ADVANCED INFORMATION ON MULTIPLE-GRANULATION APPROXIMATION SPACES

To define the optimistic multiple-granulation(OMG) supra interior operator i n t R A and the OMG-supra closure operator c l R A associated with a set A in a multiple-granulation approximation space, we used the concepts of the OMG-lower set O L Σ m i = 1 R i ( A ) and the OMG-upper set O U Σ m i = 1 R i ( A ) . These operators establish an approximate topological space referred to as optimistic multiple-granulation supra topological spaces. Additionally, we introduce the concepts of OMG-supra-open and OMG-supra-closed approximation sets, as well as OMG-supra-continuous and OMG-irresolute approximations.