Some Algebraic Properties of Multigranulations and an Analysis of Multigranular Approximations of Classifications
Bala Krushna Tripathy, R. S. Raghavan · International Journal of Information Technology and Computer Science · 2013
Ever since the introduction of rough sets by Pawlak as a model to capture uncertainty, it has drawn much attention fro m both theoretical and application point of view.Classifications of universes play very important roles in several fields of study.The study of rough definability of classifications was initiated by Busse.The properties of approximations of classifications were established in the form of four theorems and were used to define the types of classifications.These results were generalised to develop two theorems of necessary and sufficient type were established by Tripathy et al , fro m wh ich several results including the four theorems of Busse could be derived as corollaries.Recently, rough sets based on Multigranulation were introduced and studied by Qian et al.Also, it has been extended to include incomp lete informat ion systems.Many of these results are extended to the mult igranular cases.In this paper, we extend the properties of types of classifications to the mu ltigranular context.Also, we introduce some parameters like the accuracy of approximat ion and the quality of appro ximat ion of classifications with respect to Multigranulations.We have obtained interesting criteria under which both types of Multigranulations reduce to single granulation.Also, some algebraic properties of Multigranulations are derived.