In this paper, we introduce probabilistic interval-valued hesitant fuzzy sets (PIVHFS) and probabilistic interval-valued hesitant fuzzy elements (PIVHFE), then define correlation operations. At the same time, the hybrid distance measures of PIVHFE and interval fuzzy number are defined, and the hybrid distance measures of two PIVHFEs are also defined. Considering the psychological behavior of decision makers, we use interval fuzzy number decision makers' psychological interval reference points to calculate the gains and losses of evaluation value. Furthermore, based on incomplete weight information, the grey relational analysis (GRA) method is extended to calculate the optimal weight. Then, based on the traditional TOPSIS method, the decision-making method is proposed. Finally, the proposed method is applied to an example, and the sensitivity analysis and stability analysis of the proposed method are also discussed.

YunFei Xing. A Prospect Theory Based Probabilistic Interval-Valued Hesitant Fuzzy Sets with Interval Reference Point and Incomplete Weight Information for Multi-Criteria Decision Making. The Frontiers of Society, Science and Technology (2019) Vol. 1 Issue 10: 1-20. https://doi.org/10.25236/FSST.2019.011001.

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