Study on the Necessity Operator to Factorize Formal Contexts in a Multi-adjoint Framework

Dubois and Prade have already shown that the necessity operator is helpful in the decomposition of Boolean data tables into independent sub-tables. In this paper, we carry out a preliminary study on the properties satisfied by the necessity operator to factorize formal contexts. We will see what properties this operator satisfies in the classical framework and how these properties are translated into more general frameworks, such as the fuzzy framework provided by the multi-adjoint paradigm.