By far the clearest practical explanation of AHP. Now I have to go back to the math behind for a more complete and exhaustive understanding of this powerful MCDA technique.
To those who wondered about where the values from C came from, she mentioned matrix [C] on track 7:00 in her previous video, AHP Part 1 (remember, it's NOT the normalized one). Just take that matrix MINUS the sum-row, multiplicate it with vector [W] and you will get Ws. Another thing is thank you so much for your time, Ma'am! I have seen both Part 1 and 2 and could not find any AHP-video better than this!
@@zainabal-baldawi9768 She started explaining matrix C from 4:00 in AHP Part 1. You choose the numbers in this matrix yourself based on your own evaluation of two and two of the criteria. She's categorized the levels of criterium importance into three right below matrix C, so here you can understand why she chose certain numbers in C. She chose Mfg Cost to be moderately more important than Mat Cost with 3.00, thus Mat Cost is moderately less important than Mfg Cost with 0.33. So actually you only need to choose numbers half of C and use this to calculate the rest of C, so 1/3.00 = 0.33. Work with the number 1s standing diagonally in C and divide by the number below it to get number to the right of it. For checking, do the reverse which is multiplying 1 with the number to the right of it to get the number below it. You may have to draw one vertical line and one horizontal line through the numbers below and to the right of 1 in C to see clearer. You'll see the diagonal pattern because the criteria stand in the same order vertically downwards and horizontally rightward. Is this clear, Ms. Allawi?
Hi Gloria, thank you very much for explaining!!! I spent a lot of time by Saathy readings, but You saved me hours of work, really. Thank you very much!
A very comprehensive illustration of the AHP method. May I ask you how to incorporate the input of more than one respondents in the method? Moreover, if you could guide use on multi-level AHP problem, it will be a great favor to the research community. Please consider replying this at your earliest convience. Thanks
ah, I was distracted by the rounding issues calculating the {consist} part!! With only the values for {W} shown in Part 1 (with 3 decimals) and those in {Ws} the results of {consist} are slightly different than those shown in the Video. (might be helpful for someone stuck at the same point) But other than that, this is really helpful to get to understand the logic behind the whole process. THANK YOU! :)
I'm lost where you multiplied the pairwise comparisons with the criteria weights. Please can you show how you multiplied [C] with {W} to calculate the (Ws)? Thanks.
+Olayinka Abikoye You can do this for 1st row of [C] (not normalized [C])(1.000x0.047 + 0.333x0.079 + 0.200x0.124 + 0.111x0.445 + 0.143x0.272 + 3.000x0.033) = 0.286. Keep going and you will fill the rest elements of vector {Ws}. In EXCEL, you can use function =MMULT(1.000:3.000,0.047:0.033) as well (where 1.000:3.000 and 0.047:0.033 are the array of row and column respectively) and it will produce the same result.
Thank you very much for this series .. The last step after transposing, how , was the weightage applied/ multiplied to rows, to arrive at the final results to decide Riveting. Thanks
Hadi, to multiply two matrices [A] X [B] in Excel, first make sure that the number of columns in A is = to the rows in B. Assume [A] is m x n and [B] is n x k. Drag out an area in Excel that is m x k (rows, columns)--that m x k space will be for the product of [A] x [B], say [C]. In the formula bar, type =mmult( and then drag over the cells where the values of A are stored. Add a comma after the last cell of the first matrx in the mmult function appears. Next drag over the area where the values of B are stored then add a right parenthesis to the close off the mmult function. The formula bar will look something like this: =mmult(A1:c3, e1:j6). A would be stored in A1:C3 and B would be stored in E1:j6). Next hold down the keys at the same time and hit enter. The m x k matrix, matrix [C] will appear in the area you drug over that occupies a space of m x k. There should be plenty of UA-cam videos that will show you how to perform matrix multiplication using Matlab or Excel. Hope this helps you get started.
