关键词: 多属性决策, 不确定语言变量, 幂平均算子, Bonferroni平均算子

Abstract: Multiple attribute decision making is a prominent area of research in normative decision theory. This topic has been widely discussed and studied. Considering that experts may have vague knowledge about the preference degree of objective things, uncertain linguistic variables are often used for decision makers as the evaluation information in some complex multiple attribute decision-making problems. For the sake of aggregating the uncertain linguistic evaluation information in multiple attribute decision-making problems, some uncertain linguistic information aggregation operators are developed and designed. However, it is worth noting that most of the uncertain linguistic information aggregation operators do not take into account the interrelationship between data and the overall balance of data simultaneously, which is unreasonable for the decision results in uncertain linguistic multiple attribute decision making problems. Therefore, it is necessary to pay attention to this issue.
In order to better solve this issue, we combine uncertain linguistic variables, power averaging operator, and Bonferroni mean operator to define the uncertain linguistic power Bonferroni mean (ULPBM) operator and the uncertain linguistic weighted power Bonferroni mean (ULWPBM) operator, which is able to make the decision results more accurate. The ULPBM operator and ULWPBM operator have some characteristics in the process of aggregating uncertain linguistic variables. On the one hand, two new operators utilize the crossover operation of the Bonferroni mean (BM) operator to represent the interrelationship between data. On the other hand, two new operators use the support degree coefficient of the power averaging (PA) operator to denote the overall balance of data. At the same time, the commutativity, idempotency, boundary, and monotonicity of these operators are investigated, which validates that these operators are feasible. Based on the above analysis, the ULWPBM operator is used for solving uncertain linguistic multiple attribute decision making problems, and a novel uncertain linguistic multiple attribute decision making method with the ULWPBM operator is put forward.
The talent selection is an important part for the development of enterprises, and the enterprises that own some excellent talents will make more profits and gain more space for survival. In this scenario, how to effectively find the most appropriate talent from several candidates has become a significant problem for every enterprise. However, there are a lot of factors that affect the capacity of talents, including ideology and morality, work attitude, work style, cultural level, knowledge structure, etc. Moreover, the experts often use uncertain linguistic variables when they evaluate the preference of these factors with regard to the enterprise talent selection. It is obvious that the enterprise talent selection is a classical uncertain linguistic multiple attribute decision-making problem. Therefore, we take an example with regard to the enterprise talent selection to prove the feasibility and effectiveness of the proposed method. The research results show that not only can the proposed method better solve the interrelationship between attributes, but the proposed method can also effectively alleviate the adverse influence of abnormal attribute values.
The main contributions of this paper are that we define the ULPBM operator and ULWPBM operator, and then we put forward a novel uncertain linguistic multiple attribute decision making method with ULWPBM operator. It should be noted that two new operators are the supplement and improvement of uncertain linguistic information aggregation operators, and the proposed method can give some references for solving real-world complex decision-making problems. In the future, the power Bonferroni mean operator could be extended to hesitant fuzzy linguistic preference relations and probabilistic linguistic environments. In addition, the uncertain linguistic multiple attribute group decision making approach with ULWPBM operator is also an interesting research topic, which needs further investigation.

Key words: multiple attribute decision making, uncertain linguistic variables, power averaging operator, Bonferroni mean operator