**1. Introduction**

Many complex issues in engineering, economics, environmental science and medical science involve uncertainties. In order to address these issues, the theory of possibility, fuzzy set [1], rough set [2], and interval mathematic [3] have been developed successively. However, the above theories have their inherent defects, which are mainly reflected in the inadequacy of parameterization tools [4]. In 1999, Molodtsov [4] initiated the soft set theory for modeling uncertainties from the parameterized point of view.

After Molodtsov, the research interests in the soft set theory have been growing rapidly, such as the algebraic structure [5,6], topology [7,8], normal parameter reduction [9], medical diagnosis [10], game theory [4], and decision making under uncertainties [11,12]. In addition, the study of hybrid models that are developed by combining the soft set theory with other mathematical tools, such as rough sets [13], fuzzy sets [14], and intuitionistic fuzzy sets [15], has also been an important research topic.

Under uncertain environments, a mass of inconsistent information appears due to diversities of source platforms and the differences in the acquisition time. To address issues involving inconsistencies, Smarandache [16] initiated neutrosophic sets from the perspective of philosophy. Subsequently, Maji [17] integrated neutrosophic sets into soft sets to propose neutrosophic soft sets, which retain the characteristics of neutrosophic sets and have adequate parameterization tools. Neutrosophic soft sets are characteristic by three independent functions, including a pair of asymmetric functions: Truth-membership and false-membership, and an indeterminacy-membership function. Among them, the truth-membership and false-membership represent the degree of belongingness and non-belongingness of an element with respect to parameters. The indeterminacy-membership shows the neutrality degree of an element related to parameters.

In recent years, the theory extensions of neutrosophic soft sets have made a rapid progress. Sahin and Küçük [18] constructed generalised neutrosophic soft sets. Deli and Broumi [19] refined the concept and operations of Maji's neutrosophic soft sets. In addition, they also studied the neutrosophic soft matrix and their operators. Considering that the approximate range is usually used to describe complex situations when there is no su fficient information, Deli [20] expanded the values of the truth-membership, indeterminacy-membership, and false-membership to the form of interval values to construct interval-valued neutrosiphic soft sets. Karaaslan [21] introduced the possibility of neutrosophic soft sets by assigning probability to the three function values and defined related properties and operations. In addition, the concepts of single-valued neutrosophic refined soft sets [22], generalized neutrosophic soft expert sets [23], and neutrosophic soft rough sets [24] were presented successively.

Meanwhile, neutrosophic soft sets are also employed in the fields of clustering, prediction and decision making under uncertainties, among which decision making under uncertainties is the most widely applied. Deli [20] proposed a decision making method of interval-valued neutrosophic soft sets by level soft sets, and illustrated it by an example. Peng and Liu [25] constructed three decision making algorithms of neutrosophic soft sets by evaluation based on the distance from average solution (EDAS), similarity measure, and level soft sets, respectively. Abu Qamar and Hassan [26] presented the similarity, distance, and fuzzy degree measures of Q-neutrosophic soft sets, and put forward the corresponding decision rule. Karaaslan [21] constructed a decision making method for the possibility of neutrosophic soft sets based on the and-product.

However, the existing studies mainly focus on decision making methods under a single decision maker, few scholars have studied group decision making problems by neutrosphic soft sets. At the same time, we also noticed that the existing methods have the following defects. On one hand, the above methods are mainly based on the expected utility theory, which assumes that decision makers are completelyrational. Actually, in decision making processes, decision makers do not make decisions in a complete rational manner, mainly showing that psychological expectations will greatly affect the actual decision making behavior. On the other hand, the parameter subjective weights are directly given determinate values [25], which do not fully reflect the hesitancies of decision makers' judgments under uncertain environments.

To make up for the gaps of existing researches, this study constructs an algorithm for the stochastic multi-criteria group decision making based on neutrosophic soft sets. Stochastic means that the weights of decision makers and parameters are uncertain or completely unknown under uncertainties. In this paper, neutrosophic numbers rather than determinate values are adopted to express the stochastic of the weights of decision makers and parameters. This method employs the prospect theory [27] rather than the expected utility theory to integrate the hesitancies of alternatives by decision makers' judgements. The prospect theory, a new theory of bounded rationality, is proposed from the point of view of cognitive psychology. In addition, it integrates the influence of psychological expectations on actual decision making behaviors into the decision making model. Therefore, the prospect theory is more in line with actual decision making behaviors under uncertainties [28]. Then, to establish the prospect decision matrix, we put forward the conflict degree measure of neutrosophic numbers and modify it to adapt group decision making. Moreover, on the purpose of aggregating in group decision making processes, this study proposes the weighted average aggregation rule and weighted geometric aggregation rule of neutrosophic soft sets.

To promote our discussion, some fundamental concepts of neutrosophic sets, soft sets, neutrosophic soft sets, and prospect theory are reviewed in Section 2. In Section 3, we establish the measures of determinacy degree and conflict degree, and construct the weighted average aggregation rule and weighted geometric aggregation rule of a neutrosophic soft set. In Section 4, this paper presents an algorithm for neutrosophic soft sets in the stochastic multi-criteria group decision making based on the prospect theory. In Section 5, to demonstrate the feasibility and effectiveness of the proposed algorithm, we perform an illustrative example and a comparative analysis.