Hi, I have some problem understanding Ws and Consistency vector mentioned in UA-cam video AHP1&2. In the videos of AHP1 & 2, the formula to calculate Ws is C x W And the values of Ws of material costs given in AHP2 are 0.286, 0.515, 0.839, 3.090, 1.908, 0.210 The value of C of material costs before normalized are 1, 0.333, 0.2, 0.111, 0.143, 3 In AHP1, the W of material cost is 0.047 If I calculate based on the above values, the values of Ws would be 0.047, 0.156, 0.0094, 0.005217, 0.006721, 0.141 The values of Ws calculated are very different from the values of Ws provided in AHP2. Is my calculation correct? Also, if Ws = C x W, and {Consis} = dot product of Ws x 1/W Then isn’t that {Consis} = C x W x 1/W = C Would like to seek for help in clarifying the above.
I am having little problem in calculation in random index I didnot understand how do i calculate it. suppose If i have 7*7 matrix then what is value or if i have 8*8 matrix then how does i calculate it.
Gloria Starns Hi Gloria! I have done so. I'm just having a problem in getting the C to calculatethe Ws in the formula: Ws = [C]{W}. Could you please explain?
Itchell, You need to drag out an area in the spread sheet that will be the resulting size of Ws. Ws will be a column vector with n rows in it. For example: if [C] is n x n {W} should be n X 1; {Ws} will be n rows x 1 column. 1. drag out an area in the spreadsheet that is n x 1. This area will be where the values for {Ws} are computed. 2. Go to the formula bar and type =mmult(. and drag over the contents of the C matrix 3. Add a comma after the cell range in the mmult function The formula will now look something like this =mmult(B8:D11, B8:D11 would be the cell range occupied by the matrix [C] 4. now drag over the range that {W} is in 5. The formula will now look like =mmult(b8:D11, E8:E11 add a right parenthesis 6. now hit ctrl-shift-enter and {Ws} elements will be determined in the area you drug over in order to store {Ws}
Gloria Starns Hi, thanks a lot for these explanations. But I'm confused with the dot product of Ws and (1/W) you discuss around 3:30. A dot product of two same sized vectors should return a scalar, no?
The consistency index is given by (lambda-n)/(n-1) where lambda is the largest eigenvalue of the pairwise consistency matrix. n is the number of items being compared. If the matrix is perfectly consistent, lambda will be = n and the consistency index will be 0.0. Perfect consistency, or a consistency index of 0.0 is the smallest consistency index expected; a negative consistency index would not have meaning in the context of AHP. Some people even use an approximation of the consistency index using square roots of functions which clearly would not produce negative numbers.
Hi maam, could you please share a citation for the formulas, for thesis purposes only. And also I have a question regarding with the C matrix, can anybody show me how did she multiplied the C with W to calculate the (Ws)? Thank you so much :)
Hi Marcos, I think it is instructive for people trying to understand AHP to create their own code. The Excel spreadsheet is for a particular example and is for use by the students completing my class. So, I am not willing to share the spreadsheet.
![Lp. Сердце Вселенной #60 РОЖДЕНИЕ ЛОЛОЛОШКИ [Финал] • Майнкрафт](http://i.ytimg.com/vi/YoR0pAV9FVQ/mqdefault.jpg)
By far the clearest practical explanation of AHP. Now I have to go back to the math behind for a more complete and exhaustive understanding of this powerful MCDA technique.
To those who wondered about where the values from C came from, she mentioned matrix [C] on track 7:00 in her previous video, AHP Part 1 (remember, it's NOT the normalized one). Just take that matrix MINUS the sum-row, multiplicate it with vector [W] and you will get Ws.
Another thing is thank you so much for your time, Ma'am! I have seen both Part 1 and 2 and could not find any AHP-video better than this!
Please, could you explain more with example (w* first value how she calculated it )in same her example if possible how she calculate the C
@@zainabal-baldawi9768 She started explaining matrix C from 4:00 in AHP Part 1. You choose the numbers in this matrix yourself based on your own evaluation of two and two of the criteria. She's categorized the levels of criterium importance into three right below matrix C, so here you can understand why she chose certain numbers in C. She chose Mfg Cost to be moderately more important than Mat Cost with 3.00, thus Mat Cost is moderately less important than Mfg Cost with 0.33. So actually you only need to choose numbers half of C and use this to calculate the rest of C, so 1/3.00 = 0.33. Work with the number 1s standing diagonally in C and divide by the number below it to get number to the right of it. For checking, do the reverse which is multiplying 1 with the number to the right of it to get the number below it. You may have to draw one vertical line and one horizontal line through the numbers below and to the right of 1 in C to see clearer. You'll see the diagonal pattern because the criteria stand in the same order vertically downwards and horizontally rightward.
