Contents Introduction
In In the context of transport systems, resilience is described as the system’s ability to quickly recover from disruptions, returning operational functionality to pre-disruption levels. The resilience’s efficiency decreases according to the duration and intensity of the experienced disturbances. When transportation network and supply chain planners and operators prioritise efficiency, they frequently presume that disruptions would be uncommon and random. This assumption, however, ignores the fact that disturbances, which are typically caused by traffic sensors, can have a major impact [1]. Traffic sensors, which are essential for the effective operation of transportation systems, are powered by a variety of sources, including light, heat, chemical processes, and mechanical motion. When putting sensors in remote regions, such as environmental monitoring stations, or integrating them into infrastructure, the difficulty of sustaining their power becomes obvious. Maintaining constant service levels for end-users and customers requires ensuring the robustness of these sensors. Integration of self-powered sensors into C-ITS appears to be a promising answer to these difficulties. This technique provides a promising solution, providing flexibility in deployment across multiple C-ITS scenarios [2], [3].
Furthermore, communication technology’s importance in expanding transportation networks cannot be emphasised. C-ITS, as demonstrated by technologies such as intelligent transportation systems (ITS) applications, use wireless communication to enable seamless data exchange among various elements of the transportation ecosystem, such as vehicles and infrastructure. This intentional integration not only tackles both spontaneous and deliberate interruptions in transportation networks, but also improves the system’s general robustness and resilience. C-ITS’s data transmission process begins with sensor-based data collecting, with subsequent upgrades focusing on the introduction of self-powered sensors.
The fundamental goal of C-ITS applications is to provide drivers with timely information about various factors such as ongoing roadworks and the presence of slow or stopped cars. The goal of roadworks and stopped or slow-moving vehicle notifications is to improve motorist safety by informing them of the presence of roadworks or immobile vehicles ahead, according to [4]. This is accomplished through the network-wide deployment of sensors, including self-powered sensors, that detect stationary cars or road works and communicate this information to the roadside unit (RSU). Following that, the RSU transmits this data to the vehicle’s onboard unit (OBU), telling the driver. The informed driver can modify their speed or position in response to the notice, resulting in an overall improvement in traffic safety, according to Santamaria et al. [5].
The benefits of notifying drivers ahead of stationary vehicles have been established in research using the SUMO simulation software, confirming the positive impact of the slow or immobile vehicle warning application on traffic safety. The findings suggest that early driver awareness, together with the increased headway provided by warnings, contributes to an overall improvement in traffic safety. C-ITS strive to inform drivers about current legislation and road conditions, including data such as speed limits, weather conditions, and vehicle signage, in addition to safety-focused applications. These apps are critical in maintaining network order and optimizing traffic for increased efficiency. According to a study conducted in Northern Finland, the deployment of self-powered sensors is an efficient strategy for monitoring network parameters, notably real-time road weather information transfer, utilizing ITS-5G and 5G technologies, [6]. As urban populations and traffic volumes continue to climb, the need for traffic management systems to improve traffic efficiency and safety has expanded, [7]. The effectiveness of traffic management projects is dependent on critical data such as traffic density, flow, and speed, which can be obtained sustainably with the use of self-powered sensors, as highlighted by [8]. Through the onboard device, vehicles receive instructions to modify their location and speed based on the collected data and traffic management algorithms. Various traffic management programmes, such as the green light best speed advisory (GLOSA) in the domain of C-ITS, are meant to minimise average waiting times at traffic signals by advising drivers with recommended speeds. According to Sharara et al. [9], this method attempts to improve overall traffic safety, reduce congestion, and improve driving comfort. The use of GLOSA-based route planning algorithms inside C-ITS, as evidenced by studies such as those done by Karoui et al. [10], demonstrates a balanced strategy that results in reduced travel time and fuel savings for drivers.
