| Summary: | Interval-valued Fermatean fuzzy sets (IVFFSs) as an extension of Fermatean fuzzy sets (FFSs) are a new powerful mathematical tool that apply interval value to describe uncertainty. Compared to interval-valued intuitionistic fuzzy sets (IVIFSs) and interval-valued Pythagorean fuzzy sets (IVPFSs), IVFFSs can handle more uncertain information. This paper presents a novel fuzzy three-way multi-attribute decision-making approach with the probabilistic dominance relation, based on the model of IVFSSs. The proposed method firstly uses the probabilistic dominance relation to calculate the conditional probability of each alternative. Subsequently, it builds loss functions from the perspective of the ideal solution. Our suggested method is able to rank and classify the alternatives into the positive region, the boundary region, and the negative region while the existing MADM approaches under IVFSSs only sort them without classification. Additionally, the suggested solution involves a much lower error rate than the existing methods. And our method's conditional probability may be determined objectively and takes the relation between attributes and interactions among alternatives into account, which reduce the risk associated with subjectivity in the decision-making process of existing approaches. The effectiveness and suitability of the suggested approach are illustrated by two real-world applications such as the photovoltaic poverty alleviation project selection and the hotel location evaluation and experimental findings. © 2023 Elsevier Ltd
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