How to Master Multi‑Criteria Decision Making for Comprehensive Evaluations

1 Comprehensive Evaluation Problem

Comprehensive evaluation problems refer to measuring several (similar) objects from multiple dimensions and aggregating these measurements into an overall score or ranking, e.g., comfort rankings of jobs, university rankings, coach performance rankings. In English literature these are called Multi‑criteria decision making or Multi‑attribute decision making.

The difficulty lies in competing indicators; balancing their importance is key.

Comprehensive evaluation models are among the most basic and frequently used models in mathematical modeling contests.

2 Elements of Evaluation Model

An evaluation system solves the evaluation problem and consists of five elements:

Evaluation object : the objects being assessed; assume there are n objects, denoted …

Evaluator : the individual or group performing the assessment.

Evaluation indicators : metrics used to measure attributes of the objects; typically a vector of m indicators, each reflecting a specific aspect.

Weight coefficients : quantify the relative importance of each indicator; the credibility of the final ranking depends heavily on reasonable weight determination.

Comprehensive model : a mathematical model that aggregates indicator values into a final score.

References for comprehensive evaluation research include:

Tzeng, Gwo‑Hshiung, and Jih‑Jeng Huang. Multiple attribute decision making: methods and applications . CRC Press, 2011.

Alinezhad, Alireza, and Javad Khalili. New methods and applications in multiple attribute decision making (MADM) . Springer, 2019.

Many academic papers also address evaluation problems; keywords such as “comprehensive evaluation model”, “multi‑criteria evaluation”, and “multi‑criteria decision making” are useful for literature searches.

3 Common Comprehensive Evaluation Methods

Classic and widely used evaluation models include:

TOPSIS

Rank‑sum ratio method

Grey relational analysis

Entropy weight method

Analytic hierarchy process (AHP)

Fuzzy evaluation method

Beyond model selection, attention should be paid to:

Indicator selection: choosing reasonable, representative, measurable attributes.

Data preprocessing: transforming raw data for comparability and consistency.

Model suitability: balancing simplicity, comprehensiveness, and implementation difficulty.

Result validation: performing sensitivity and robustness analysis to ensure model usability.

References

Wikipedia: https://en.wikipedia.org/wiki/Multiple-criteria_decision_analysis

ThomsonRen’s GitHub: https://github.com/ThomsonRen/mathmodels

司守奎，孙玺菁 Python数学实验与建模