# The Modification in TOPSIS Method

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3.4 The modification in TOPSIS method

For simplification reasons, a modified TOPSIS method is presented. The TOPSIS method includes the following steps:

Suppose a given matrix.

1. Normalized matrix construction

2. Weighted normalized matrix construction

3. Find the ideal and negative ideal sets

4. Calculate the separation measurers from ideal and negative ideal sets

5. Calculate the relative closeness

6. Select the maximum value

The steps in the modified TOPSIS method are the same with a slight difference.

The step 3. Find the ideal and negative ideal sets changes to the following: 3. Find the ideal sets.

An example will shed light to this difference.

Suppose we want to choose a house. The criteria are Cost, Safety and Distance. The alternatives are House1, House2, House3 and House4. There will be used a scale from 1 to 9. 1 is for the least important and 9 is for the most important. For example, in terms of Safety, House1 has 5 while House2 has 2. This means that safety in House1 is 3 times better that Safety in House 2.

In this example, Safety and Distance are positive criteria. This means that the bigger value they have the better it is. However, Cost is a negative criterion, meaning that the lower the better. In the modified TOPSIS, the Cost is a positive criterion because the cheapest house will have the bigger number from the scale one to nine. Suppose that House1 costs £10.000,00 and House2 costs £17.320,78. The value of House1 in the decision table is 6 and the value of House2 is 3.

Cost Safety Distance

House1 6 4 3

House2 3 5 5

Table 3-7 Judgements in TOPSIS method

In the previous TOPSIS method, negative and positive criteria should be determined.

The prototype will implement TOPSIS with ...

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...” includes the use case “Choose Project”. This means that if the decision maker wants to view a project s/he must choose this project.

The <> relationship

In the <> relationship, the use case which is included by another case is compulsory for the completion of this another use case. On the contrary, in the <> relationship, the child use case enhances the functionality of the parent use case. We can infer from this that the child use case is not compulsory for the completion of the parent use case.

For example, the use case “View Projects” is the parent use case and the use case “View Project Details” is the child use case. The latter use case is optional for the decision maker.

Another important aspect of this diagram is that the actors Moderator and Participants inherit the use cases of the parent actor who is the Decision Maker.