A Balancing and Ranking Method based on Hesitant Fuzzy Sets for Solving Decision-making Problems under Uncertainty

The purpose of this paper is to extend a new balancing and ranking method to handle uncertainty for amultiple attribute analysis under a hesitant fuzzy environment. The presented hesitant fuzzy balancingand ranking (HF-BR) method does not require attributes’ weights through the process of multipleattribute decision making (MADM) under hesitant conditions. For the rating of possible alternatives,firstly, they are defined as hesitant fuzzy terms and then converted into hesitant fuzzy sets. Second, anoutranking matrix indicates that a possible alternative overcomes the other alternatives regarding toeach chosen attribute. Third, the outranking matrix is triangularized which means that we prepareprovisional order of possible alternatives or implicit preordering under hesitant conditions. Eventually,the empirical order of alternatives goes through variant operations of balancing and screening thatneeds continuous application of a balancing axiom to the advantages–disadvantages table. It linksincompatible attributes with pair-wise comparisons of the possible alternatives for the multipleattribute analysis. Finally, we present an application example for the supplier selection to show theapplicability and feasibility of the proposed HF-BR method in the hesitant fuzzy setting.