Multi-Criteria Decision-Making Methods and Applications

Multi-Criteria Decision-Making (MCDM) encompasses a suite of mathematical and analytical tools designed to support complex decisions involving multiple, often conflicting criteria. At its core, MCDM requires the construction of a decision matrix in which alternatives are evaluated against criteria that may span quantitative measures (cost, performance, risk) and qualitative attributes (social impact, stakeholder preference). Key steps include criteria weighting, data normalisation and aggregation of performance scores. Classic methods such as the Weighted Sum Model and Simple Additive Weighting remain popular for their transparency, while distance-based techniques like TOPSIS identify solutions closest to an ideal reference. More recent developments have introduced multi-method frameworks that harmonise outputs from several MCDM models to increase reliability and account for methodological sensitivity. Applications range from selecting renewable energy technologies and optimising supply-chain networks to urban planning, healthcare prioritisation and environmental management. In an era of heightened sustainability awareness, MCDM frameworks guide policy designers and industry leaders in balancing economic, ecological and social objectives, ensuring that decisions remain robust under uncertainty and adaptable to evolving data.

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Recent investigations have refined the theoretical underpinnings of MCDM by demonstrating equivalences among several established models. A 2024 study introduced a unified Multi-Method Model (3M) that shows the Weighted Sum Model, MABAC, TOPSIS (L1) and the Ratio System yield identical rankings when calibrated via a Relative Performance Indicator. This work offers a streamlined framework for combining methods and enables direct aggregation of heterogeneous ratings through stepwise linear transformations.

Comparative assessments continue to inform method selection. A 2023 analysis contrasted TOPSIS and Simple Additive Weighting under various distance metrics, revealing that TOPSIS with Manhattan distance closely mirrors SAW rankings. Such insights clarify conditions under which more complex distance-based approaches confer added value over straightforward additive models.

Meanwhile, practical evaluations of decision frameworks have highlighted both merits and limitations of simpler techniques. A 2024 review of the SMART method underscored its ease of implementation in technology choice, healthcare system design and environmental planning, while noting potential biases in weight assignment and the need for integration with more sophisticated models to capture decision intricacies.

Multi-Criteria Decision-Making Methods and Applications publication trend

The graph below shows the total number of articles in multi-criteria decision-making methods and applications across all publications each year (not limited to Nature Index journals).

Technical terms

Decision matrix: A tabular representation of alternatives evaluated against multiple criteria.

Normalisation: A process of scaling criterion scores to a common basis to enable fair aggregation.

Aggregation function: A mathematical rule that combines normalised criterion scores into a single performance index for each alternative.

Weighted Sum Model (WSM): An additive approach that multiplies each criterion’s normalised score by its weight and sums the results.

TOPSIS: Technique for Order Preference by Similarity to Ideal Solution, which ranks alternatives by their proximity to an ideal and distance from a nadir point.

SMART: Simple Multi-Attribute Rating Technique, an intuitive value-function-based method for scoring and ranking options.

References

1. "Thin" Structure of Relations in MCDM Models. Equivalence of the MABAC, TOPSIS(L1) and RS Methods to the Weighted Sum Method. Decision Making Applications in Management and Engineering (2024).
2. A comparison between TOPSIS and SAW methods. Annals of Operations Research (2023).
3. Using SMART Method for Multi-criteria Decision Making: Applications, Advantages, and Limitations. Archives of Advanced Engineering Science (2024).