Fuzzy linguistic summaries and the double negation property

In this contribution, we formalize the general case of linguistic summaries with multiple summarizers and qualifiers. We extend the definitions present in the literature to handle cases in the following form: Q R1 ⋆. .. ⋆ R k y's are P1 ⋄. .. ⋄ P l where ⋆, ⋄ ∈ {AND, OR}. Moreover, we study the consistency of fuzzy summaries, focusing mainly on the double negation property (DN). We consider different negations for linguistic quantifiers and show which can be used for preserving the DN property.