###### Abstract  
Evaluating the capabilities of a satellite communication system (SCS) is challenging due to its complexity and ambiguity. It is difficult to accurately analyze uncertain situations, making it difficult for experts to determine appropriate evaluation values. To address this problem, this paper proposes an innovative approach by extending the Dempster-Shafer evidence theory (DST) to the probabilistic hesitant fuzzy evidence theory (PHFET). The proposed approach introduces the concept of probabilistic hesitant fuzzy basic probability assignment (PHFBPA) to measure the degree of support for propositions, along with a combination rule and decision approach. Two methods are developed to generate PHFBPA based on multi-classifier and distance techniques, respectively. In order to improve the consistency of evidence, discounting factors are proposed using an entropy measure and the Jousselme distance of PHFBPA. In addition, a model for evaluating the degree of satisfaction of SCS capability requirements based on PHFET is presented. Experimental classification and evaluation of SCS capability requirements are performed to demonstrate the effectiveness and stability of the PHFET method. By employing the DST framework and probabilistic hesitant fuzzy sets, PHFET provides a compelling solution for handling ambiguous data in multi-source information fusion, thereby improving the evaluation of SCS capabilities. D 2024 26 94  
DST is widely applied in various fields, including classification [17; 18; 19], decision making [20], risk assessment [21; 22], medical diagnosis [23], and others, and others, as it offers rigorous and effective data fusion solutions. In traditional DST, the probability assignment of a focal element represents the level of support for a proposition and is typically a precise value. However, in situations where evaluation criteria are ambiguous and experts are hesitant to express their opinions, the probability assignment may become uncertain or inaccurate. To address this challenge, fuzzy sets such as IFS have been employed for decision-making under uncertainty [24]. As a result, researchers have integrated DST with various approaches such as IFS, hesitant fuzzy linguistic term sets, Pythagorean fuzzy sets, hesitant fuzzy sets (HFS) theory, and others to capture and describe uncertainty in the decision-making process [20; 25; 26; 27]. HFS was developed by [PERSON] and [PERSON] [28; 29] as an extension of fuzzy sets that models the hesitancy by allowing multiple degrees of membership values for each element. It has been proven that the envelope of the HFSs is an IFS [28]. Compared to IFS, HFS provides more precise information descriptions, enabling accurate characterization of the degree associated with each evaluation value. Moreover, HFS aligns with people's intuitive feelings and diversity of opinions. Therefore, HFS is a valuable tool for decision-making and analysis, especially in uncertain and ambiguous scenarios. However, all elements in the hesitant fuzzy element (HFE) have equal occurring probabilities, implying equal importance for all membership values. To address this issue, [PERSON] and [PERSON] [30] introduced the probabilistic hesitant fuzzy set (PHFS) and probabilistic hesitant fuzzy element (PHFE), which generalize the fuzzy form by incorporating probabilities with the associated membership values. The academic community has shown considerable interest in the research on PHFS, leading to numerous findings [31; 32] since PHFS enables more precise characterization of fuzziness and hesitation in human thinking. In [33], a ranking model under PHFS is introduced by extending the concept of evidence theory. However, this approach converts probabilistic hesitant fuzzy information into a single value before combining it with evidence theory. This premature transformation eliminates uncertainty in PHFS, potentially overlooking uncertainties and hesitations important for decision-making in complex systems.