## 1 Introduction
Although hesitant fuzzy sets can better express the ideas of experts, there is the problem of information loss, and it cannot fully reflect the decision information. To cope with this issue, some researchers have introduced the concept of probability. For example, [PERSON] and [PERSON] [21] introduced probability into hesitant fuzzy sets, and put forward the concept of probabilistic hesitant fuzzy sets, and gave its operation rules. [PERSON] [22] introduced a MAGDM method based on correlation coefficient to use probabilistic hesitant fuzzy information. It is undeniable that researchers have effectively improved and extended the hesitant fuzzy sets to make it more comprehensive to express decision information. [PERSON] et al. [23] defined a probabilistic interval-valued intuitionistic hesitant fuzzy set (PIVIHFS) as an extended mathematical expression of fuzzy sets and established some new measure models deduced by the axiomatic concepts of PIVIHFSs. [PERSON] [24] proposed the probabilistic linguistic term sets (PLTSs), in which each provided linguistic term has a probability. [PERSON] [25] defined the modified-PLTS (M-PLTS) and transformed it to the ordered weighted hesitant fuzzy element (OWHFE). [PERSON] [26] built a consensus among the decision makers for probabilistic hesitant fuzzy preference relations (PHFPRs) with expected additive consistency. [PERSON] [27] proposed the uncertain probabilistic hesitant fuzzy element (UPHFE) and extended it to the uncertain probabilistic hesitant fuzzy preference relations (UPHFPRs). On the one hand, the aggregation of decision attribute information is an important research topic in MAGDM problems. From the above analysis, we can find that the most of current interval-valued information aggregation operators are put forward under interval-valued hesitant fuzzy information and interval-valued intuitionistic fuzzy information environment. However, there is no research on the probabilistic interval-valued hesitant fuzzy information aggregation operators at present. On the other hand, although there exist some useful algorithms, there are still some problems such as loss of decision information and inaccuracy of decision results. In this paper, the concept of probability is added to give the corresponding degree of possibility for decision information value, which enhances the reliability and effectiveness of decision results. In addition, the Archimedes norm makes the aggregation algorithm more flexible and the decision making process more convenient. Therefore, the algorithm model proposed in this paper is necessary. In this paper, we apply the Archimedes norm to investigate the aggregation method for probabilistic interval-valued hesitant fuzzy information. To do so, the rest of this paper is structured as follows. In Section 2, we review some basic concepts and notations of the IVHFSs and define the PIVHFSs. Then, we introduce the Archimedes norm, and (based on this) the probabilistic interval-valued hesitant fuzzy operation rules are discussed. In Section 3, we define the probabilistic interval-valued hesitant fuzzy information aggregation operators whose related properties are explored in detail. Based on the additive operator \(g(t)\) which takes different functions, Section 4 studies some common information aggregation operators and analyzes the relationship among these proposed operators. Based on the proposed operators, a method to multiple attribute group decision making with probabilistic interval-valued hesitant fuzzy information is provided in Section 5. An example is given to show the effectiveness and feasibility of the proposed method in Section 6. Section 7 summarizes the full text and draws the main conclusions.