Getting knowledge from massive data is nowadays a primary challenge for information processing. The goal of knowledge discovery from data describing decision situations is to help making better decisions. One of the difficulties in knowledge discovery is a vague character of data due to inconsistency. The Dominance-based Rough set Approach (DRSA) is a methodology for reasoning about vague data, which handles monotonic relationships between values of condition and decision attributes, typical for data describing decision situations. The origin of the vagueness is inconsistency due to violation of the dominance principle which requires that (assuming a positive monotonic relationship) if object x has an evaluation at least as good as object y on all condition attributes, then it should not get evaluation worse than y on all decision attributes. We show that DRSA is a natural continuation of the Pawlak’s concept of rough set, which builds on the ideas coming from Leibniz, Frege, Boole, Łukasiewicz and Zadeh. We also show that the assumption admitted by DRSA about the ordinal character of evaluations on condition and decision attributes is not a limiting factor in knowledge discovery from data. In particular, it is an obvious assumption in decision problems, like multicriteria classification or ranking, multiobjective optimization, and decision under risk and uncertainty. Moreover, even when the ordering of data seems irrelevant, the presence or the absence of a property can be represented in ordinal terms, because if two properties are related, the presence, rather than the absence, of one property should make more (or less) probable the presence of the other property. This is even more apparent when the presence or the absence of a property is graded or fuzzy, because in this case, the more credible the presence of a property, the more (or less) probable the presence of the other property. This observation leads to a straightforward hybridization of DRSA with fuzzy sets. Since the presence of properties, possibly fuzzy, is the base of information granulation, DRSA can also be seen as a general framework for granular computing. We also comment on stochastic version of DRSA, and on algebraic representations of DRSA, as well as on topology for DRSA.
References
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