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With the increasing need and expectation for a better life, people have higher and higher requirements for the new smart city. To promote construction of the new smart city, an efficient evaluation should be performed to make the final effect of the construction comparative and measurable. At present, some studies focus on the evaluation of new smart city construction. Shen et al. (2018) evaluated the performance of the smart city by using the “technique for order preference by similarity to an ideal solution” and the entropy method. Topaloglu et al. (2018) evaluated the alternative waste collection systems in the smart city environment by a type-2 fuzzy multiple-criteria method. Macke et al. (2019) used factorial analysis and linear regression for the evaluation of smart sustainable cities. To evaluate smart-city selection eligibility and design smart city rankings, Kumar et al. (2019) proposed a weighted criteria model, and Escolar et al. (2019) proposed a multiple-attribute decision-making method. Deveci et al. (2020) used the interval agreement approach to evaluate smart city initiatives. The above studies evaluated the new smart city from the perspective of its construction. There are few studies from the perspective of users, that is, citizens. The evaluation of the new smart city should take the feelings of citizens, especially the citizens’ sense of gain (CSG), into account since the citizens are observers and perceivers of the city. At the same time, compared with traditional urban development, the most prominent characteristic of the new smart city is that it can attach importance to human development. Thus, the evaluation of CSG is a key for the new smart city.
For the evaluation of CSG, a large number of citizens can participate through various ways, such as visits, telephone interviews, and online questionnaires. The evaluation of CSG can be regarded as the group decision-making (GDM) problem where these citizens are the decision makers (DMs). Considering the complexity of the practical problems, the amount of knowledge and information is greatly increased. It is difficult for the decision-making method with a single DM to solve the complex decision problem. The GDM methods have emerged. Zuo et al. (2019) proposed a large GDM method of generalized multi-attribute and multi-scale based on the linear programming technique for multi-dimensional analysis of preference. Yu et al. (2018) developed a method for heterogeneous multi-attribute GDM problems with preference deviation of DMs and incomplete weight information. Li (2009) presented the extended linguistic variables based method for solving multi-attribute GDM problems under linguistic assessments. Li (2010) proposed a method for solving fuzzy multi-attribute GDM problems with non-homogeneous information. Yu (2024) established a multi-objective decision model for the grade assessment of network security situations under multi-source information and multiple experts. Yu and Zuo (2024) proposed a grade assessment method for cybersecurity situations of online retailing with DMs’ bounded rationality.
Considering the uncertainties and hesitations in the judgment of DMs, it is not easy for the DMs to provide accurate evaluation information for the decision-making problem (Li, 2014; Yu et al., 2018). The linguistic information not only is closer to the natural thinking and reasoning ways of DMs but also can reflect their true feelings, which is utilized to express evaluation information directly and effectively (F. Wang et al., 2025). Pang et al. (2016) pointed out that DMs may have hesitancy among several possible linguistic terms (LTs) when expressing their preferences. Moreover, the complete probabilistic distribution on these LTs is usually not so easy to be provided accurately. With the probabilistic linguistic term set (PLTS), the DMs can not only provide several possible linguistic values over an object but also reflect the probabilistic information of the set of values (Pang et al., 2016). Thus, the PLTS utilizes multiple LTs to express DMs’ opinions and reflects the degree of preference of DMs for different LTs, which is flexible in characterizing the opinions of DMs in the decision group.