On the Correctness of Rough-Set Based Approximate Reasoning - Doherty, Patrick; Szałas, Andrzej (Rough Sets and Current Trends in Computing, 2010)
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?