Generalized probabilistic approximations of incomplete data

• We discuss a generalization of probabilistic approximations.
• We propose global and local probabilistic approximations.
• Approximations are compared experimentally using 16 data sets.
• The best approach should be selected individually.
• We found that the number of distinct probabilistic approximations is limited.

In this paper we discuss a generalization of the idea of probabilistic approximations. Probabilistic (or parameterized) approximations, studied mostly in variable precision rough set theory, were originally defined using equivalence relations. Recently, probabilistic approximations were defined for arbitrary binary relations. Such approximations have an immediate application to data mining from incomplete data because incomplete data sets are characterized by a characteristic relation which is reflexive but not necessarily symmetric or transitive. In contrast, complete data sets are described by indiscernibility which is an equivalence relation.The main objective of this paper was to compare experimentally, for the first time, two generalizations of probabilistic approximations: global and local. Additionally, we explored the problem how many distinct probabilistic approximations may be defined for a given data set.