Attribute Reduction for Set-Valued Ordered Fuzzy Decision System

Attribute reduction for set-valued ordered fuzzy decision system that considers attributes with preference-ordered domains and fuzzy decision attributes is investigated. Firstly, a δ-dominance relation is proposed, and δ-dominance relation-based rough fuzzy set model is defined for set-valued ordered fuzzy decision system. Then, judgment theorem of attribute consistent set is derived, and attribute reduction approach based on the 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 results.