Approximate distribution reducts in inconsistent interval-valued ordered decision tables
Many methods based on the rough set theory to deal with information systems have been proposed in recent decades. In practice, some information systems are based on dominance relations and may be inconsistent because of various factors. Moreover, taking the imprecise evaluations and assignments in the description of objects into account, single-valued information systems have been generalized to interval-valued information systems. In this paper, by introducing a dominance relation to interval-valued ordered information systems, we establish a dominance-based rough set approach, which is mainly based on substitution of the indiscernibility relation by the dominance relation. To extract the minimal decision rules, approximate distribution reducts are proposed in inconsistent interval-valued ordered decision tables. This paper presents a theoretical method based on the discernibility matrix to enumerate all reducts and a practical approach on the basis of significance to find one reduct. And two equivalent definitions of approximate distribution reducts are also introduced. In addition, numerical examples are employed to examine the validity of the approaches proposed in this paper.
inconsistent interval-valued ordered decision tables dominance-based rough sets attribute reduct discernibility matrix approach rule acquisition