The proliferation index (PI) is crucial in histopathologic diagnostics, in particular tumors. It is calculated based on Ki-67 protein expression by immunohistochemistry. PI is routinely evaluated by a visual assessment of the sample by a pathologist. However, this approach is far from ideal due to its poor intra- and interobserver variability and time-consuming. These factors force the community to seek out more precise solutions. Virtual pathology as being increasingly popular in diagnostics, armed with artificial intelligence, may potentially address this issue. The proposed solution calculates the Ki-67 proliferation index by utilizing a deep learning model and fuzzy-set interpretations for hot-spots detection. The obtained region-of-interest is then used to segment relevant cells via classical methods of image processing. The index value is approximated by relating the total surface area occupied by immunopositive cells to the total surface area of relevant cells. The achieved results are compared to the manual calculation of the Ki-67 index made by a domain expert. To increase results reliability, we trained several models in a threefold manner and compared the impact of different hyper-parameters. Our best-proposed method estimates PI with 0.024 mean absolute error, which gives a significant advantage over the current state-of-the-art solution.

In this research, we introduce a classification procedure based on rule induction and fuzzy reasoning. The classifier generalizes attribute information to handle uncertainty, which often occurs in real data. To induce fuzzy rules, we define the corresponding fuzzy information system. A transformation of the derived rules into interval type-2 fuzzy rules is provided as well. The fuzzification applied is optimized with respect to the footprint of uncertainty of the corresponding type-2 fuzzy sets. The classification process is related to a Mamdani type fuzzy inference. The method proposed was evaluated by the F-score measure on benchmark data.

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