A. Literature Review
A significant advancement was made in the management of imprecision in decision-making contexts through the introduction of the concept of “fuzzy sets” (FS), which was proposed by Zadeh [11]. As a means of navigating the complexities of decision-making processes, Zadeh’s mathematical approach served as a useful tool for communicating information that was imprecise and ambiguous. Atanassov [12] extended this work by introducing “intuitionistic fuzzy sets” (IFS), analyzing both membership and non-membership aspects, and improving fuzzy sets’ ability to deal with complex decision-making circumstances. Cuong [13], [14] suggested “picture fuzzy sets” (PFS), in the search for more complete models, employing visual representations for a realistic depiction of human viewpoints in decision-making. Cuong and Hai [15], [16] introduced key operators and properties. Through the provision of projection models [17], generalized dice similarity measurements [18], and specialized similarity measures [19] designed specifically for PFSs, Wei et al. [17], [18], [19] made a contribution. Singh’s work on “correlation coefficients for picture fuzzy sets” [20] develops specialized metrics for assessing relationships inside PFSs. Son [21] introduced a novel clustering technique specialized for PFSs. Phong et al. [22] conducted a study to investigate the fundamental characteristics of fuzzy relations within PFSs. Ashraf et al. [24], [25] and Li et al. [23] offered new ideas, such as generalised simplified neutrosophic Einstein AOs and a distinct distance metric for fuzzy collections of cubic PFSs. Both of these ideas were proposed by the authors. The discovery of “spherical fuzzy sets” (SFS) was driven by constraints in PFSs, particularly when combined values were more than one [26], [27].
For decision-making with several attributes, Munir et al. [28] developed T-SF Einstein hybrid aggregation processes. The selection of photovoltaic cells was investigated by Zeng et al. [29] using T-SF Einstein interactive aggregation operators. The power of T-SF The use of Muirhead mean operators in group decision-making with many attributes was examined by Liu et al. [30]. The use of T-SF Hamacher aggregation operators was examined by Ullah et al. [31] in the testing of search and rescue robots. To evaluate prospective social banking systems, Zdemirci et al. [32] used a T-SF DEMATEL approach. Sarkar et al. [33] investigated Sugeno-Weber triangular norm-based aggregation operators in the context of T-SF Hypersoft. In their study, Gurmani et al. [34] suggested Multi-Criteria Decision-Making (MCDM) model with several attributes that uses the linguistic interval-valued T-SF TOPSIS technique to select the most appropriate construction firm. These contributions improve our understanding and implementation of T-SFSs in a variety of domains, demonstrating their effectiveness in complicated decision-making settings.
The CRITIC technique was first introduced by Diakoulaki et al. [35]. Assigning relative importance to various MCDM criteria is a challenging problem, but this approach provides a reliable solution. CRITIC relies on ratio analysis for comparison. It uses pairwise comparisons to determine the relative value of each criterion. Ali [36] introduced the CRITIC-MARCOS approach, which incorporated a novel score function based on spherical fuzzy information and extended the underlying ideas of CRITIC. This advancement highlighted CRITIC’s adaptability to various information architectures as well as improved its utility in decision-making situations. Mukhametzyanov [37] increased the grasp of objective methods for finding weights, highlighting CRITIC’s ability to manage the complexity of weight determination within MCDM situations. Zafar et al. [38] illustrated CRITIC’s versatility by integrating it into a blockchain evaluation system, demonstrating its relevance in analyzing sophisticated systems. CRITIC’s adaptability is also visible in technology assessments, such as the 5G industry assessment [39], material selection for the automotive sector [40], and sustainable practices in green energy source evaluation [41]. These examples highlight CRITIC’s usefulness in a variety of decision-making contexts, emphasizing its potential contribution to long-term and innovative solutions. The comparative analysis in air conditioner selection by Vujii et al. [42] provided practical insights into CRITIC’s real-world performance. CRITIC’s integration with the grey relational analysis for investment portfolio selection [43] and its implementation in the virtual reality metaverse for customer requirements ranking [44] demonstrated CRITIC’s adaptability to different decision-making contexts. Saxena et al. [45] demonstrated the importance of CRITIC in software engineering, particularly in the best selection of reliability growth models. Vadivel et al. [46] emphasized the importance of CRITIC in sustainable supply chain management; i.e. the context of green supplier selection. Kumari and Acherjee [47] used the CRITIC-CODAS approach to select non-conventional machining processes. Their research took a holistic strategy, combining CRITIC for criterion weight determination and CODAS for overall decision-making. The thermo-hydraulic characterization and design optimization of delta-shaped barriers in a solar water heating system were the topics of Khargotra et al. [48].
