Mastering Evaluation Models: From TOPSIS to Entropy‑AHP for Decision‑Making

1 Evaluation Models

2020 A problem “The Best Summer Job” is a typical evaluation (or comprehensive decision) problem. An evaluation problem measures multiple similar objects across several dimensions, aggregates these measures, and produces an overall score or ranking. The difficulty lies in balancing competing indicators.

Summer jobs like office clerk, teaching assistant, or sales clerk each have distinct features; we assess them holistically rather than focusing on a single aspect. Evaluation models provide the mathematical framework for such problems.

Evaluation problems consist of five elements:

Evaluation object : the alternatives being assessed (e.g., various jobs).

Evaluator : the individual or group performing the assessment (the modeling team).

Evaluation indicators : metrics that capture attributes of the objects; multiple indicators describe different aspects of the system.

Weight coefficients : quantitative representation of each indicator’s relative importance.

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

2 Common Evaluation Models

Classic and frequently used models include:

TOPSIS

Rank Sum Ratio

Grey Relational Analysis

Entropy Weight Method

Analytic Hierarchy Process (AHP)

Fuzzy Evaluation Method

TOPSIS integrates data, entropy weight and AHP handle weight determination, and fuzzy evaluation refines imprecise information. These methods are common in HiMCM competitions and were prominent in the 2020 award‑winning papers.

Beyond model selection, attention must also be paid to:

Indicator selection – choosing representative, measurable attributes.

Data preprocessing – transforming raw data for consistency and comparability.

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

2.1 Composite Indicators

Abstract indicators such as “fatigue”, “distance”, or “difficulty” are often hard to quantify directly. Instead, concrete factors (e.g., work content, location, required education) are combined to form composite indicators like “job difficulty”. This synthesis makes the model more feasible and user‑friendly.

Smaller, concrete indicators are easier to obtain data for, and a model essentially aggregates these sub‑indicators into higher‑level metrics.

The purpose of composite indicators is not to complicate the problem but to make the model more practical by using easily measurable inputs.

2.2 Combining Evaluation Models

Different models have distinct strengths; they can be combined. For example, entropy weight can determine indicator weights, which are then fed into TOPSIS (where all indicators share the same weight). This yields an “Entropy‑TOPSIS” (ETOPSIS) or “modified TOPSIS” model, representing a micro‑innovation. The 2020 A problem award‑winning paper 10549 used entropy weight and AHP averaged together to balance subjective and objective weights.

Paper 10701 combined AHP and TOPSIS:

2.3 Merging Evaluation Models with Other Models

Beyond internal combinations, evaluation models can be paired with different model types. For instance, after building an evaluation model, one could incorporate a predictive model (e.g., classification or clustering) to recommend top‑scoring jobs, similar to recommendation systems in apps. Introducing such cross‑model innovation can make a solution stand out.

Finally, while classic evaluation model workflows are clear, rigidly applying a single method limits creativity. Each problem has unique traits; understanding and exploiting these nuances leads to more suitable and distinctive models.

Materials Download

The papers mentioned can be obtained by replying with the following codes in the public account chat:

2020A10549 and 2020A10701