Now you’ll weight the sub-criteria according to the weights of the main criteria the complete results will look like this. As a result, you will get the percentages as shown here. Again you arrange the result of that comparison in the matrix and compute the normalized principal eigenvector of the matrix. In total, because you have 5 criteria, you need to do 10 comparisons. Pink compared to green, in your opinion pink is being 3 times better than green and so on. Now you make the same pairwise comparison for the sub-criteria, in this case, the different colors.įor example, you compare the pink color and the blue color, you think pink is 2 times nicer than blue so you put a 2. So the most important criteria are memory followed by delivery followed by color. Colour- 17 percent, Memory- 43 percent ,and Delivery- 40 percent. From this matrix, you compute the normalized principal eigenvector.Īs a result, you get the following weighting. In the next step, you’ll arrange your comparisons into a matrix as shown in this image. Memory and delivery are equally important in your opinion, so you put in a 1. Then you compare the color with delivery you say delivery is 2 times more important than color then you get the result as 1/2. You compare the color with memory and in your opinion memory is 3 times more important than color so on the scale you will have 1/3. 1/9 means memory is 9 times more important than color. 9 means criteria color is 9 times more important than memory. 1 means both criteria have the same importance and they are equal. You start to compare the color with memory and you are using a scale ranging from 9 to 1/9. So in the first step, you have to compare the criteria, color, memory, and delivery. You then have to compare all elements pairwise concerning the objective. To each criterion, you have sub-criteria, the color, the memory space, and the delivery times. The objective is to buy the gadget and your criteria are color, memory, and delivery time. Now in the first step, you structure the elements in groups of criteria, sub-criteria, and alternatives. 2 models with a price of $120 and 2 models with a price of $150. The memory space ranges from 8GB to 64GB and the delivery time is immediate or 5 days, or 4 weeks.Ĥ models are available as shown here. The colors pink, blue, green, and black are available. The criteria are the colors of the model, the memory, and the delivery time. Your objective is to buy a gadget like a smartphone or MP3 player. Then you can evaluate the alternatives according to the weighing and get a ranking. In each group, you make a pairwise comparison of elements and calculate the weighing and consistency ratio. First, you have to define your objective, Then you have to structure the elements in groups of criteria, sub-criteria, and alternatives. The ratio scales result from eigenvectors and the consistency index from the eigenvalue. So, The method is based on the solution often an eigenvalue problem. As an import, you can use actual measurements like price, weights, and so on or subjective opinions like satisfactory feelings or preferences, and as an output, you will get ratio scales and a consistency index. It also allows some small inconsistency in judgment. The method is to derive ratio scales from paired comparisons. Saaty, later partnering with Ernest Forman developed the Expert Choice in 1983. Saaty suggested the AHP for the first time and revolutionized the studies of MCDM. the Analytical Hierarchy Process.Īlso, The AHP or Analytical Hierarchy Process is an organized strategy for arranging and breaking down complex choices, based on arithmetic and brain research.Īs said in Wikipedia, in the 1970s Thomas L. Now the question is how to derive the weights, For this, a mathematical method is available which is called AHP, i.e. When you combine individual performance indicators to one key performance indicator you can give each one a different weight.
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