Is this clear, Ms. Allawi?
By now the best video in explaning this topic clearly and understandable out of about 5 others I watched, great work!
Hi Gloria, thank you very much for explaining!!! I spent a lot of time by Saathy readings, but You saved me hours of work, really. Thank you very much!
After searching for a while, this is the best video which helped me understand AHP
Thank You!
part 2 done . thank you for the explanation . glad I didn't click on wrong video . easy to understand :)
once again, thank you.
how do we find the table at 9:49 i mean where do we get those 1,1 and 3 numbers in columns
How and where did you find the value of [C] to determine {Ws}?
A very comprehensive illustration of the AHP method. May I ask you how to incorporate the input of more than one respondents in the method? Moreover, if you could guide use on multi-level AHP problem, it will be a great favor to the research community.
Please consider replying this at your earliest convience.
Thanks
ah, I was distracted by the rounding issues calculating the {consist} part!!
With only the values for {W} shown in Part 1 (with 3 decimals) and those in {Ws} the results of {consist} are slightly different than those shown in the Video. (might be helpful for someone stuck at the same point)
But other than that, this is really helpful to get to understand the logic behind the whole process. THANK YOU! :)
Great video, but how did you come up with the final values for welds, rivets, casting?
Thank you, the explanation was very clear and easy to understand
I'm lost where you multiplied the pairwise comparisons with the criteria weights.
Please can you show how you multiplied [C] with {W} to calculate the (Ws)?
Thanks.
+Olayinka Abikoye You can do this for 1st row of [C] (not normalized [C])(1.000x0.047 + 0.333x0.079 + 0.200x0.124 + 0.111x0.445 + 0.143x0.272 + 3.000x0.033) = 0.286. Keep going and you will fill the rest elements of vector {Ws}. In EXCEL, you can use function =MMULT(1.000:3.000,0.047:0.033) as well (where 1.000:3.000 and 0.047:0.033 are the array of row and column respectively) and it will produce the same result.
You sir, have saved the day. 11 Months on and your comment is still very much appreciated! Thanks
Canh-Toan Nguyen Thanks for the explanation
Thanks, your explanation was very helpful!
Excellent video
do you know how she came up with final values for welds rivets casting?
Thank you so much.. regards from India
Thank you very much for this series .. The last step after transposing, how , was the weightage applied/ multiplied to rows, to arrive at the final results to decide Riveting. Thanks
Very helpful video ..thanks
Hadi, to multiply two matrices [A] X [B] in Excel, first make sure that the number of columns in A is = to the rows in B. Assume [A] is m x n and [B] is n x k. Drag out an area in Excel that is m x k (rows, columns)--that m x k space will be for the product of [A] x [B], say [C]. In the formula bar, type =mmult( and then drag over the cells where the values of A are stored. Add a comma after the last cell of the first matrx in the mmult function appears. Next drag over the area where the values of B are stored then add a right parenthesis to the close off the mmult function. The formula bar will look something like this: =mmult(A1:c3, e1:j6). A would be stored in A1:C3 and B would be stored in E1:j6). Next hold down the keys at the same time and hit enter. The m x k matrix, matrix [C] will appear in the area you drug over that occupies a space of m x k. There should be plenty of UA-cam videos that will show you how to perform matrix multiplication using Matlab or Excel. Hope this helps you get started.
Where I can find the spreadsheet of this data because it make me confuse in second part that what data you used for the [C] *[W]
when you find out, please let me know... I am so confused what you used from the C matrix X Weighted Sum from W to get the Ws.
Yep where do you get the figure of C
Hi could you please share a citation for the formulas used to derive the weights sum vectors and the consistency vectors? THANK YOU !
Why do you transpose the final rating matrix?
Hi,
I have some problem understanding Ws and Consistency vector mentioned in UA-cam video AHP1&2.
In the videos of AHP1 & 2, the formula to calculate Ws is C x W
And the values of Ws of material costs given in AHP2 are
0.286, 0.515, 0.839, 3.090, 1.908, 0.210
The value of C of material costs before normalized are
1, 0.333, 0.2, 0.111, 0.143, 3
In AHP1, the W of material cost is 0.047
If I calculate based on the above values, the values of Ws would be
0.047, 0.156, 0.0094, 0.005217, 0.006721, 0.141
The values of Ws calculated are very different from the values of Ws provided in AHP2. Is my calculation correct?
