Traditional cars consume energy and cause pollution, so electric vehicles have become a key focus of industry development (Wang et al., 2013; Zhang et al., 2014). A survey shows that the concern of users about the range of electric vehicles greatly hinders the development of electric vehicles. In order to promote the development of electric vehicles, we need to establish sufficient and reasonably arranged electric vehicle charging facilities (Lin and Hua, 2015; Kong et al., 2017). In 2009, the planning and layout of charging facilities in the United States began construction projects in multiple states. In February 2022, the US Department of Energy announced that it would spend $5 billion to build a charging network for electric vehicles. In order to significantly promote the development of the electric vehicle industry, Japan is expected to reach 30000 fast charging stations by 2030 (Zhang and Wei, 2023; Zhao et al., 2023). According to data from the National Energy Administration, the annual growth of charging facilities in China in 2022 is about 2.6 million units, a year-on-year increase of nearly 100%. New energy electric vehicle charging stations refer to various charging facilities that provide charging services for electric vehicles, mainly including dedicated charging stations, public charging stations, and personal charging stations (Zhang and Shi, 2023; Sisman, 2023). Among them, dedicated charging stations are mainly used for passenger car services and provide fast charging services to meet the travel needs of car owners; public charging stations mainly provide services for public transportation such as buses, taxis, and shared cars; personal charging stations are mainly used for private cars, personal taxis, and personal ride hailing services (Zu and Sun, 2022; Banegas and Mamkhezri, 2023). Currently, developing a low-carbon economy has become a trend in global economic development and an inevitable way to achieve sustainable development. A low-carbon economy is an economic form based on low energy consumption, low pollution, and low emissions. Its core lies in the innovation of energy-saving and emission reduction technologies, as well as the innovation of industrial structure and system (Seikh and Mandal, 2022; Wang et al., 2022; Wei et al., 2022). At present, China is in a period of accelerated industrialization and urbanization, and the demand for energy is constantly increasing. At the same time, China’s energy intensive and high emission industries account for a large proportion of the entire industry, and there is a rough development model (Liang et al., 2022). Therefore, in the process of developing a low-carbon economy, it is necessary to focus on energy conservation and emission reduction. In the process of developing a low-carbon industry, more attention should be paid to “industrial carbon reduction” in order to save energy, reduce pollution, and alleviate pressure on resources, energy, environment, and other aspects. The automotive industry is a high energy consuming industry, and while the number of motor vehicles continues to grow, the exhaust gases it produces are a major source of pollution (Li et al., 2022a, 2022b). Compared with traditional fuel vehicles, electric vehicles have advantages such as high efficiency, low environmental pollution, and low noise. Therefore, it is an inevitable trend to transform the energy drive system of vehicles (Bian et al., 2022). Electric vehicles are a transportation vehicle with great development prospects, and their development is of great strategic significance for ensuring energy security, achieving energy conservation and emission reduction, and comprehensively promoting the transformation of economic development mode. This is an important historical opportunity for China to revitalize the automotive industry and build a strong automotive country (Yazdekhasti et al., 2021; Asna et al., 2022).

