Generalized quantifiers in formal concept analysis

Abstract

Usually, datasets contain imprecise data (noise), which can produce unsuspected results on the considered mappings. For instance, this can happen with the infimum and supremum operators, since both operators are straightforwardly associated with the universal and existencial quantifiers, respectively. An interesting possibility, of decreasing the impact of this possible noise in the final results, is the consideration of generalized quantifiers. This paper introduces four kinds of generalized quantifiers based on adjoint triples, which generalize the current approaches to a more flexible framework. Different properties and characterizations are studied and they have been applied to formal concept analysis, presenting the conjunctive and implicative concept-forming operators in this outstanding theory.