There has been a considerable increase in the use of MCDM methods in diverse sectors, with a particular emphasis on methodologies such as WASPAS. Büşra and Abacolu [49] did a bibliometric investigation of MCDM methodologies. This research serves as a foundational examination of the MCDM research environment. Vaid et al. [50] demonstrated the practical used the VIKOR-WASPAS-entropy approache in the field of quiet Genset selection. Using fuzzy IDOCRIW and WASPAS algorithms, Eghbali-Zarch et al. [51] prioritized viable options for building and demolition waste management. This application demonstrated WASPAS’s adaptability in handling complicated waste management concerns. Nguyen et al. [52] provided a spherical fuzzy WASPAS-based entropy goal weighting for international Payment method selection. This exhibited WASPAS’s adaptability in the financial area. Al-Barakati et al. [53] evaluated renewable energy sources using an extended interval-valued Pythagorean fuzzy WASPAS technique. This study contributed to the evaluation of renewable energy options, with a focus on sustainability. Masoomi et al. [54] used a fuzzy BWM-WASPAS-COPRAS model to explore the strategic supplier selection problem in the context of renewable energy supply chains. Bathrinath et al. [55] investigated factors influencing long-term performance in building sites using fuzzy AHP-WASPAS methodologies. This study advanced our understanding of sustainable practices in the building business. Thanh and Lan [56] used a hybrid SWOC-FAHP-WASPAS model to analyze solar energy deployment for Vietnam’s sustainable future. They offered a detailed assessment of the potential and constraints of solar energy in the context of sustainable development. In the context of online English course selection, Handayani et al. [57] used the WASPAS technique. This application demonstrated WASPAS’s versatility in educational decision-making processes.
A variety of MCDM models and approaches have been employed for the evaluation and prioritization of public transport systems. Bouraima et al. [58] proposed in their work an integrated fuzzy MCDM model to prioritize strategies in the design and operation of bus rapid transit systems, addressing the complexities of strategic decision-making in public transportation. Ghoushchi et al. [59] made an important contribution by examining sustainable passenger transportation systems in an uncertain environment, utilizing MCDM approaches to shed light on the confluence of sustainability and transportation. Kundu et al. [60] used an integrated fuzzy multi-criteria group decision-making model to evaluate public transportation systems in the context of sustainable cities, broadening our understanding of the significance of sustainability in urban transportation design. To analyze public transport systems, Çelikbilek et al. [61] proposed a combined grey MCDM model. Kalifa et al. [62] focused on the application of MCDM, adding sustainable indices to prioritize public transportation systems, and emphasizing the incorporation of sustainable aspects into public transportation infrastructure decision-making processes. Finally, Deveci et al. [63] made an important contribution to the field by analyzing C-ITS scenarios, focusing on transportation resilience. Their research made use of type-2 neutrosophic fuzzy VIKOR to improve transportation resilience. Liu et al. [64] propose a dynamic mission abort policy utilizing deep reinforcement learning for transportation systems with stochastic dependence. Their work contributes to reliability enhancement in transportation operations. Meanwhile, Cynthia et al. [65] offer a comprehensive review of ITS, specifically focusing on VANET applications in urban areas. Their study explores various technologies and protocols, providing insights into the current landscape of ITS research and development. Our study successfully filled critical gaps in the existing literature on C-ITS. We discovered a large gap in the prioritization of self-powered sensor-based C-ITS solutions, which our study solves by offering a systematic and data-driven approach to prioritizing several categories of self-powered sensor-based C-ITS implementations. Furthermore, by incorporating the T-SF-based CRITIC-WASPAS version, we address the difficulty of dealing with imprecise information in C-ITS decision-making, a gap we observed. This sophisticated technology employs fuzzy sets in a spherical domain to provide a flexible representation of uncertainty. Recognizing the lack of a robust and personalized tool for DMs, we created the CRITIC-WASPAS approach, which is enriched with inter-criteria correlations, to fill this void by providing a powerful and adaptable tool for systematically evaluating and prioritizing self-powered sensor-based C-ITS implementations. In summary, our research not only identifies these gaps but also adds novel approaches for efficiently bridging them, considerably expanding the field of C-ITS research and application.