Since 2015, the sales of new energy vehicles in China have continued to rise. In 2018, the sales of new energy vehicles reached 1.256 million units, a year-on-year increase of 61.7%. In 2022, the production and sales of new energy vehicles reached 7.058 million and 6.887 million, respectively, with year-on-year growth of 96.9% and 93.4%, maintaining the world’s first place for 8 consecutive years (He et al., 2022; Huang et al., 2022). Meanwhile, the construction of charging facilities is also accelerating. According to data from the Ministry of Industry and Information Technology, as of the end of 2022, a total of 5.21 million charging stations and 1973 swapping stations have been built nationwide. Among them, 2.593 million new charging stations and 675 swapping stations were added in 2022, and the construction speed of charging and swapping infrastructure has significantly accelerated. In order to ensure the safety of electric vehicle charging in China, the National Development and Reform Commission and 10 other departments have clearly stated that by the end of the 14th Five Year Plan, China’s charging infrastructure system can meet the charging needs of over 20 million electric vehicles (Li et al., 2021; Rani and Mishra, 2021; Wang et al., 2021). It is expected that by 2025, the number of new energy vehicles in China will reach 26.72 million, pure electric vehicles will reach 23.24 million, and the total number of charging stations in China will reach 6.543 million. The relevant factors involved in the site selection process of charging piles mainly include the construction cost, construction period, and operation and maintenance cost of charging piles, and other factors need to be considered, such as market demand, power supply situation, transportation convenience, etc. (Karasan et al., 2020; Liu et al., 2020; Luo et al., 2020; Bao and Xie, 2021). Therefore, the selection of charging station locations needs to comprehensively consider multiple factors, and then determine the optimization plan for charging station locations based on the relationship between each factor (Yang and Cao, 2019; Yi et al., 2019; Jiang and Wan, 2020). The main evaluation indicator in optimizing the location of charging stations is the demand of new energy electric vehicles for existing charging infrastructure. In addition, it is necessary to consider multiple aspects such as power supply, transportation convenience, parking charging, and operation and maintenance costs (Ju et al., 2019; Kizhakkan et al., 2019). The evaluation indicators for the demand for charging infrastructure construction mainly include the number of public parking lots, the number of charging stations in public parking lots, the number of taxi charging stations, and the number of bus charging stations. The number of public parking lots is generally determined based on the actual situation of the city, but can also be obtained through survey statistics, while the number of charging stations is calculated based on the number of new energy electric vehicles in the city. The number of charging stations in public parking lots needs to take into account the construction cost of charging facilities, power supply, and operation and maintenance costs. The number of taxi charging stations can be determined based on the existing number of taxis. Bus charging stations are generally set up in bus stops to meet the charging needs of new energy electric buses. Based on the evaluation indicators for the construction needs of charging piles, the optimization plan for the site selection of charging piles can be determined, and corresponding conclusions can be drawn (Liu et al., 2018; Ahn et al., 2019; Fredriksson et al., 2019). For the optimization problem of charging station location, multiple methods such as fuzzy comprehensive evaluation, analytic hierarchy process, and expert consultation can be combined to obtain the optimal solution (Li et al., 2017; Cui et al., 2018; Erbas et al., 2018). With the development of the national new energy vehicle industry and the continuous progress of electric vehicle technology, charging stations have become a key link and infrastructure in the development of the electric vehicle industry, and also an important infrastructure to promote the rapid development of the electric vehicle industry. As one of the key links in the construction of new energy electric vehicle charging stations, reasonable site selection planning plays a decisive role in the construction of charging stations. It can not only reduce resource waste, but also lower investment costs, improve service quality and efficiency, and increase user stickiness (Liu et al., 2019; Wang et al., 2019).

