Valued Dominance-Based Rough Set Approach to Incomplete Information System
In this paper, we present an explorative research focusing on dominance–based rough set approach to the incomplete information systems. In most of the rough set literatures, an incomplete information system indicates an information system with unknown values. By assuming that the unknown value can be compared with any other values in the domain of the corresponding attributes, the concept of the valued dominance relation is proposed to show the probability that an object is dominating another one. The fuzzy rough approximations in terms of the valued dominance relation are then constructed. It is shown that by the valued dominance–based fuzzy rough set, we can obtain greater lower approximations and smaller upper approximations than the old dominance–based rough set in the incomplete information systems. Further on the problem of inducing “at least” and “at most” decision rules from incomplete decision system is also addressed. Some numerical examples are employed to substantiate the conceptual arguments.
KeywordsDominance Relation Decision System Decision Class Multicriteria Decision Analysis Indiscernibility Relation
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