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Intuitionistic Fuzzy Dominance-based Rough Set Approach: Model and Attribute Reductions

The dominance--based rough set approach plays an important role in the development of the rough set theory. It can be used to express the inconsistencies coming from consideration of the preference--ordered domains of the attributes. The purpose of this paper is to further generalize the dominance--based rough set model to fuzzy environment. The constructive approach is used to define the intuitionistic fuzzy dominance--based lower and upper approximations respectively. Basic properties of the intuitionistic fuzzy dominance--based rough approximations are then examined. By introducing the concept of approximate distribution reducts into intuitionistic fuzzy dominance--based rough approximations, four different forms of reducts are defined. The judgment theorems and discernibility matrixes associated with these reducts are also obtained. Such results are all intuitionistic fuzzy generalizations of the classical dominance--based rough set approach. Some numerical examples are employed to substantiate the conceptual arguments.