A necessary and sufficient condition for two relations to induce the same definable set family
This addresses a fundamental issue in relation-based rough sets, providing a theoretical foundation for the field, but it is incremental as it builds on existing work in generalized rough sets.
The paper tackles the problem of determining when two relations in generalized rough sets induce the same definable set family, presenting a necessary and sufficient condition based on the closure of relations.
In Pawlak rough sets, the structure of the definable set families is simple and clear, but in generalizing rough sets, the structure of the definable set families is a bit more complex. There has been much research work focusing on this topic. However, as a fundamental issue in relation based rough sets, under what condition two relations induce the same definable set family has not been discussed. In this paper, based on the concept of the closure of relations, we present a necessary and sufficient condition for two relations to induce the same definable set family.