This paper develops a new method based on generalized hybrid Shapley Choquet integral for interval-valued hesitant fuzzy uncertain linguistic multi-criteria group decision making (MCGDM), where interactive characteristics of criteria is taken into account. First, a score function and a new accuracy function are defined to rank the interval-valued hesitant fuzzy uncertain linguistic elements (IVHFULEs). Based on the Shapley Choquet integral, some generalized Shapley Choquet operator for IVHFULEs are proposed including an interval-valued hesitant fuzzy uncertain linguistic generalized Shapley Choquet (IVHFULGSC) operator and an interval-valued hesitant fuzzy uncertain linguistic generalized hybrid Shapley Choquet (IVHFULGHSC) operator and some attractive properties for these two operators are investigated in detail. Then a Shapley Choquet integral-based Minkowski distance between interval-valued hesitant fuzzy uncertain linguistic sets (IVHFULSs) is defined. Subsequently, based on the maximization deviation method, a linear programming model is built to determine the individual fuzzy measure on criteria set for each decision maker (DM). By utilizing the individual closeness coefficients matrices, a new multi-objective fractional programming model which maximizes the collective relative closeness degrees of all alternatives is constructed to obtain the fuzzy measure on DMs set. The individual decision matrices are aggregated into the collective one by using the IVHFULGHSC operator. To obtain the collective Shapely fuzzy measure on criteria set, a linear programming model is established by maximizing the deviation of the evaluations of different alternatives on each criterion. Then, the collective closeness coefficients of alternatives are calculated to rank the alternatives. Thus, a new method based on generalized hybrid Shapley Choquet integral operator is brought forward for MCGDM with IVHFULEs. Finally, an example of investment on shared bikes is provided to illustrate the applicability of the proposed method and a validity test is conducted to demonstrate the effectiveness of the proposed method.

In recent decades, the data envelopment analysis (DEA) model has been applied to various fields. However, the current research on DEA for land utilization efficiency is based on the assumption that each decision making unit (DMU) is independent and does not distinguish different preference to output indexes. Therefore, this paper proposes a new game cross efficiency model which considers the different levels of concern to different output indexes. In the proposed model, the output indexes are divided into several groups and DMUs present their preferences to these groups. Subsequently, this paper develops an algorithm to solve this model and proves the convergence of the algorithm. Then, taking the evaluation of land utilization efficiency as an example, the importance of game cross efficiency and group indexes in evaluations is presented. The output indexes are separated as two classes including economy output indexes and environment output indexes. The land utilization efficiency of cities in Pearl River Delta in 2019 is evaluated by the proposed model. The analysis shows that when there is a significant difference between different groups of output indexes, the ranking result for decision making units is different from the traditional DEA. The model reveals that the efficiency of some cities depends much on some special output indexes.

Yue et al. [1] presented some theories of triangular intuitionistic fuzzy numbers (TIFNs) and triangular intuitionistic fuzzy sets (TIFSs) in Alexandria Engineering Journal. These theories have not been proved in the above reference; hence they are proved in this paper. In addition, this paper also provides some novel theorems and related proofs on TIFNs and TIFSs. Moreover, the presented theories are applied in the field of two-sided matching decision-making. A numerical case is adopted for demonstrating the effectiveness of the proposed theorems and method. This work will effectively complement the theories of TIFNs and TIFSs, and popularize their application scope.