Maintenance of approximations in incomplete ordered decision systems while attribute values coarsening or refining

Approximations in rough sets theory are important operators to discover interesting patterns and dependencies in data mining. Both certain and uncertain rules are unraveled from different regions partitioned by approximations. In real-life applications, an information system may evolve with time by different factors such as attributes, objects, and attribute values. How to update approximations efficiently becomes vital in data mining related tasks. Dominance-based rough set approaches deal with the problem of ordinal classification with monotonicity constraints in multi-criteria decision analysis. Data missing frequently appears in the Incomplete Ordered Decision Systems (IODSs). Extended dominance characteristic relation-based rough set approaches process the IODS with two cases of missing data, i.e., "lost value" and "do not care". This paper focuses on dynamically updating approximations of upward and downward unions while attribute values coarsening or refining in the IODS. Under the extended dominance characteristic relation based rough sets, it presents the principles of dynamically updating approximations w.r.t. attribute values' coarsening and refining in the IODS and algorithms for incremental updating approximations of an upward union and downward union of classes. Comparative experiments from datasets of UCI and empirical results show the proposed method is efficient and effective in maintenance of approximations. (C) 2012 Elsevier B.V. All rights reserved.