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The consensus of randomness and ambiguity exists in real-world problems. To depict fuzziness, randomness, and statistical ambiguity in a single framework, the authors develop an interactive approach to MCDM method in which assessment of alternative over attributes are provided by probabilistic hesitant fuzzy elements (PHFEs). This method provides a tool to the decision makers for reasonable ranking of alternatives. The core intention of this paper is to define a series of novel distance and similarity measures and score function for PHFEs. To demonstrate the effectiveness of developed model, a real case study is taken as an example. To completely describe statistical and non-statistical uncertainty, suitable probability distribution function is associated with each element of constructed HFSs. The proposed method is superior to other MCDM methods because of introducing probabilistic information in HFEs, which can be helpful to ensure the integrality and accurateness of hesitant fuzzy information.

Novel Distance and Similarity Measures for Probabilistic Hesitant Fuzzy Set and Its Applications in Stock Selection Problems