Roughness of a vague set

Abstract — Both rough sets theory and vague sets theory are emerging as powerful tool for managing uncertainty, incomplete and imprecise information. An integration between vague sets theory and rough sets theory is developed in this paper. We con-struct the lower and upper approximation operators of a vague set in the universe, which is partitioned by an indiscernibility relation. Furthermore, a parameterized roughness measure of a vague set is given followed by an analysis of its properties