Dominance-based rough set approach to case-based reasoning

Case-based reasoning is a paradigm in machine learning whose idea is that a new problem can be solved by noticing its similarity to a set of problems previously solved. We propose a new approach to case-based reasoning. It is based on rough set theory that is a mathematical theory for reasoning about data. More precisely, we adopt Dominance-based Rough Set Approach (DRSA) that is particularly appropriate in this context for its ability of handling monotonicity relationship between ordinal properties of data related to monotonic relationships between attribute values in the considered data set. In general terms, monotonicity concerns relationship between different aspects of a phenomenon described by data: for example, "the larger the house, the higher its price" or "the closer the house to the city centre, the higher its price". In the perspective of case-based reasoning, we propose to consider monotonicity of the type "the more similar is y to x, the more credible is that y belongs to the same set as x". We show that rough approximations and decision rules induced from these approximations can be redefined in this context and that they satisfy the same fundamental properties of classical rough set theory.