# SJSU MATH 108 - TOPSIS (21 pages)

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## TOPSIS

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## TOPSIS

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Pages:
21
School:
San Jose State University
Course:
Math 108 - Introduction to Abstract Mathematics and Proofs

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1 Multi Criteria Decision Making TOPSIS METHOD TOPSIS METHOD Technique of Order Preference by Similarity to Ideal Solution This method considers three types of attributes or criteria Qualitative benefit attributes criteria Quantitative benefit attributes Cost attributes or criteria 2 TOPSIS METHOD In this method two artificial alternatives are hypothesized Ideal alternative the one which has the best level for all attributes considered Negative ideal alternative the one which has the worst attribute values TOPSIS selects the alternative that is the closest to the ideal solution and farthest from negative ideal alternative 3 Input to TOPSIS TOPSIS assumes that we have m alternatives options and n attributes criteria and we have the score of each option with respect to each criterion Let xij score of option i with respect to criterion j We have a matrix X xij m n matrix Let J be the set of benefit attributes or criteria more is better Let J be the set of negative attributes or criteria less is better 4 Steps of TOPSIS Step 1 Construct normalized decision matrix This step transforms various attribute dimensions into non dimensional attributes which allows comparisons across criteria Normalize scores or data as follows rij xij x2ij for i 1 m j 1 n i 5 Steps of TOPSIS Step 2 Construct the weighted normalized decision matrix Assume we have a set of weights for each criteria wj for j 1 n Multiply each column of the normalized decision matrix by its associated weight An element of the new matrix is vij wj rij 6 Steps of TOPSIS Step 3 Determine the ideal and negative ideal solutions Ideal solution A v1 vn where vj max vij if j J min vij if j J i i Negative ideal solution A v1 vn where v min vij if j J max vij if j J i i 7 Steps of TOPSIS Step 4 Calculate the separation measures for each alternative The separation from the ideal alternative is Si vj vij 2 i 1 m j Similarly the separation from the negative ideal alternative is S i vj vij 2 i 1 m j 8 Steps of TOPSIS Step 5

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