###### Abstract
Therefore, in this paper, we extend the evidence theory to the probabilistic hesitant fuzzy evidence theory (PHFET). The probabilistic hesitant fuzzy basic probability assignment (PHFBPA), a new probability assignment based on PHFS, along with the combination rule are introduced. Moreover, we designed two methods for generating PHFBPs using distance and the multi-classifier approach, respectively. In addition, to address the conflicts and uncertainty in the evidence, we employ an entropy measure and the Jousselme distance of PHFBPA to modify the evidence before fusion. Based on the PHFET, we develop a model for evaluating the degree of satisfaction of the SCS capability demand. Furthermore, the proposed method is applied to the classification experiments and an SCS capability demand evaluation experiment, demonstrating the feasibility and effectiveness of the PHFET approach. The main contributions of this work are summarized as follows:  
* We introduce the PHFBPA, which effectively represents information that is difficult to describe with exact values. The PHFBPA incorporates both membership degrees and probabilities, allowing for more ambiguous information representation. When the PHFBPA element is a single value, it degenerates to the basic probability assignment (BPA). * The combination rule for PHFBPA based on the operators of PHFS and the decision-making strategy to make the final decision are proposed. A numerical example is provided to illustrate the feasibility of the combination rule. * We develop two methods for generating PHFBPs. The first method is based on the difference between actual and expected values, with the probability distribution of the element in the PHFE being determined by experts through system analysis. The second method is multi-classifier-based, where membership degrees and probabilities are obtained through training on a dataset. * Discounting factors are designed to modify the PHFBPA. An entropy measure of PHFBPA is proposed as the credibility discounting factor, and its axiomatic properties are proven. The Jousselme distance of PHFBPs is used as the reliability discounting factor to measure conflict between evidence. * We compare the PHFET method with several machine learning algorithms for the classification of some UCI data sets, and the results demonstrate the effectiveness of the PHFET method. * A model for evaluating SCS capability demand satisfaction degree based on PHFET is provided, which involves establishing a capability indicator system through task decomposition and fusing data from different indicators using the PHFET method. Furthermore, we simulate a representative case digitally to analyze the stability of PHFET and compare it with some traditional methods, highlighting the robustness and superiority of the PHFET method. The remainder of the paper is structured as follows. The relevant knowledge of evidence theory, PHFS, and Jousselme distance is introduced in Section 2. In Section 3, the PHFBPA, combination rule and generation methods of PHFBPA, and discounting factors are proposed. Section 4 designs the process to evaluate the capability demand satisfaction degree of SCS. In Section 5, the PHFET is applied to target recognition and an SCS capability demand satisfaction degree evaluation. Section 6 summarizes this paper.