Accuracy of approximation operators during covering evolutions

We express our concern over two issues in this paper: one is which characters are foundational for multitudinous covering-based rough models as generalizations of Pawlak's rough sets, i.e., which properties of covering-based rough sets guarantee the consistency of them and Pawlak's over partitions; the other is how to utilize this equivalence in simplifying diverse covering-based approximation operators. We demonstrate that covering-based rough models are equivalent to Pawlak's on partitions if they satisfy granule selection principles, which are weaker than a combination of contraction, extension, monotonicity, addition and granularity. In order to take advantage of their equivalence, we illustrate a method named “covering evolution” to change granules from given coverings to corresponding partitions for covering-based approximation operators. The evolutions can be divided into three steps: at the beginning, coverings are transformed into 1-neighborhood systems based on some quintessential neighborhood operators, then in the middle, more-refined 1-neighborhood systems are built by using “cores” from general topology, and at last, core systems (in fact, partitions) are extracted from these more-refined 1-neighborhood systems. We lay a strong emphasis on the variations in accuracy of six representative covering-based approximation operators during three evolutions, two of which preserve the accuracy of approximation operators. The investigation carried on covering evolutions helps us to establish the corresponding mapping relationship from covering spaces to partition spaces directly, and therefore provides a convenient method for making choice of covering-based approximation operators as they are consistent with the classical Pawlak's rough sets over partitions.