STRUCTURAL ANALYSIS OF PESSIMISTIC MULTI-GRANULATION NANO GENERALIZED TOPOLOGICAL SPACES

Resumo

In this paper, we mainly investigate the pessimistic multi-granulation nano-generalized topological structures of multi-granulation rough sets, which are created by constructing partitions for a universe set. Firstly, we introduce the concept of pessimistic multi-granulation nano-generalized topological spaces. Then, we discuss the relationships between multi-granulation approximation spaces and pessimistic multi-granulation nano-generalized topological spaces. Concretely, a family of equivalence relations can induce the pessimistic multi-granulation nano generalized topological space such that the pessimistic multi-granulation nano generalized interior (closure) operator is the pessimistic multi-granulation lower (upper) approximation operator induced by this family of equivalence relations, respectively. Conversely, the pessimistic multi-granulation nano generalized interior (closure, respectively) operator derived from the pessimistic multi-granulation nano generalized topological space is just the pessimistic multi-granulation lower (upper, respectively) approximation operator derived from a multi-granulation approximation space under some conditions.