Analytic Hierarchy Process (AHP) - YouTube

hello today I am going to explain about a famous MCDM method known as AHP

that is analytic hierarchy process this method can be used to calculate

weights of criteria this is a simple decision matrix with four criteria that

is price, storage space, camera and looks with five alternative, each alternative

have their own value of criteria associated with them the first and

foremost step in AHP is creating the hierarchical structure in which goal is

kept in the first level in this example the goal is to buy the best mobile-phone

criteria is kept in the second level and alternative is kept in level three each

alternative have their own value of criteria associated with them example

each mobile phone will have their own price or cost associated with them

similarly each mobile phone will have their own value of storage space. Second

step is to create a pairwise comparison matrix. This pairwise matrix gives the

relative importance of various attribute with respect to the goal. If we take this

example how important is price while buying a mobile or what is the

importance of storage space when we buy mobile phone. This pairwise comparison

matrix is created with the help of scale of relative importance this is the scale

of relative importance in which one is for equal importance 3 is given for

moderate importance five for strong importance 7 for very strong 9 and

extremely important values

the length of pairwise matrix is equivalent to the number of criteria

used in decision making process here we have a 4x4 matrix as we have four

criteria that is price, storage space, camera and looks we will have a 4x4

matrix the value in the pairwise matrix depend upon the decision maker

or the person who want to buy the mobile phone what will be the value of this cell

for that some question should be asked to the person who is buying the

mobile phone how important is price or cost with

respect to storage space for a person like me price of cost is of a strong

importance than storage space if storage space is given X value then price or

cost will be given 5X value we can see here that for strong importance a value

of 5 is given now next what we have to do, we have to divide the row element by

the column element now here price is the row element and storage space is a

column element the storage space has became an x value and price as 5x so

here the value will be 5X divided by X which is equivalent to 5 here storage

space is given X value and price 5X so it will give 1/5.

For this particular

cell the question asked should be how important is price or cost with respect

to camera price or cost is of moderate to strong importance than camera so if

camera is given X value, price and cost will be given 4X value so we can also

take anything in intermediate between 3 & 5 that is of 4 importance that is

moderate to strong importance will be assigned a 4 value similarly we can

see here camera to price will be given 1/4 value. Now how important is

camera with respect to storage space camera is of equal to moderate

importance than storage space so if camera is given 2X value storage

space will be given X value so here we will get a value of 2 well vice versa

storage to camera will be given 1/2 value similarly we can assign values

to each cell you can see that the diagonal elements takes a value of one

because price will be of equal importance to price. The fractional value

has been converted to decimal value and the sum of each value is calculated that

is 1 + 0.2 + 0.25 + 0.14 will give 1.59.

Normalized

pairwise matrix is calculated all the elements of the column is divided by the

sum of the column here we can see that one is divided by one point five nine

point two is divided by one point five nine and so on this is the normalized

pairwise matrix, here I have calculated the criteria weights, the weights are

calculated by averaging all the elements in the row we have just added all these

elements and divided it with the number of criteria which will give the criteria

of weight next step is calculating the consistency that is to check whether the

calculated value are correct or not for this I have taken the same pairwise

comparison matrix which is not normalized I have multiplied each value

in the column with the criteria value so here you can see that one has been

multiplied by the criteria weight that is 0.6038

similarly 0.2 is the multiplied with the criteria 0.6038

similarly I have done it for all other values,

on solving we get this

matrix the weighted sum value is calculated by taking the sum of each

value in the row so we you can see that by adding all this term we will get the

weighted sum value just I have written the criteria weight next to the weighted

sum value, next we calculate this ratio of weighted sum value and criteria

weight now we calculate it for each row on solving we get this value now lambda

max is calculated by taking the average of all these values next we calculate

the consistency index CI which is given by the formula lambda max minus n upon n

minus 1 in this example n is 4 as we have four criteria finally we calculate

the consistency ratio which is given by dividing the consistency index with

random index (RI) random index is the consistency index of randomly generated

pairwise matrix I have shown the random index table for up to 10 criteria in our

example the random index for n equal to 4 is

0.90 so have just calculated the consistency ratio since

the value of consistency ratio CR is 0.037311

for the proportion of inconsistency CR is less than 0.10

which is the standard we can assume that our metrics is reasonably consistent so

we may continue with the process of decision making using AHP based on the

requirement of buyer these criteria weights can be used by

the decision maker for further calculation so you can see here that

price has been given 60 percent weighted storage space 13.65

percent weight-age camera 19.58 percent and looks a

weight-age of 6.46 percent thank you and have a nice day