Research on Fuzzy Order Variable Precision Rough Set Over Two Universes and Its Uncertainty Measures

Aiming at the problem that the U-X V-type double-domain rough set can't deal with fuzzy data in the past, this paper firstly established the variable precision rough set model on the basis of U-X V-type double-domain rough set,and made an in-depth study on the upper approximation set and the lower approximation set of this model. Then the variable precision rough set model of U-X V-type double-domain fuzzy order information system is established by introducing the U-X V-type double-domain fuzzy dominance relation, and its related properties are discussed.The uncertainty measures are studied by defming the U-X V-type double-domain fuzzy order precision rough set roughness and rough entropy. The conclusions are that as the precision threshold increases, its roughness and roughness entropy decrease gradually. These conclusions are verified by an example, which provides a theoretical basis for further revealing the uncertainty measure law of U-X V-type double-domain fuzzy order variable precision rough set. (C) 2019 The Authors. Published by Elsevier Ltd.