Rough Fuzzy Set Model for Set-Valued Ordered Fuzzy Decision System

The classical rough set theory can not be directly used to reduce knowledge in set-valued ordered fuzzy decision system. Firstly, we propose a dominance relation-based rough fuzzy set model in set-valued ordered fuzzy decision system, and some important properties are investigated. Then, based on rough fuzzy set, the definitions of approximation consistent set and assignment consistent set are given. Judgment theorems of approximation consistent set and assignment consistent set are also obtained, meanwhile, attribute reduction approach based on discernibility matrices is proposed to eliminate redundant attributes that are not essential from the view of fuzzy decisions. Finally, an example is given to illustrate the effectiveness of the proposed method.