A new fuzzy ranking method using fuzzy preference relations

In this paper, a new fuzzy ranking method for both type-1 and interval type-2 fuzzy sets (FSs) using fuzzy preference relations is proposed. The use of fuzzy preference relations to rank FSs with vertices has been introduced, and successfully implemented to undertake fuzzy multiple criteria hierarchical group decision-making problems. The proposed fuzzy ranking method is an extension of the results published in [1], and it is able to rank FSs with and without vertices. Besides that, it is important for a fuzzy ranking method to satisfy six reasonable fuzzy ordering properties as discussed in [6]-[8]. As a result, the capability of the proposed fuzzy ranking method in fulfilling these properties is analyzed and discussed. Issues related to time complexity of the proposed method are also examined.