## 1 Introduction
On the other hand, suitable methods should be chosen to carry out capacity evaluation and the sorting of different spare parts support solutions, thus facilitating the spare parts support work of civil aircrafts. As for the expression of decision information, fuzzy mathematics theory has been a research hotspot in this field since it was put forward by Professor [PERSON] [13] in 1965, with its unique advantages in dealing with fuzziness and uncertainty. With the realistic needs and the ever-deepening research, fuzzy sets have been well extended based on the research carried out by [PERSON] [14; 15; 16]. [PERSON] [17] put forward the intuitionistic fuzzy set, which describes uncertain information from two aspects--membership and non-membership--and reflects the three attitudes of decision-makers in the decision process: support, neutrality, and opposition. [PERSON] et al. [18] and [PERSON] et al. [19] extended the research on intuitionistic fuzzy sets from different angles, mainly exploring their multi-attribute decision problems. [PERSON] put forward the Pythagorean fuzzy set [20] and q-order orthogonal fuzzy set [21] successively, which solved the decision-makers' restriction on the value of evaluation information, allowed decision-makers to represent evaluation information in a wider range, and could better describe the uncertainties in reality. [PERSON] et al. [22] proposed a q-rung orthopair fuzzy definite integral to aggregate continuous information according to the loose constraints of q-order orthogonal fuzzy sets. The above studies have provided a beneficial reference for dealing with multi-attribute decision problems. However, decision-makers are usually hesitant during the practical decision process. [PERSON] [23] creatively put forward hesitant fuzzy sets, which effectively solved the hesitation of decision-makers in the decision process or the different decision values given by different decision-makers. On this basis, [PERSON] et al. [24] raised dual hesitant fuzzy sets by combining hesitant fuzzy sets and intuitionistic fuzzy sets. [PERSON] et al. [25] proposed q-order triangular hesitant fuzzy sets combining q-order hesitant fuzzy sets and triangular fuzzy numbers. The above hesitant fuzzy sets and their extended forms are beneficial for handling the hesitation and fuzziness of decision information. At present, the preferential sorting in multi-attribute decisions has been realized mainly by the following common methods: TOPSIS [26], grey relational analysis (GRA) [27], elimination et choice translating reality (ELECTRE) [28], and VseKrierijumska Optimizacija and Kompromisno Resenje (VIKOR) [29]. Therein, the TOPSIS method [30] determines the advantages and disadvantages of solutions by setting positive and negative ideal solutions and calculating the distance of evaluation schemes from the positive and negative ideal solutions. The closer distance to the positive ideal solution and the greater distance from the negative ideal solution indicate a better solution, otherwise, the solution will be poorer. The GRA method [31] determines the reference sequence that can reflect system behavior characteristics and the data sequence composed of factors that affect system behavior, calculates the grey relational coefficient between the two groups of data, and then calculates the grey relational degree to determine the advantages and disadvantages of the solutions. The higher the grey relational degree, the better the solution is, or otherwise, the worse the solution will be. The core idea of the ELECTRE method [32] is to compare the advantages and disadvantages of alternatives by establishing preference relations rather than relying on specific numerical indicators. This method mainly helps decision-makers make the final choice by gradually eliminating unqualified alternatives and finally expressing the characteristics of the optimal alternative.