Multi-adjoint fuzzy rough sets: Definition, properties and attribute selection

•An extension of fuzzy rough sets is introduced: multi-adjoint fuzzy rough sets.•A family of adjoint pairs are used to compute the lower and upper approximations.•Our model allows to represent preferences among the objects in a decision system.•We have verified mathematical properties of the model.•We have discussed attribute reduction in the proposed general framework.

This paper introduces a flexible extension of rough set theory: multi-adjoint fuzzy rough sets, in which a family of adjoint pairs are considered to compute the lower and upper approximations. This new setting increases the number of applications in which rough set theory can be used. An important feature of the presented framework is that the user may represent explicit preferences among the objects in a decision system, by associating a particular adjoint triple with any pair of objects.Moreover, we verify mathematical properties of the model, study its relationships to multi-adjoint property-oriented concept lattices and discuss attribute selection in this framework.