Relative Reduction of Incomplete Interval-valued Decision Information Systems Associated with Evidence Theory

Relative reduction is regarded as a significant problem in rough set theory, which needs to eliminate some attributes that are not required in information system. Dempster-Shafer evidence theory is a serviceable means to explore uncertain information. This article establishes rough set model in incomplete interval-valued decision information system (IIDIS). Belief (plausibility) function is introduced for studying relative belief (plausibility) reduction in IIDIS. We aim to study several relative reductions based on evidence theory and explore relations among different relative reductions in the consistent/inconsistent IIDIS via four importance degrees. Relative reduction is not only equivalent to relative belief reduction but also equivalent to relative plausibility reduction in the consistent IIDIS. In the inconsistent IIDIS, relative plausibility consistent set can conclude it be deemed as relative belief consistent set, not vice versa. Furthermore, the feasibility about presented theorems are verified by several experiments from six UCI data set.