Replacing standard confusion matrix with overestimates and underestimates for ordinal classification problems

In multiclass classification problems, the standard confusion matrix is typically replaced by a series of confusion matrices, each corresponding to a specific class (or decision variable in MCDM literature). The ordinal classification problems differ from multiclass classification, but they share the same performance metrics as used in multiclass classification. We argue that ordinal classification has unique characteristics that set it apart from other classification. In ordinal classification, the concepts of false positive and false negatives are replaced by overestimates and underestimates. We suggest using different mathematical operators to measure the extent of overestimates and underestimates. The proposed metrics, designed for ordinal classifiers,<br/>not only introduce a new evaluation framework but also represent a significant advancement in the performance assessment of ordinal classification algorithms.