General Characterization of Classifications in Rough Set on Two Universal Sets

Abstract

Rough set was conceptualized to deal with indiscernibility or imperfect knowledge about elements in numerous real life scenarios. But it was noticed later that an information system may establish relation with more than one universe. So, rough set on one universal set was further extended to rough set on two universal sets. This paper presents eleven possible types of classifications on the whole and it is proved that out of those eleven types only five types which were hypothesized by are elementary and the rest six types can be reduced to the elementary five types either directly or transitively. This paper also analyzes to predict the all possible combinations of types of elements for a classification of 2 and 3 numbers of elements. It is established that, the number of classification with 2 elements is 3 whereas with 3 elements is 8 instead of 64.