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

1 TOPSIS Method

TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) is a widely used multi‑criteria decision analysis method, first proposed by C.L. Hwang and K. Yoon in 1981 and further developed in later years.

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

The basic process uses a normalized decision matrix to identify the optimal and worst alternatives, then computes distances of each alternative to these extremes, and finally ranks alternatives based on their relative closeness to the ideal solution.

This method imposes no strict requirements on data distribution or sample size and is simple to compute.

2 Basic Procedure

TOPSIS basic steps:

Step 1: Construct a decision matrix with m alternatives and n criteria, denoted as ...

Step 2: Normalize the matrix.

Step 3: Compute weighted normalized values.

Step 4: Determine the negative ideal solution (NIS) and positive ideal solution (PIS).

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

Step 6: Compute the similarity to the ideal solution.

Step 7: Rank the alternatives based on the similarity scores.

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). "A framework for the selection of the right nuclear power plant". International Journal of Production Research. 50 (17): 4753–4766.

ThomsonRen github https://github.com/ThomsonRen/mathmodels