Flexible categorization using formal concept analysis and Dempster-Shafer theory

Based on the intuitive idea that sets of objects or entities can be categorized in very different ways, and that some ways to categorise objects are better than others, depending on the purpose of the categorization, in this paper, a formal framework is introduced for parametrically generating a space of possible categorizations of a set of objects, based on the features which individual agents or groups thereof regard as relevant (formally encoded in the notion of interrogative agenda ). This formal framework accounts both for two-valued (crisp), and for many-valued (fuzzy) judgments about the relevance of given features, and introduces ways to aggregate individual agendas to group agendas. As an application on this framework, we discuss a machine-learning meta-algorithm for outlier detection and classification which provides local and global explanations of its results. • Parametric framework to generate categorization systems aligned with agent goals and knowledge stance. • Formal model of interrogative agendas with crisp and fuzzy importance judgments for feature relevance. • Operators to aggregate individual agendas into coherent group-level prioritization of categories. • FCA-based foundation for hierarchical, explainable, and uncertainty-aware categorization structures. • Meta-algorithm that learns agendas for classification, outlier detection, and explainable decision-making.