B. Motivation and contribution
C-ITS allows vehicles to communicate with one another, with the surrounding infrastructure, and with other transportation users, providing drivers with immediate information suited to their location and faced scenarios. This dynamic interplay improves traffic efficiency and driver comfort. However, there is a considerable void in the available literature regarding the prioritization of C-ITS solutions that use self-powered sensors. As a result, the purpose of this study is to fill this void by prioritizing distinct categories of self-powered sensor-based C-ITS implementations using criteria developed from a thorough literature assessment. Recognizing resilience as a critical aspect of transportation, expert evaluations play an important role in establishing prioritization strategies. A precisely designed survey provides a solid framework for these assessments, methodically examining each alternative against criteria developed from a thorough literature review. A detailed case study is methodically produced before face-to-face expert evaluations, giving these experts facts to guide their opinions. Following the collection of expert opinions, the data is easily integrated into recommended MCDM models, systematically prioritizing the advantages of each choice. This novel technique seeks to close a knowledge gap by providing a systematic and data-driven prioritization of self-powered sensor-based C-ITS implementations. The combination of expert evaluations and a solid MCDM model ensures a full and objective assessment, providing vital insights into the field of C-ITS research and implementation.
As C-ITS grow more prevalent in current transportation infrastructures, there is an increasing need for a prioritization framework suited specifically to self-powered sensor-based implementations. With C-ITS playing a growing role in defining transportation systems, there is a conspicuous gap in methodologies particularly developed to address the unique difficulties and opportunities given by self-powered sensors. The drive for this research comes from recognizing the existing inadequacies of prioritization systems in navigating the dynamic and intricate landscape of C-ITS decision-making. The ultimate goal is to provide a nuanced, systematic framework that allows for the diverse character of self-powered sensor implementations, providing intelligent and robust decision-making in the face of an altering transportation paradigm.
The contribution of the paper is given as below.
Utilization of fuzzy sets within a spherical domain to represent uncertainty in decision-making.
Significantly enhanced assessment of criteria importance and aggregation of criteria weights.
Effective handling of imprecise information in complex systems like C-ITS.
Introduction of T-SF logic in the CRITIC-WASPAS framework for improved analytical precision.
Inclusion of intercriteria correlations for comprehensive criteria and alternatives aggregation.
Potential to fill a significant gap in existing literature, emphasizing the novelty and importance of the work.
Provision of a personalized tool for decision-makers (DMs) to prioritize self-powered sensor-based C-ITS projects systematically.
Addressing complexities in C-ITS decision-making, leading to improved resilience and efficiency in modern transportation systems.
