Handling missing values in rough set analysis of multi-attribute and multi-criteria decision problems

Rough sets proved to be very useful for analysis of decision problems concerning objects described in a data table by a set of condition attributes and by a set of decision attributes. In practical applications, however, the data table is often not complete because some data are missing. To deal with this case, we propose an extension of the rough set methodology. The adaptation concerns both the classical rough set approach based on indiscernibility relations and the new rough set approach based on dominance relations. While the first approach deals with multi-attribute classification problems, the second approach deals with multi-criteria sorting problems. The adapted relations of indiscernibility or dominance between two objects are considered as directional statements where a subject is compared to a referent object having no missing values. The two rough set approaches handling the missing values boil down to the original approaches when the data table is complete. The rules induced from the rough approximations are robust in a sense that each rule is supported by at least one object with no missing values on condition attributes or criteria used by the rule.