Rough Set Learning of Preferential Attitude in Multi-Criteria Decision Making

Rough set theory is a useful tool for analysis of decision situations, in particular multi-criteria sorting problems. It deals with vagueness in the representation of decision maker's (DM's) preferences, caused by granularity of the representation. Using the rough set approach, it is possible to learn a set of sorting rules from examples of sorting decisions made by the DM. The rules involve a minimum number of most important criteria and they do not correct vagueness manifested in the preferential attitude of the DM; instead, produced rules are categorized into deterministic and non-deterministic. The set of sorting rules explains a decision policy of the DM and may be used to support next sorting decisions. The decision support is made by matching a new case to one of sorting rules; if it fails, a set of the ‘nearest’ sorting rules is presented to the DM. In order to find the ‘nearest’ rules a new distance measure based on a valued closeness relation is proposed.