In practical life, people often face various decision-making problems, ranging from personal clothing, food, housing, and transportation to national policies and guidelines (Chen et al., 2021; Dong et al., 2021; Verma and Alvarez-Miranda, 2023; Saghari et al., 2023). Multiple-attribute group decision-making (MAGDM), as an important branch of modern decision science, refers to the process, where a group of experts is sorting and selecting a finite number of options under the consideration of multiple attribute constraints (Garg, 2021; Garg et al., 2021a; Liao et al., 2021). The theory and methods of MAGDM have been widely applied in various fields such as engineering design, economics, management, medicine, and military, such as investment decision-making, project evaluation, factory site selection, medical diagnosis, supply chain selection, and weapon system performance evaluation (Shabu et al., 2023; Sankar et al., 2023; Palanikumar et al., 2023). In order to portray the fuzzy information, in 1965, Zadeh (1965) put forward the fuzzy sets (FSs) to portray the ambiguity of things. As a new extended form of FSs, spherical fuzzy sets (SFSs) (Mahmood et al., 2019; Gundogdu and Kahraman, 2019) combined the advantages of PFSs (Yager and Abbasov, 2013) and picture fuzzy sets (Cuong, 2014), expressing the ambiguity of things from four aspects. The location selection problem of electric vehicle charging stations could be solved as MAGDM. Mahmood et al. (2019) and Gundogdu and Kahraman (2019) used the spherical fuzzy sets (SFSs) which could consist of the uncertainty and fuzziness during the location selection problem of electric vehicle charging stations. Yazdani et al. (2018) put forward the CoCoSo technique for MADM issues. Compared with other techniques, the main advantages of CoCoSo technique consisted of high efficiency and low computational complexity. More and more scholars have studied the CoCoSo technique based on different uncertain MAGDM (Yazdani et al., 2019; Peng and Smarandache, 2020; Torkayesh et al., 2021; Kharwar et al., 2022; Lai et al., 2022; Turskis et al., 2022). Unfortunately, we have not been able to find efficient research works for CoCoSo technique (Yazdani et al., 2018) based on the cosine similarity measure (Ye, 2016) and Euclidean distance under SFSs in the existing MADM and MAGDM. Therefore, it is of great significance to investigate the novel CoCoSo technique based on the cosine similarity measure (Ye, 2016) and Euclidean distance based on the CRITIC technique (Diakoulaki et al., 1995; Badi et al., 2023; Narang et al., 2022; Pamucar et al., 2022) under SFSs. The basic main goal of this research is to put forward the spherical fuzzy number CoCoSo (SFN-CoCoSo) technique based on the cosine similarity measure and Euclidean distance that can address MAGDM based on the CRITIC technique (Diakoulaki et al., 1995) under SFSs more efficiently. Finally, a numerical example is presented to demonstrate the SFN-CoCoSo technique and several comparative analyses are utilized to verify the advantages of SFN-CoCoSo technique. Therefore, the research motivations and aims of this research work are outlined: (1) the CRITIC technique (Diakoulaki et al., 1995) is utilized to derive the attribute’s weight; (2) the novel CoCoSo technique is extended to the SFSs environment; (3) the novel spherical fuzzy number CoCoSo (SFN-CoCoSo) technique based on the Cosine similarity measure and Euclidean distance is put forward to solve the MAGDM; (4) a numerical example for location selection problem of electric vehicle charging stations is presented to demonstrate the SFN-CoCoSo technique and several comparative analyses are utilized to verify the advantages of SFN-CoCoSo technique.

The remaining framework of this paper proceeds as follows. The SFSs are used in Section 2. The SFN-CoCoSo technique is put forward to solve the MAGDM in Section 3. A numerical example for location selection problem of electric vehicle charging stations and several comparative analysis are utilized to verify the advantages of SFN-CoCoSo technique in Section 4. Lastly, a useful conclusion is presented in Section 5.

Mahmood et al. (2019) and Gundogdu and Kahraman (2019) used the SFSs.

Mahmood et al. (2019) and Gundogdu and Kahraman (2019) determined the order relation for SFNs.

The SFN weighted averaging (SFNWA) technique and SFN weighted geometric (SFNWG) technique are used. Definition 6

Let EA j = ( ET j , EI j , EF j ) ( j = 1 , 2 , … , n ) be a family of SFNs, the SFNWA technique is used: (4) SFNWA e ω ( EA 1 , EA 2 , … , EA n ) = ⨁ j = 1 n ( e ω j EA j ) = 1 − ∏ j = 1 n ( 1 − ET j 2 ) e ω j , ∏ j = 1 n ( 1 − ET j 2 ) e ω j − ∏ j = 1 n ( 1 − ET j 2 − EI j 2 ) e ω j , ∏ j = 1 n ( EF j ) e ω j , , where e ω = ( e ω 1 , e ω 2 , … , e ω n ) T is the weight of EA j ( j = 1 , 2 , … , n ) and e ω j > 0, ∑ j = 1 n e ω j = 1.

