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With aim of detecting breast cancer at the early stages using mammograms, this study presents the formulation of five feature types by extending the information set to encompass the concept of an intuitionist fuzzy set. The resulting pervasive information set gives not only the certainty of the pixel intensities of mammograms to a class but also the deficiency in the fuzzy modeling referred to as the hesitancy. The generalized adaptive Hanman Anirban fuzzy entropy function is shown to be equivalent to the hesitancy entropy function. The probability-based fuzzy Hanman transform and the pervasive Information with probability taking the role of hesitancy degree help derive the above five feature types termed as probability-based pervasive Information set features. The effectiveness of each feature type is demonstrated on the mini-MIAS and DDSM databases for the multi-class categorization of mammograms using the Hanman transform classifier. The statistical analysis by ANOVA test proves that the features are statistically significant and the experimental results are shown to be clinically relevant by the expert radiologists. The performance of the five feature types is either superior to or equal to that of some deep learning architectures on comparison but they outperform the state-of-the-art literature methods in the classification of breast cancer using mammograms.

Formulation of probability-based pervasive information set features and Hanman transform classifier for the categorization of mammograms