Divide and conquer in granular computing topological partitions

Divide and conquer are classical problem solving strategy. Implicitly the divide is a mathematical partitioning; no overlapping is allowed. However, in practices the divide cannot be very clean; some degree of overlapping is unavoidable. A binary granulation, which is a granulation defined by a binary relation, is not a partition; so overlapping does exist. However, by looking at the problem skillfully a binary granulation can be interpreted as a topological partition. By a topological partition is a partition in which each equivalence class has a neighborhood. These neighborhoods do overlap. So a granulation is a "topological divide and conquer".

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