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In this paper, some drawbacks to existing ordering relations for hesitant fuzzy sets are examined using examples. To overcome these flaws, a priority degree formula for comparing two hesitant fuzzy sets is presented and the desirable priority degree properties studied. Then, based on an introduced priority degree formula, a new hesitant fuzzy multiple attribute decision making methodology is proposed. Finally, a numerical example together with a comparison analysis is given to illustrate the effectiveness and feasibility of the new approach to decision making applications. Keywords: Priority degree, Order relations, Hesitant fuzzy sets, Multiple attribute decision making