Implementation of Simple Additive weighting using Alogorithm

What Is SAW And WHY Do We Need SAW?

The Simple Additive Weighting (SAW) is a methodology that is used for identifying the problem and the right level of sequence in a sorting task. which is used to make the right decision taking even if it is multiple criteria. It is capable of Analyzing cases based on the criteria. The number of criteria values that can be used in this approach is limitless. The higher number the higher accuracy we get.

     There are two types of benefits criteria like cost and benefits. cost is used when the criteria value is high and lower is used when the possibility of receiving the highest score. The benefits are on the other hand is used if the criterion value is high, then it is a greater chance of receiving the top position. it has been done by finding the sum of numbers performance and rating on each alternative attribute so that we can get a right decision or we can say best alternatives. Using this method will solve decisions that can be fully manual. 

Advantage – The benefits of the SAW method is used compared with the other decision-making model in that it can make more precise judgments. And another advantage of this method is it provides value and cost to the value of each alternative.

Formula For benefits and cost attributes

preference value for each attribute

 

STEPS FOR PERFORMING SAW METHOD

Step 1

 1. As an appraiser, define criteria for the benefits of a variable.

 2. Calculate the match rate for each of the Tab's alternatives.

 3. Make criteria-based decision matrixes

 4. On each attribute, perform normalization based on benefits and costs.

5. Using the defining weights for each R-value on the normalization matrix to calculate the final result.

  Step 2   

  Data Collection        

1.     Criteria

2.     Crisp

3.     Alternative  

    Step 3

  EXAMPLE 

    Table 1. Criteria

Criteria	Remark	Weight
C1	Qualification	4
C2	Health	4
C3	Age	2
C4	salary	4
C5	Family member	5

   

 Here I have taken a trial. There are five types of criteria.  Were the qualification, health, and family member the three criteria? Age and salary are the second type of criteria considered. These are intended to help voters to choose the best candidates as per their criteria.

There are five different kinds of criteria. Whereas the three criteria are qualification, health, and family member, the second type of criteria is age and salary. This is to assist voters in selecting the best person for eligibility in a government scheme based on their criteria.

     Very high  = 1

High= 2

Enough=3

Low=4

Very low=5

The following table describes the criteria for Qualification

     The following table describes the criteria from school to graduation.

Criteria	Weight
A1	01
A2	02
A3	03
A4	04
A5	05

 

  

  The following table describes the Health table  from weak to very strong

Criteria	Weight
A1	01
A2	02
A3	03
A4	04
A5	05

 

Criteria of Age table describes the criteria like 22-60

Criteria	Weight
A1 60-50	01
A2 30-20	02
A3 20-30	03
A4 25-60	04
A5 22-22	05

   

Criteria of salary 20k-620k criteria

Criteria	Weight
A1  100k-200k	01
A2  250-620k	02
A3   20k-60	03
A4   30k-40k	04
A5    60k-40k	05

  

Criteria of Family member

Criteria	Weight
A1  2	01
A2  3	02
A3 4	03
A4 5	04
A5 6	05

 

    Result

   The test data are samples taken for experiment and testing of SAW algorithm in village head election. In this data, several names are taken as examples in the election of the village head. The following table describes the names and capabilities based on the criteria table in the previous chapter.

Data set

Sr no.	Name	C1	C2	C3	C4	C5
1.	Aman	2	3	4	5	2
2.	Shreyas	2	4	3	2	2
3.	Rahul	3	2	3	3	4
4.	Sahil	4	2	4	2	4
5	om	5	1	2	4	3

The above criterion is a benefit criterion, which means that if the value is large, each value in the criteria has the best value.  W = (2, 2, 1, 2, 3). As seen below, a decision matrix was created using the match table.

 

Like this find each alternative 1 (1-5)

 

R1,1= min(2,2,3,4,5)/2

=2/2

=1

R1,2= min(3,4,2,2,1)/3

=1/3

=0.33

R1,3= min(4,3,3,4,2)/4

=2/4

=1

R1,4= min(5,2,3,2,4)/5

=2/5

=1

R1,5= min(5,2,3,2,4)/2

=2/2

=1

Find each alternative of  2(1-5), alternative 4, (1-5), alternative 4 (4-5), alternative 5(1-5)

This is the normalization value matrix as shown below.

 

VI = (2*1)+(2-0.33)+(1+0.5)+ (2 - 0.4) + (3 - 1)

=2 + 0.66 + 0.5 + 0.8 + 3

=6,96

V2 = (2*1)+(2*0.25)+(1*0.67)+

=(2 - 1) + (3 - 1)

= 2 + 0.5 + 0.67 + 2 + 3

V3 = (2*0,67) + (2*05) + (1*067) +(2 * 0.67) + (3 * 0.5)

=1.34 + 1 + 0.67 + 1.3a + 15 -5.015

=5,85

V4 = (2*0,5)+(2*0,5) + (1*0,5) +(2 *1) + (3 *0.5)

= 1+1+0.5+2+1.5

=6

V5 = (2*0.4)+(2*1)+(1*1)+(2*0.5)+(3*0.67)

=0.8+2+1+2.01

=6.81

V2(8.17) >V4 (6) As a result, it is clear that Shreyas is the best candidate for the role of the village chief.

Conclusion

 

     The SAW method's core principle is to calculate the weighted sum of performance ratings for each alternative across all criteria. The SAW approach necessitates the normalization of the choice matrix to a  scale that is comparable to all others.

 

 

 

Simple Additive Weighting Method (SAW) - Simplest Method - #MCDM - Spearman Rank correlation