Dual rough approximations in possibilistic information systems

Rough sets have been examined in possibilistic information systems where attribute values are expressed by normal possibility distributions. Like incomplete information systems, rough approximations, which consist of lower and upper approximations, are essentially dual. Rough approximations are derived from dealing with certain rough approximations as well as possible ones that are lower and upper bounds of the actual rough approximations, respectively. In the case of rough approximations for a set of discernible objects. certain and possible rough approximations are linked with each other. Furthermore, we show rough approximations where objects in a set approximated have possibilistic information. This enables us to obtain rough approximations between arbitrary sets of attributes in possibilistic information systems. Each object comprising possible rough approximations possibly supports rules. On the other hand, all objects comprising certain rough approximations do not certainly support rules. Only objects with single values for attributes related with rough approximations certainly support rules.