Multi-criteria outranking approach with hesitant fuzzy sets

As a generalization of fuzzy sets, hesitant fuzzy sets constrain the membership degree of an element to be a set of possible values between zero and one. Those sets are considered useful in handling decision problems defined under uncertainties where decision-makers hesitate among several values before expressing their preferences. Motivated by the idea of traditional ELECTRE methods, the dominance relations and the opposition relations for hesitant fuzzy sets are introduced in this paper. In addition, several desirable properties are studied. Then, a novel outranking relation is developed, based on systematic comparison of assessments given to alternatives for each criterion. An outranking approach for multi-criteria decision-making problems with hesitant fuzzy sets, similar to ELECTRE III, is proposed for ranking alternatives. Finally, an example is given to verify the developed approach and demonstrate its validity and feasibility.