A three-way confirmatory approach to formal concept analysis in classification

Formal concept analysis (FCA) has demonstrated its effectiveness in classification through various studies. A few types of FCA-based classifiers, such as rule-based, concept-cognitive-learning-based, and hypothesis-based models, have been introduced for different purposes and distinct contexts. Nevertheless, these diverse models share fundamental principles that underlie the construction of effective FCA-based classifiers. This study contributes to the field in at least two aspects. Firstly, we present a general framework of FCA-based classification by reviewing, reformulating, and generalizing the existing models. The framework consists of four essential steps: intent learning, intent grouping, rule induction, and rule application. Secondly, following the presented framework, we integrate Bayesian confirmation theory and propose a novel three-way confirmatory approach to FCA-based classification. The proposed approach provides a fresh lens of formulating, analyzing, and interpreting results from FCA-based classifiers. Moreover, this approach can also be used to re-interpret existing hypothesis-based models, potentially leading to new insights and advancements in the field. The integration of Bayesian confirmation theory enriches the theoretical foundation of FCA-based classifiers, fostering the exploration of promising avenues for future research and development.