Graded polygons of opposition in fuzzy formal concept analysis

Quantifier-based operators are fuzzy quantifiers that are, similarly to the intermediate quantifiers, based on the evaluative linguistic expressions not small, very big and extremely big. This article focuses mainly on achieving two goals. Firstly, quantifier-based operators are introduced to create extended fuzzy concept lattices that capture more detailed information from datasets compared to the existing ones. Then, graded extensions of Aristotle's square, named polygons of opposition, are constructed using quantifier-based operators. Our results highlight new connections between three different research areas: the theory of evaluative linguistic expressions, fuzzy formal concept analysis, and the studies on Aristotle's square.1