A probabilistic interval-valued hesitant fuzzy gained and lost dominance score method based on regret theory

• The proposed method considers the regret aversion psychology of experts. • We propose a novel regret function with PIVHF information based on interval projection measure. • An extended GLDS method based on regret theory and interval evidential reasoning is developed. With the increasing complexity of the decision environment, the fuzzy theory has attracted the extensive attention of scholars. Probabilistic interval-valued hesitant fuzzy set, as a complex ambiguous information representation tool, dedicates to depict uncertain information as complete as possible. Thus, this paper proposes a probabilistic interval-valued hesitant fuzzy gained and lost dominance score method based on regret theory and interval evidential reasoning approach. In view of the uncertainties in evaluations, the interval evidential reasoning approach is an effective tool to deal with the fuzziness and ignorance, which is first applied in probabilistic interval-valued hesitant fuzzy information in this paper. Besides, an interval projection measure is proposed to consider both distance and direction simultaneously, so as to avoid the problem of information losses in the decision process. On this basis, a novel regret-rejoice function is developed. Then, an extended gained and lost dominance score method based on regret theory and interval evidential reasoning approach is developed, which considers the regret avoidance behavior of experts. Finally, a case study on supplier selection of epidemic prevention products is applied to elucidate and illustrate the application of the proposed method in this paper.