Also, if Ws = C x W, and {Consis} = dot product of Ws x 1/W
Then isn’t that {Consis} = C x W x 1/W = C
Would like to seek for help in clarifying the above.
Thanks a lot mam..Really helpful
I am having little problem in calculation in random index I didnot understand how do i calculate it. suppose If i have 7*7 matrix then what is value or if i have 8*8 matrix then how does i calculate it.
Hi maam, do you have reference book for this? What is your reference method in getting the Eigenvalue?
Hello. I got negative CR value with CR = -0.94. Does it make sense or how can i interpret it. Thank you.
very clear discussion thanks
Can you please share how to calculate a multi level AHP problem...a working example of the same would be great
did u found any solution? if so please share
Any reference for the materials in the video ?
Hi! Where can I find the spreadsheets?
Hi Itchell,
You will have to create your own spreadsheet--the process of doing that will help you better understand AHP.
Gloria Starns Hi Gloria! I have done so. I'm just having a problem in getting the C to calculatethe Ws in the formula: Ws = [C]{W}. Could you please explain?
Itchell,
You need to drag out an area in the spread sheet that will be the resulting size of Ws. Ws will be a column vector with n rows in it. For example: if [C] is n x n {W} should be n X 1; {Ws} will be n rows x 1 column.
1. drag out an area in the spreadsheet that is n x 1. This area will be where the values for {Ws} are computed.
2. Go to the formula bar and type =mmult(. and drag over the contents of the C matrix
3. Add a comma after the cell range in the mmult function
The formula will now look something like this =mmult(B8:D11,
B8:D11 would be the cell range occupied by the matrix [C]
4. now drag over the range that {W} is in
5. The formula will now look like =mmult(b8:D11, E8:E11 add a right parenthesis
6. now hit ctrl-shift-enter and {Ws} elements will be determined in the area you drug over in order to store {Ws}
Gloria Starns Hi, thanks a lot for these explanations. But I'm confused with the dot product of Ws and (1/W) you discuss around 3:30. A dot product of two same sized vectors should return a scalar, no?
+Gloria Starns Gloria, could you please provide some references for the material presented in the video ?
How did you calulated Ws= [c].w??? how to find value of [C] its a matrix
how to set the Ws column
and RI ??
thank you mam for the simplification.
is it OK to get "Consistency Index" CI in minus!!?
The consistency index is given by (lambda-n)/(n-1) where lambda is the largest eigenvalue of the pairwise consistency matrix. n is the number of items being compared. If the matrix is perfectly consistent, lambda will be = n and the consistency index will be 0.0. Perfect consistency, or a consistency index of 0.0 is the smallest consistency index expected; a negative consistency index would not have meaning in the context of AHP. Some people even use an approximation of the consistency index using square roots of functions which clearly would not produce negative numbers.
ok i'll try to recalculate it again.. thank you very much for ur answer
Hi maam, could you please share a citation for the formulas, for thesis purposes only. And also I have a question regarding with the C matrix, can anybody show me how did she multiplied the C with W to calculate the (Ws)? Thank you so much :)
Hi, did you find an answer to this on how she got the "Ws"? What did she multiply the "W" with?
Dear Ma'am, May I know how I could input data from many experts in AHP?
WHAT IS A DIFFERENT BETWEEN PRIORITYVECTOR AND EIGEN VECTOR
How to calculate the value of [C].... Various users are confused.... Please clarify it
Could you share the spreadsheet?
Hi Marcos,
I think it is instructive for people trying to understand AHP to create their own code. The Excel spreadsheet is for a particular example and is for use by the students completing my class. So, I am not willing to share the spreadsheet.
Well, thanks for explaining your reasons...
duuude you're cool. anyway what is [C]?
could you pleas show us how to multiply 3 by 6 matrix in excel? or on mat lab?
thank you so much
Très intéressant Génial
thank u mam
THANK YOU MAM
Hi, How do I derive [C] ? ? ?
It's the matrix she started with in part 1. Not normalized