Bireducts with tolerance relations

Reducing the number of attributes by preventing the occurrence of incompatibilities and eliminating existing noise in the original data is an important goal in different frameworks, such as in those focused on modelling and processing incomplete information in information systems. Bireducts were introduced in Rough Set Theory (RST) as one of successful solutions for the problem aimed at achieving a balance between elimination of attributes and characterization of objects that the remaining attributes can still distinguish. This paper considers bireducts in a general framework in which attributes induce tolerance relations over the available objects. In order to compute the new reducts and bireducts a characterization based on a general discernibility function is given.