three products in order to
minimalize costs of production and time. It will be shows what decisions need to be taken to
minimize the cost in 24 hours work day, utilize a maximum possibility of the company and
employees to achieve the goal of 4500 medals.
The Linear Programming (Optimisation) Model
Linear programming has gained widespread use in decision theory, e.g., to optimize
production plan. Many optimization problems find a solution by bringing them into a linear
programming problem. To find the solution of this problem we will use the supplementary
program solver in the Microsoft Excel. Linear Programing shows, how much time is needed
to achieve 4500 medals and prepare schedule for this. This is very important, because the
mint has time constraints terms of production. It means that the available machines are able to
produce up to a certain amount medals per 24 hours, not more. It is therefore the venture
term.

7. BIS2218 – DECISION SUPPORT SYSTEMS
Coursework, 2013/14
© Middlesex University, 2013/14
A screenshot from Microsoft Excel shows the best solution for 24hours day in production medals.
A screenshot shows how many days need to produce 1500 medals from each metal and total cost produce.

8. BIS2218 – DECISION SUPPORT SYSTEMS
Coursework, 2013/14
© Middlesex University, 2013/14
Results and conclusion
To get the best results in the production of Olympic medals and preserve as much as possible
of funds, Mint is able to produce the 29 medals per day. It costs £14 100 per day. Olympics
are advertised with a big advance. Olympic host knows about organizing such a great event
about six years before the start. Thanks to this you can schedule everything exactly at the
time. The Linear Programing shows that to produce all medals, needs to 188 days. This
method can achieve the best outcome, in this case lower cost and good management all 24
hours at work.
References
[1]. Agnieszka Pasztyła (). Analiza koszykowa danych transakcyjnych - cele i metody. [ONLINE]
Available at: http://www.statsoft.pl/pdf/artykuly/basket.pdf
[Last Accessed 25.03.2014].
[2]. Terence Bell (). London 2012's Olympic Metals. [ONLINE]
Available at: http://metals.about.com/od/metalworking/a/London-2012s-Olympic-Metals.htm.
[Last Accessed 26.03.2014].