Some concepts of incomplete multigranulation based on rough intuitionistic fuzzy sets

Abstract

The definition of basic rough sets depends upon a single equivalence relation defined on the universe or several equivalence relations taken one each taken at a time. In the view of granular computing, classical rough set theory is based upon single granulation. The basic rough set model was extended to rough set model based on multi-granulations (MGRS) in [6], where the set approximations are defined by using multi-equivalences on the universe and their properties were investigated. Using the hybridized rough fuzzy set model introduced by Dubois and Prade [2], rough fuzzy set model based on multi-granulation is introduced and studied by Wu and Kou [15]. Topological properties of rough sets introduced by Pawlak in terms of their types were recently studied by Tripathy and Mitra [11]. These were extended to the context of incomplete multi granulation by Tripathy and Raghavan [12]. Recently, the concept of multi-granulations based on rough fuzzy sets by Tripathy and Nagaraju [13]. In a recent paper, Tripathy et al [14] introduced the concept of incomplete multigranulation on rough intuitionistic fuzzy sets (MGRIFS) and studied some of its topological properties. In this paper we continue further by introducing the concept of accuracy measures on MGRIFS and prove some of their properties. Our findings are true for both complete and incomplete intuitionistic fuzzy rough set models based upon multi granulation. The concepts and results established in [13] and [14] open a new direction in the study of multigranulation for further study. © 2012 Springer-Verlag GmbH.