Characterizing reducts in multi-adjoint concept lattices

The construction of reducts, that is, minimal sets of attributes containing the main information of a database, is a fundamental task in different frameworks, such as in Formal Concept Analysis (FCA) and Rough Set Theory (RST). This paper will be focused on a general fuzzy extension of FCA, called multi-adjoint concept lattice, and we present a study about the attributes generating meet-irreducible elements and on the reducts in this framework. From this study, we introduce interesting results on the cardinality of reducts and the consequences in the classical case.