Mastering Grey Relational Analysis: Step-by-Step Guide for Multi-Criteria Evaluation

Grey Relational Analysis

Consider a comprehensive evaluation problem with multiple objects and indicators. The observed values of the indicators form the basis for analysis.

The specific steps of Grey Relational Analysis are as follows:

(1) Preprocess the evaluation indicators by unifying them (transform all into large‑type indicators) and nondimensionalizing, then construct the evaluation matrix.

(2) Determine the comparison sequence (evaluation objects) and the reference sequence (evaluation standard). The comparison sequence consists of the normalized indicator vectors of each evaluation object. The reference sequence represents a virtual best evaluation object, often denoted as the ideal values for each indicator.

(3) Compute the grey relational coefficient. The coefficient measures the relationship between the comparison sequence and the reference sequence for each indicator, incorporating a discrimination coefficient (usually denoted ρ) and the minimum and maximum differences between the sequences.

(4) Calculate the grey relational degree. The formula aggregates the relational coefficients across all indicators, weighted by each indicator’s importance. If weights are not predetermined, equal weights can be assumed. This yields the grey relational degree of each evaluation object relative to the ideal object.

(5) Perform evaluation analysis. Objects are ranked according to their grey relational degrees; a larger degree indicates a better evaluation result.

Reference

Si Shou‑kui, Sun Xi‑jing. Python Mathematics Experiments and Modeling