Theory and applications of granular labelled partitions in multi-scale decision tables

A new approach of optimal scale selection to multi-scale decision tables

“…For example, Harvard University is located at Cambridge 1 in a finer granule compared to Boston University, or at Massachusetts in a fine granule compared to Yale University, or at New England 2 in a coarse granule compared to Duke University, or at the United States in a coarser granule compared to University of Oxford. In [46,47] , such information tables are called multi-scale information tables (MSITs). For a given subset of attributes, two different levels of scales may induce a kind of granules being either a refinement or a coarsening of the others, which is the main difference between SSIT and MSIT.…”

“…Namely, we usually consider and analyze knowledge at the optimum level of granularity [47] . In [46] , Wu and Leung introduced the notion of multi-scale decision tables (MSDTs) from the perspective of GrC and analyzed the knowledge acquisition in MSDTs under different levels of granulations. In [47] , Wu and Leung mainly studied optimal scale selection for multi-scale decision tables with an assumption that each attribute is granulated with the same number of levels of granulations.…”

Multigranulation rough set: A multiset based strategy

“…For instance, in Qian et al's classical multigranulation rough set approach, the target is approximated through a set of partitions; Yang et al 52 and Xu et al 43 presented the multigranulation fuzzy rough set through a family of fuzzy relations, respectively; Lin et al 14 presented the neighborhood multigranulation rough set by using a family of neighborhoods, i.e. neighborhood system 53 ; Khan and Banerjee 12 introduced the concept of the multiple-source approximation systems, which are multigranulation fusions of Pawlak's approximation spaces; Abu-Donia 1 studied the rough approximations based on multi-knowledge; Wu and Leung 40 investigated the multi-scale information system, which reflects the explanation of same problem at different scales (levels of granulations); Dou et al 4 integrated variable precision rough set 56 with multigranulation rough sets; She et al 39 studied the algebraic structure of multigranulation rough set.…”

Multigranulation decision-theoretic rough sets in incomplete information systems

“…Multigranulation rough sets have received more attention from many researchers. Wu and Leung [28] proposed a formal approach to granular computing with multiscale data measured at different levels of granulations, and studied theory and applications of granular labelled partitions in multi-scale decision information systems. Xu et al [30] applied multigranulation rough sets to order information systems.…”