Grey Relational Analysis MATLAB Implementation

Grey Relational Analysis is a method that treats factor values of research objects and influencing factors as points on a line, comparing them with curves generated from factor values of unidentified objects and their influencing factors. The method quantitatively assesses the proximity between these curves, calculating relational degrees that represent the closeness between various influencing factors of research objects and unidentified objects. By comparing the magnitudes of these relational degrees, we can determine the impact level of unidentified objects on research objects. The MATLAB implementation typically involves key steps: data normalization to eliminate dimensional differences, calculation of absolute differences between reference and comparison sequences, determination of grey relational coefficients using resolution coefficients, and finally computing the grey relational degree through weighted averaging. Common functions used include data preprocessing with z-score or min-max normalization, vectorized operations for efficient difference calculations, and matrix operations for handling multiple sequences simultaneously. Furthermore, Grey Relational Analysis enables deeper understanding of relationships between research objects and unidentified objects. By analyzing comparative relational degrees, researchers can draw more detailed conclusions and perform comprehensive analyses of both research and unidentified objects. The algorithm's strength lies in its ability to handle incomplete information systems and small sample sizes typical in grey system theory. Therefore, Grey Relational Analysis serves as a valuable tool in research, facilitating better understanding of inter-object relationships and providing more accurate conclusions through systematic numerical analysis. The MATLAB implementation allows for customizable resolution coefficients, flexible weighting schemes, and visualization capabilities for result interpretation.