General Characterization of Classifications in Rough Set on Two Universal Sets

General Characterization of Classifications in Rough Set on Two Universal Sets

Tapan Kumar Das (School of Information Technology and Engineering, VIT University, Vellore, India), Debi Prasanna Acharjya (School of Computing Sciences and Engineering,VIT University, Vellore, India) and Manas Ranjan Patra (Department of Computer Science, Berhampur University, Brahmapur, India)
Copyright: © 2015 |Pages: 19
DOI: 10.4018/IRMJ.2015040101
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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.
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2. Foundations Of Rough Sets

Real time data contains uncertainties. Therefore, paying no attention to it often leads to the failure of system. Traditional statistical tools overlook these uncertainties and, therefore, lack in accuracy. Computational intelligence techniques such as artificial neural networks, evolutionary algorithms, fuzzy sets, rough sets etc. consider these uncertainties and deal with them specifically. Fuzzy set of Zadeh (1965) is the first successful method that captures impreciseness in information. On the other hand, rough set of Pawlak (1982) capture indiscernibility among objects to model imperfect knowledge. The basic definition of rough sets is based upon the approximation of a set by a pair of sets known as lower and upper approximation.

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