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As an extension of hesitant fuzzy set, the probabilistic hesitant fuzzy set (PHFS) can more accurately express the initial decision information given by experts, thus the decision method based on PHFS is more true and reliable. In this paper, multi-attribute decision-making (MADM)method is proposed under probabilistic hesitant fuzzy environment, which is based the new distance measures of probabilistic hesitant fuzzy elements (PHFEs) and the COmplex PRoportional ASsessment (COPRAS) method. Firstly, the existing problems of some distances are analyzed and we propose some new distance measures including new Hamming distance, new Euclidean distance and new generalized distance under probabilistic hesitant fuzzy environment. Secondly, a maximizing deviation method based on the new Hamming distance measure is proposed to obtain the attribute weights in probabilistic hesitant fuzzy information. Then, the COPRAS method is extended to solve MADM problems under probabilistic hesitant fuzzy environment. Finally, compared other methods, an example is given to demonstrate the effectiveness of the proposed method.

Multi-Attribute Decision-Making Method Based Distance and COPRAS Method with Probabilistic Hesitant Fuzzy Environment