In this section, SFN-CoCoSo technique is used for MAGDM. Let EA = { EA 1 , EA 2 , … , EA m } be alternatives. Let E G = { EG 1 , EG 2 , … , EG n } be attributes with weight information e ω = { e ω 1 , e ω 2 , … , e ω n }, where e ω j ∈ [ 0 , 1 ], ∑ j = 1 n e ω j = 1. Assume EE = { EE 1 , EE 2 , … , EE l } be a family of DMs with weight values e w = { e w 1 , e w 2 , … , e w l }, where e w k ∈ [ 0 , 1 ], ∑ k = 1 l e w k = 1. And EE ( k ) = ( EE i j ( k ) ) m × n = ( ET i j ( k ) , EI i j ( k ) , EF i j ( k ) ) m × n is the SFN-matrix, EE i j ( k ) = ( ET i j ( k ) , EI i j ( k ) , EF i j ( k ) ) means the SFNs of EA i for the attribute E G j through EE k . Subsequently, the calculating steps are carried out (see Fig. 1).

Step 1. Determine the group SFN-matrix EE ( k ) = ( EE i j ( k ) ) m × n = ( ET i j ( k ) , EI i j ( k ) , EF i j ( k ) ) m × n and the overall SFN matrix EE = ( EE i j ) m × n using the SFNWG technique. (8) EE ( k ) = [ EE i j ( k ) ] m × n = EE 11 ( k ) EE 12 ( k ) … EE 1 n ( k ) EE 21 ( k ) EE 22 ( k ) … EE 2 n ( k ) ⋮ ⋮ ⋮ ⋮ EE m 1 ( k ) EE m 2 ( k ) … EE m n ( k ) , (9) EE = [ EE i j ] m × n = EE 11 EE 12 … EE 1 n EE 21 EE 22 … EE 2 n ⋮ ⋮ ⋮ ⋮ EE m 1 EE m 2 … EE m n , (10) EE i j = ( ET i j , EI i j , EF i j ) EE i j = ∏ k = 1 l ( ( ET i j ( k ) ) 2 ) e w k , ∏ k = 1 l ( 1 − ( EF i j ( k ) ) 2 ) e w k − ∏ k = 1 l ( 1 − ( EF i j ( k ) ) 2 − ( EI i j ( k ) ) 2 ) e w k , 1 − ∏ k = 1 l ( 1 − ( EF i j ( k ) ) 2 ) e w k .

Step 2. Normalize the EE = ( EE i j ) m × n to NEE = [ NEE i j ] m × n . (11) NEE i j = ( NET i j , NEI i j , NEF i j ) = ( ET i j , EI i j , EF i j ) , EG j is a benefit criterion , ( EF i j , EI i j , ET i j ) , EG j is a cost criterion .

Step 3. Determine the SFN positive ideal solution (SFNPIS) and SFN negative ideal solution (SFNNIS): (12) SFNPIS j = ( NET j + , NEI j + , NEF j + ) , (13) SFNNIS j = ( NET j − , NEI j − , NEF j − ) , (14) SV ( SFNPIS j ) = max i SV ( NET i j , NEI i j , NEF i j ) , (15) SV ( SFNNIS j ) = min i SV ( NET i j , NEI i j , NEF i j ) .

Step 4. Construct the SFNCSM between NEE i j = ( NET i j , NEI i j , NEF i j ) and SFNPIS j = ( NET j + , NEI j + , NEF j + ). (16) SFNCSM ( NEE i j , SFNPIS j ) = 1 2 cos π 6 | ( NET i j ) 2 − ( NET j + ) 2 | + | ( NEI i j ) 2 − ( NEI j + ) 2 | + | ( NEF i j ) 2 − ( NEF j + ) 2 | + cos π 2 max | ( NET i j ) 2 − ( NET j + ) 2 | , | ( NEI i j ) 2 − ( NEI j + ) 2 | , | ( NEF i j ) 2 − ( NEF j + ) 2 | .

