Incomplete Multigranulation Based on Rough Intuitionistic Fuzzy Sets

Rough set theory introduced by Pawlak [8] is based on equivalence relations. 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 [10], where the set approximations are defined by using multi-equivalences on the universe and their properties were investigated. Using hybridization of fuzzy set [20] with rough set the concept of fuzzy rough set was introduced by Dubois and Prade [2]. Recently, Fuzzy Rough Set Model Based on Multi-Granulation is introduced and studied by Wu and Kou [18]. Topological properties of rough sets introduced by Pawlak in terms of their types were recently studied by Tripathy and Mitra [16]. These were extended to the context of incomplete multi granulation by Tripathy and Raghavan [17]. In this paper we introduce incomplete multigranulation on intuitionistic fuzzy rough sets, study their basic properties and extend the topological properties in [17] to this context. Our findings are true for both complete and incomplete intuitionistic fuzzy rough set models based upon multi granulation. Keywords— Rough Sets, Fuzzy rough sets, Intuitionistic Fuzzy Rough Sets, type of rough sets, multi granular fuzzy rough sets and multigranular intuitionistic fuzzy rough sets.