The meta-synthesis method has achieved good results in China’s aerospace engineering and population economic regulation. This theoretical achievement obtained from engineering practice becomes an effective way to solve complex decision-making problems. The meta-synthesis method obtains the final decision-making result by comprehensively considering qualitative and quantitative criteria and gathering multivariate heterogeneous attribute information. In view of the broad application of entropy theory in quantitative evaluation and fuzzy decision-making, this paper proposes a meta-synthesis decision-making method based on probabilistic linguistic cross-entropy and priority relations for multicriteria decision-making problems including qualitative and quantitative multivariate heterogeneous attribute information. First, the quantitative attribute weight is calculated based on the entropy weight method, and the qualitative attribute weight is calculated by considering the individual effects and interactions of the probabilistic linguistic term sets under qualitative attributes comprehensively through probabilistic linguistic entropy and cross-entropy. Then, the weight preference coefficient is used to integrate the qualitative and quantitative heterogeneous attribute weights to obtain standardized processing weight information, and, on the basis of the 0–1 priority relation matrix, we compare and analyze the advantages and disadvantages of alternatives under all criteria and obtain an overall ranking result of the alternatives. Finally, the effectiveness and superiority of the proposed method are verified by a comparative analysis of a numerical example and the decision-making method.

Existing decision-making methods are mostly a simple aggregation of expert decision information when solving large group decision-making problems. In these methods, priority should be given to expert weight information; however, it is difficult to avoid the loss of expert decision information in the decision-making process. Therefore, a new idea to solve the problem of large group decision-making by combining the expert group clustering algorithm and the group consensus model is proposed in this paper in order to avoid the disadvantages of subjectively assigning expert weights. First, expert groups are classified by the clustering algorithm of breadth-first search neighbors. Next, the decision information of the experts in the class is corrected adaptively using the group consensus model; then, expert decision information in the class is integrated using probabilistic linguistic translation methods. This method not only avoids the shortcomings of artificially given expert weights, but also reduces the loss of expert decision information. Finally, the method comprehensively considers the scale of the expert class and the difference between the classes to determine the weight of the expert class, and then it weights and integrates the consensus information of all expert classes to obtain the final decision result. This article verifies the effectiveness of the proposed method through a case analysis of urban water resource sustainability evaluation, and provides a scientific evaluation method for the sustainable development level of urban water resources.

In some complex decision-making problems such as talent selection, experts often hesitate between multiple evaluation values during their decision making and can only give a range of information due to the fuzziness and imprecision of qualitative decision-making attributes. Interval intuitionistic fuzzy sets and their decision-making methods provide a useful tool to describe the fuzziness of decision attributes and decision experts’ hesitation. However, the abnormal information in the expert decision information has not been considered in the previous works; that is, some interval intuitionistic fuzzy numbers exceed the defined interval range. This kind of abnormal decision information often makes it difficult to obtain accurate decision results using the decision model. To avoid the abnormal information influence on decision-making results, the hesitancy degree-based interval intuitionistic fuzzy sets are employed to propose an adaptive correction method of abnormal information, which can correct the abnormal decision information without changing the decision preference of experts. The abnormal information correction method is utilized to construct a new interval intuitionistic fuzzy entropy by combining hesitancy and fuzziness. This provides a multiattribute decision-making method, including abnormal decision information. Finally, the effectiveness and superiority of the proposed method and decision-making model are evaluated using an application case study of talent selection.

With the development of the cloud computing era, the decision-making environment and algorithm models have become increasingly complex, and traditional decision-making methods have been unable to meet the needs of large group decision-making (LGDM) problems. Firstly, in order to solve this problem, the concept of double hierarchy interval hesitant fuzzy language (DHIHFL) is proposed. Compared with the traditional double hierarchy hesitant fuzzy language (DHHFL), it contains all elements from the lower limit to the upper limit and more comprehensively characterizes the hesitation of language information. Secondly, for LGDM problems, a self-confident double hierarchy interval hesitant fuzzy language (SC-DHIHFL) is developed, and the integration of self-confident degree can better enrich the evaluation information and promote the achievement of group consensus. Thirdly, a new two-stage LGDM method is proposed. The first stage is clustering and grouping and reaching consensus within the group, and the second stage is the integration of LGDM information. The two-stage method contains novel methods such as expert clustering algorithm, subjective and objective comprehensive weight, consensus degree, and deviation weight considering minority opinions. Finally, the proposed LGDM consensus method is applied to a practical LGDM problem, and the effectiveness is verified by comparative analysis with existing methods.

A scientific, reasonable, and novel talent evaluation index system is the foundation of talent training and selection. Based on the novel “Man-Machine-Environment System Engineering” (hereinafter referred to as MMESE) theory, this paper proposes a novel talent evaluation index system that considers the ontological attributes and the external environment of the object comprehensively for talent evaluation, which could help the evaluator obtain more accurate evaluation results. Since the comprehensive evaluation of MMESE talents is a complex decision-making problem that is both qualitative and quantitative, a corresponding decision-making method that integrates qualitative and quantitative approaches is proposed here based on probabilistic language entropy and the possibility of superior order relationships. First, the weights of quantitative and qualitative attributes are calculated based on entropy theory and probabilistic fuzzy language. Second, the standard weight vectors of qualitative and quantitative attributes are obtained by adjusting the weight integration coefficients, and the change intervals of the pros and cons between the objects to be evaluated are calculated. Third, the pros and cons of the objects to be evaluated are compared to obtain the possibility degree matrix that describes the priority relationships among the objects, and a ranking vector is derived from the possibility degree matrix to reflect the rankings of the objects’ pros and cons. Finally, this system and the decision-making methods have been verified as scientific and effective.

An effective evaluation of the index system of talent growth factors can lay a solid foundation to build the talent pool, as well as select and establish talents. In this study, based on the theory of “Man-Machine-Environment” system engineering (MMESE), the MMESE talent growth factor index system is proposed and verified for its effectiveness by comparing it with the traditional system. Based on the text-free grammar and transformation function, expert judgments of talent growth factor indexes were transformed into hesitation fuzzy language terms, namely, pertinence, systematicness, practicability, foresight, and dynamics, which were then used to create a dataset to describe the comprehensive evaluation of the index system. The entropy of hesitation fuzzy language terms adopts the algorithm, which calculates the index weights according to the relative entropy values and adjusts the expert weights with the expert group consensus model. The expert evaluation information was weighed and transformed into the corresponding probability language combination which was calculated as the comprehensive evaluation result of the talent growth factor index system.