On Approximate Equivalences of Multigranular Rough Sets and Approximate Reasoning
Bala Krushna Tripathy, Anirban Mitra · International Journal of Information Technology and Computer Science · 2013
The notion of rough sets introduced by Pawlak has been a successful model to capture impreciseness in data and has numerous applications.Since then it has been extended in several ways.The basic rough set introduced by Pawlak is a single granulation model fro m the granular co mputing point of view.Recently, this has been extended to two types of mu ltigranular rough set models.Pawlak and Novotny introduced the notions of rough set equalities which is called appro ximate equalities.These notions of equalities use the user knowledge to decide the equality of sets and hence generate approximate reasoning.However, it was shown by Tripathy et al, even these notions have limited applicab ility to incorporate user knowledge.So the notion of rough equivalence was introduced by them.The notion of rough equalities in the mu ltigranulation context was introduced and studied.In this article, we introduce the concepts of mu ltigranular rough equivalences and establish their properties.Also, the replacement properties, which are obtained by interchanging the bottom equivalences with the top equivalences, have been established.We provide a real life examp le for both types of multigranulat ion, compare the rough mult igranular equalit ies with the rough mult igranular equivalences and illustrate the interpretation of the rough equivalences through the example.