Serving as an effective tool for describing both randomness and fuzziness of qualitative concepts, the cloud model has become a common topic of research. By realizing the uncertain transformation between qualitative concepts and quantitative data, the cloud model provides a new way to deal with group decision making problems in the linguistic environment. However, classical methods based on the cloud model mainly focus on addressing problems with a small number of decision makers. In this paper, we apply the cloud model to the decision making problems which involve a large group of decision makers. Specifically, we first define a new measure of fuzzy distance for clouds based on the α-cuts. On the basis of the proposed fuzzy distance measure, we then present a new similarity measure between clouds. Next, we construct an improved clustering approach based on the traditional hierarchical clustering algorithm. Furthermore, we develop a hybrid weight scheme to obtain the cluster weights, which takes both the subgroup size and the variance into consideration. Moreover, we present a consensus-based method based on the cloud model for large group decision making (LGDM) with linguistic information. Finally, in order to confirm the validity and effectiveness of the proposed method, we give an application in the context of the Belt and Road Initiative of China, and perform some detailed comparisons to show the advantages of the proposed method.

In recent years, some complex linguistic expression techniques with probabilistic information, such as proportional linguistic terms, probabilistic linguistic term sets, have been proposed to describe the uncertainty of opinions and preferences. However, the probability information is expressed as the crisp numbers, which is usually difficult to be estimated and information losses may exist. To capture the inherent fuzziness and vagueness of decision information more comprehensively and accurately, in this paper, we introduce a novel concept named dual linguistic term set (DLTS), which consists of two linguistic variables. The DLTS can allow the decision makers to express the probabilistic information by the means of linguistic variables. To describe the hesitant information of the decision makers, a more general concept named hesitant fuzzy dual linguistic term set (HFDLTS) is developed. Afterwards, a multi-criteria decision making method with dual linguistic information is proposed based on the normal cloud model. To do so, the DLTS is first transformed into an equivalent 2-tuple consisting of two independent normal clouds. Then, new multiplication operation and power operation of normal clouds are defined to obtain the expectation for each attribute value. After aggregating the evaluation information, we further develop a new score function to rank alternatives reasonably. Finally, an illustrative example is given to verify the effectiveness and feasibility of the proposed method, also some comparisons and analyses are provided to show the advantages of the proposed method.

Focusing on the characteristics of public participation and large group decision making of major livelihood projects, this paper proposes a multi-agent linguistic-style large group decision-making method with the consideration of public expectations. Firstly, based on the discrimination degree of evaluating information, the comprehensive weight of each attribute is calculated with the principle of maximum entropy. Secondly, the expert preference information for different alternatives is clustered and several aggregations are formed. Thirdly, the preference conflict level of experts' group for each alternative is calculated, and a conflict-oriented experts' aggregation weight optimization model is constructed to ensure the effectiveness of conflict resolution. Fourthly, the public group's satisfaction is determined with the expectation distribution of public’s and the expert group's preference, so as to obtain the sorting result of the decision alternatives. Finally, the effectiveness and applicability of the proposed method are verified by method comparison.

We examined a retrial make-to-stock system based on a double-ended queue. When the queue length was negative, the inventory system contained only products, and customers were waiting in the retrial queue when the queue length was positive. We developed a model to study the expected cost of the entire system with strategic customers in the observable case and the fully observable case. We also obtained the optimal inventory levels under these two levels of information based on numerical experiments.