Dynamic and Discernibility Characteristics of Different Attribute Reduction Criteria

We investigate different notions of decision superreducts, their interrelations, their way of dealing with inconsistent data and their so-called discernibility characteristics. We refer to superreducts understood as attribute subsets that are aimed at maintaining – when compared to original sets of attributes – unchanged rough set approximations of decision classes, positive regions and generalized decision values. We also include into our studies superreducts that maintain the same data-driven conditional probability distributions (known as rough membership functions), as well as those which let discern all pairs of objects belonging to different decision classes that are also distinguishable using all available attributes. We compare strengths of the corresponding attribute reduction criteria when applied to the whole data sets, as well as families of their subsets (which is an idea inspired by so-called dynamic reducts). We attempt to put together mostly known mathematical results concerning the considered criteria and prove several new facts to make overall picture more complete. We also discuss about importance of developing attribute reduction criteria for inconsistent data sets from the perspectives of machine learning and knowledge discovery.