How to Convert Diverse Evaluation Metrics into a Unified Large-Scale Indicator

1 Metric Standardization

Metric standardization means unifying the direction of evaluation indicators. For example, if a smaller value yields a higher score, we transform it so that larger values correspond to higher scores.

In an evaluation indicator system, there may be extremely large, extremely small, centered, and interval-type indicators, each with distinct characteristics. When different types coexist, they are often standardized before comprehensive evaluation.

For instance, all indicators can be converted to extremely large indicators; the common practice is to transform non‑extremely‑large indicators into extremely large ones.

2 Converting Small Indicators to Large Indicators

For an extremely small indicator, taking its reciprocal converts it into an extremely large indicator.

Alternatively, a translation transformation can be applied.

Other monotonicity‑preserving transformations are also possible.

3 Converting Centered Indicators to Large Indicators

For a centered indicator, apply a translation and scaling to shift it into an extremely large indicator.

4 Converting Interval Indicators to Large Indicators

For an interval indicator, values within the optimal interval are best; the farther the value from the interval, the worse. By appropriate translation, the interval indicator can be transformed into an extremely large indicator.

5 Summary

This article presented three methods for converting small, centered, and interval indicators into extremely large indicators for metric standardization.

References

ThomsonRen https://github.com/ThomsonRen/mathmodels

司守奎，孙玺菁 Python数学实验与建模