How to Master Multi‑Criteria Decision Making for Comprehensive Evaluations

1 Comprehensive Evaluation Problem

Comprehensive evaluation problems refer to situations where, among several (similar) objects, multiple dimensions are measured and the measurements are combined to produce an overall score or ranking, such as comfort rankings of jobs, university rankings, or coach performance rankings. Many foreign literature call these multi‑attribute decision making or multi‑criteria decision making (MADM).

The difficulty lies in the competition among indicators; balancing their importance and integrating them is crucial.

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

2 Elements of an Evaluation Model

An evaluation system consists of the following five elements:

Evaluation Object : the objects being assessed. Suppose there are n evaluation objects, denoted as ...

Evaluator : the individual or group that evaluates the objects.

Evaluation Indicators : metrics used to measure attributes of the objects. Typically, a problem involves multiple indicators, each representing a different aspect of the system. An indicator vector can be used, where each component reflects the state of an object on a particular side.

Weight Coefficients : quantitative representations of the relative importance of each indicator. Once object and indicator values are fixed, the overall evaluation result depends on the chosen weights; reasonable weight determination directly affects the credibility of the results and the correctness of the final decision. Weights should be set carefully according to established methods and principles.

Comprehensive Model : a mathematical model that aggregates the indicator values into a quantified overall score, serving as the basis for the final evaluation.

For further study, refer to books such as:

Tzeng, G.-H., & Huang, J.-J. Multiple Attribute Decision Making: Methods and Applications . CRC Press, 2011.

Alinezhad, A., & Khalili, J. New Methods and Applications in Multiple Attribute Decision Making (MADM) . Springer, 2019.

Many excellent academic papers also address evaluation problems; learners can search keywords like "comprehensive evaluation model", "multi‑criteria evaluation", or "multi‑criteria decision making".

3 Comprehensive Evaluation Methods

Classic and commonly used evaluation models include:

TOPSIS

Rank Sum Ratio Method

Grey Relational Analysis

Entropy Weight Method

Analytic Hierarchy Process (AHP)

Fuzzy Evaluation Method

In addition to model selection, attention should be paid to:

Indicator selection: choose reasonable, representative, and measurable attributes.

Data preprocessing: transform raw data to meet model requirements and ensure comparability.

Model suitability: different models have different characteristics; select based on problem specifics rather than pursuing overly complex methods.

Result verification and comparison: conduct sensitivity and robustness analyses 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