Articles tagged: TOPSIS

TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) is an MCDM method that ranks alternatives by measuring how far each one sits from the best possible outcome and the worst possible outcome. The idea is straightforward: the alternative closest to the ideal solution and farthest from the negative-ideal solution wins. Hwang & Yoon (1981) introduced the method as part of a broader treatment of multiple-attribute decision-making, and it has since become one of the most widely applied techniques in the field.

We describe the algorithm from a high-level perspective. First, the raw decision matrix is normalised so that criteria measured on different scales become comparable. Each criterion is then multiplied by its weight, reflecting its relative importance. From the weighted matrix, two reference points are identified: the ideal solution $A^+$ (the best value attainable on each criterion) and the negative-ideal solution $A^-$ (the worst). For each alternative $A_i$, the Euclidean distances $d_i^+$ and $d_i^-$ to these two reference points are computed, and the final ranking is determined by a closeness coefficient $C_i = d_i^- / (d_i^+ + d_i^-)$, which ranges from 0 (worst) to 1 (best). Lai, Liu & Hwang (1994) later extended TOPSIS from the discrete multi-attribute setting to continuous multi-objective programming problems.

In many real-world problems, criterion values are imprecise or expressed as verbal judgements rather than exact numbers. Fuzzy TOPSIS addresses this by replacing crisp values with fuzzy sets or linguistic variables. Chen (2000) proposed an influential extension using triangular fuzzy numbers to handle the vagueness in group decision-making, allowing experts to express preferences as “good”, “fair”, or “poor” rather than forcing a precise score. Since then, a large body of work has built on these foundations. Behzadian et al. (2012) surveyed the TOPSIS literature from 2000 to 2012, documenting its spread into supply chain management, engineering design, manufacturing, business, and health and safety.

Because TOPSIS compresses all criteria into a single distance measure, it can be sensitive to the addition or removal of alternatives, a phenomenon known as rank reversal. Methods like TODIM were developed partly as a response to this limitation, replacing geometric distance with pair-wise dominance comparisons grounded in prospect theory. That said, TOPSIS remains popular for its computational simplicity and intuitive geometric interpretation. It is a natural starting point for anyone working with multi-criteria decision-making problems, and continues to be extended and refined across disciplines.