Step 5. Construct the SFNED between NEE i j = ( NET i j , NEI i j , NEF i j ) and SFNNIS j = ( NET j − , NEI j − , NEF j − ). (17) SFNED ( NEE i j , SFNNIS j ) = 1 2 | ( NET i j ) 2 − ( NET j − ) 2 | + | ( NEI i j ) 2 − ( NEI j − ) 2 | + | ( NEF i j ) 2 − ( NEF j − ) 2 | .

Step 6. Compute the weight values through employing the CRITIC technique.

The CRITIC technique (Diakoulaki et al., 1995) is employed to compute the weight values.

(1) The SFN correlation coefficient values (SFNCCV) are determined. (18) SFNCCV j t = ∑ i = 1 m ( φ ( SFN i j ) − φ ( SFN j ) ) ( φ ( SFN i t ) − φ ( SFN t ) ) ∑ i = 1 m ( φ ( SFN i j ) − φ ( SFN j ) ) 2 ∑ i = 1 m ( φ ( SFN i t ) − φ ( SFN t ) ) 2 , j , t = 1 , 2 , … , n , where φ ( SFN j ) = 1 2 m ∑ i = 1 m ( SFNCSM ( NEE i j , SFNPIS j ) + SFNED ( NEE i j , SFNNIS j ) ) , φ ( SFN t ) = 1 2 m ∑ i = 1 m ( SFNCSM ( NEE i t , SFNPIS t ) + SFNED ( NEE i t , SFNNIS t ) ) , φ ( SFN i j ) = 1 2 ( SFNCSM ( NEE i j , SFNPIS j ) + SFNED ( NEE i j , SFNNIS j ) ) , φ ( SFN i t ) = 1 2 ( SFNCSM ( NEE i t , SFNPIS t ) + SFNED ( NEE i t , SFNNIS t ) ) .

(2) Compute the SFN standard deviation values (SFNSDV). (19) SFNSDV j = 1 m − 1 ∑ i = 1 m ( φ ( SFN i j ) − φ ( SFN j ) ) 2 .

(3) Compute the attribute weight values. (20) e ω j = SFNSDV j ∑ t = 1 n ( 1 − SFNCCV j t ) ∑ j = 1 n ( SFNSDV j ∑ t = 1 n ( 1 − SFNCCV j t ) ) , where e ω j ∈ [ 0 , 1 ], ∑ j = 1 n e ω j = 1.

Step 7. Compute the SFN weighted arithmetic values (SFNWAV). (21) SFNWAV i = ∑ j = 1 n e ω j × 1 2 SFNCSM ( NEE i j , SFNPIS j ) + SFNED ( NEE i j , SFNNIS j ) .

Step 8. Compute the SFN weighted geometric values (SFNWGV). (22) SFNWGV i = ∑ j = 1 n 1 2 SFNCSM ( NEE i j , SFNPIS j ) + SFNED ( NEE i j , SFNNIS j ) e ω j .

Step 9. The following three SFN decision strategies (SFNDS) are employed to compute the relative importance: (23) SFNDS i a = SFNWAV i + SFNWGV i ∑ i = 1 m ( SFNWAV i + SFNWGV i ) , (24) SFNDS i b = SFNWAV i min i SFNWAV i + SFNWGV i min i SFNWGV i , (25) SFNDS i c = λ SFNWAV i + ( 1 − λ ) SFNWGV i λ max i SFNWAV i + ( 1 − λ ) max i SFNWGV i , 0 ⩽ λ ⩽ 1 , where SFNDS i a is the arithmetic sum of SFNWAV i , SFNWGV i ; SFNDS i b is the relative score of SFNWAV i , SFNWGV i , and SFNDS i c is the computed compromise of SFNWAV i , SFNWGV i . Remark 1.

λ (usually λ = 0.5) is chosen by DMs. The higher the λ, the higher the each alternative.

Step 11. Sort the alternatives in line with SFNODS i ( i = 1 , 2 , … , m ), and the higher the SFNODS i , the better the alternative is.