On basic conditions to generate multi-adjoint concept lattices via Galois connections

This paper introduces sufficient and necessary conditions with respect to the fuzzy operators considered in a multi-adjoint frame under which the standard combinations of multiadjoint sufficiency, possibility and necessity operators form (antitone or isotone) Galois connections. The underlying idea is to study the minimal algebraic requirements so that the concept-forming operators (defined using the same syntactical form than the extension and intension operators of multi-adjoint concept lattices) form a Galois connection. As a consequence, given a relational database, we have much more possibilities to construct concept lattices associated with it, so that we can choose the specific version which better suits the situation.