Fuzzy formal concept analysis, Evaluative linguistic expressions, Square of opposition, Polygons of opposition, Lukasiewicz algebra

Quantifier-based operators are fuzzy quantifiers that are, similarly as the intermediate quantifiers, based on the evaluative linguistic expressions not small, very big and extremely big. This article focuses mainly on achieving two goals. %in two directions. In this article, they are mainly introduced to achieve a twice goal. Firstly, quantifier-based operators are introduced to create extended fuzzy concept lattices that, compared to the existing ones, capture more detailed information from datasets. Then, graded extensions of Aristotle's square, named polygons of opposition, are constructed by 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.