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The obvious analogy between an Objects × Properties binary relationship (called a formal context) and a binary Documents × Terms incidence matrix has led to a growing interest for the use of formal concept analysis (FCA) in information retrieval (IR). The main advantage of using FCA for IR is the possibility of creating a conceptual representation of a given document collection in the form of a lattice. Also, potentials of FCA for IR have been highlighted by a number of research studies since its inception. It turns out that almost all existing FCA-based IR approaches rely on: i) a Boolean Documents × Terms incidence matrix and, ii) the use of the classical Galois connection initially proposed by Wille. In such a case, there is no way for expressing weighted queries as well as there is no way for ranking query results that is usually done by query refinement or empirical navigation trough the concept lattice. In this paper we first enlarge the use of FCA for IR to the fuzzy setting which allows for a fuzzy incidence matrix and weighted queries. For instance, an incidence matrix may now allow for (normalized) numerical entries that may be achieved using the well known term frequency measure. Furthermore, it is worth noticing that in the existing approaches, user queries are restricted to the conjunctive form. Thus, another contribution consists in considering, in an original way, the use of other Galois derivation operators (namely the possibility, necessity and dual sufficiency) in order to express disjunction and negation in queries.