On the Correctness of Rough-Set Based Approximate Reasoning

There is a natural generalization of an indiscernibility relation used in rough set theory, where rather than partitioning the universe of discourse into indiscernibility classes, one can consider a covering of the universe by similarity-based neighborhoods with lower and upper approximations of relations defined via the neighborhoods. When taking this step, there is a need to tune approximate reasoning to the desired accuracy. We provide a framework for analyzing self-adaptive knowledge structures. We focus on studying the interaction between inputs and output concepts in approximate reasoning. The problems we address are: -given similarity relations modeling approximate concepts, what are similarity relations for the output concepts that guarantee correctness of reasoning? -assuming that output similarity relations lead to concepts which are not accurate enough, how can one tune input similarities?