Mastering TOPSIS: A Step‑by‑Step Guide to Multi‑Criteria Decision Making

1 TOPSIS Method

TOPSIS (full name: Technique for Order Preference by Similarity to an Ideal Solution) is a commonly used comprehensive evaluation method that fully utilizes the information of the original data, and its results can accurately reflect the differences among evaluation schemes. It was first proposed by C.L. Hwang and K. Yoon in 1981, further developed by K. Yoon in 1987, and later refined by Hwang, Lai and Liu in 1993.

TOPSIS is based on the idea that the selected alternative has the shortest geometric distance to the positive ideal solution (PIS) and the longest distance to the negative ideal solution (NIS).

Based on the normalized original data matrix, first identify the best and worst alternatives, then calculate the distances of each evaluation object to the best and worst alternatives, obtaining a relative closeness to the best alternative, which serves as the basis for evaluating superiority.

The method imposes no strict restrictions on data distribution or sample size, and the calculations are simple and easy to perform.

2 Basic Process

TOPSIS method basic process is as follows

Step 1: Create an evaluation matrix containing m evaluation objects and n evaluation criteria; the value of the j‑th criterion for the i‑th object is denoted as a ij , and the matrix is denoted as X.

Step 2: Perform normalization of the matrix.

Step 3: Compute the weighted normalized values.

Step 4: Determine the negative ideal solution (NIS) and the positive ideal solution (PIS). Identify which criteria are benefit (larger‑the‑better) and which are cost (smaller‑the‑better) indicators.

Step 5: Calculate the Euclidean (L2) distance of each evaluation object to the NIS and to the PIS.

Step 6: Compute the similarity to the ideal solution: the similarity equals 1 when the object equals the PIS and 0 when it equals the NIS.

Step 7: Rank the evaluation objects based on the similarity values.

3 Summary

This article introduced the concept and basic procedure of the TOPSIS method.

References

https://en.wikipedia.org/wiki/TOPSIS

Locatelli, Giorgio; Mancini, Mauro (2012-09-01). "A framework for the selection of the right nuclear power plant". International Journal of Production Research. 50 (17): 4753–4766. doi:10.1080/00207543.2012.657965. ISSN 0020-7543.

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