C. Structure of the paper
The study is structured in a logical manner, starting with Section II that introduces the reader to T-spherical fuzzy Sets (T-SFSs) and their operations, laying a firm groundwork by shedding light on basic principles, mathematical formulas, and key T-SFS characteristics. The CRITIC-WASPAS methodology, which integrates the CRITIC and WASPAS methods for aggregation and criterion weight calculation, is subsequently detailed in Section III. The intricacies of the methodology, including correlations between criteria and full aggregation, are described in great detail. Section IV applies CRITIC-WASPAS to an actual C-ITS scenario. In Section V, we cover the methodology’s outcomes, implications, and potential for future research. We conclude with a brief summary that stresses the methodology’s significance in developing decision-making frameworks for the expanding C-ITS environment. You can find the full forms of all the abbreviations used in the paper in Table 1
Preliminaries
Definition 2.1:
[66] A T-SFS in Z is defined as:
\begin{equation*} \psi = \{ \langle \zeta, {\eta }_{\psi }(\zeta), {\theta }_{\psi }(\zeta), {\varrho }_{\psi }(\zeta) | \zeta \in {Z} \rangle \}, \tag{1}\end{equation*}
Definition 2.2:
[66] When implementing T-spherical fuzzy numbers (T-SFNs) to actual situations, it is crucial to categorize them. For this, “score function” (SF) corresponds to T-SFN \begin{equation*} S(\digamma)= {\eta }^{t}_{\digamma } - {\varrho }^{t}_{\digamma }. \tag{2}\end{equation*}
\begin{equation*} {\hbar ^{\wp }}(\digamma)= {\eta }^{t}_{\digamma } + {\theta }^{t}_{\digamma } + {\varrho }^{t}_{\digamma }. \tag{3}\end{equation*}
We shall provide operational principles for aggregating T-SFNs.
Definition 2.3:
[30] Let \begin{align*} \digamma _{1}^{C}&= \Bigg \langle {\varrho }_{1}, {\theta }_{1},{\eta }_{1} \Bigg \rangle, \tag{4}\\ \digamma _{1} \vee \digamma _{2}&= \Bigg \langle max\{{\eta }_{1},{\eta }_{2}\}, min\{{\theta }_{1},{\theta }_{2}\}, min\{{\varrho }_{1},{\varrho }_{2}\} \Bigg \rangle, \tag{5}\\ \digamma _{1} \wedge \digamma _{2}&= \Bigg \langle min\{{\eta }_{1},{\eta }_{2}\}, max\{{\theta }_{1},{\theta }_{2}\}, max\{{\varrho }_{1},{\varrho }_{2}\} \Bigg \rangle, \tag{6}\\ \digamma _{1} \oplus \digamma _{2}&= \Bigg \langle \sqrt [t]{\eta ^{t}_{1}+{\eta }^{t}_{2}-{\eta }^{t}_{1}{\eta }^{t}_{2}},{\theta }_{1}{\theta }_{2}, {\varrho }_{1}{\varrho }_{2}\Bigg \rangle, \tag{7}\\ \digamma _{1} \otimes \digamma _{2}&= \Bigg \langle {\eta }_{1}{\eta }_{2}, \sqrt [t]{\theta ^{t}_{1}+{\theta }^{t}_{2} -{\theta }^{t}_{1} {\theta }^{t}_{2}}, \sqrt [t]{\varrho ^{t}_{1}+{\varrho }^{t}_{2} -{\varrho }^{t}_{1} {\varrho }^{t}_{2}} \Bigg \rangle, \tag{8}\\ \sigma \digamma _{1} &= \Bigg \langle \sqrt [t]{1-(1-{\eta }^{t}_{1})^{\sigma }},{\theta }_{1}^{\sigma }, {\varrho }_{1}^{\sigma } \Bigg \rangle, \tag{9}\\ \digamma _{1}^{\sigma }&= \Bigg \langle {\eta }_{1}^{\sigma }, \sqrt [t]{1-(1-{\theta }^{t}_{1})^{\sigma }}, \sqrt [t]{1-(1-{\varrho }^{t}_{1})^{\sigma }} \Bigg \rangle. \tag{10}\end{align*}
Definition 2.4:
Let
$\digamma _{1} \oplus \digamma _{2}=\digamma _{2} \oplus \digamma _{1}$ $\digamma _{1} \otimes \digamma _{2}=\digamma _{2} \otimes \digamma _{1}$ $\mathbb {E}\left ({\digamma _{1} \oplus \digamma _{2}}\right)=\left ({\mathbb {E} \digamma _{1}}\right) \oplus \left ({\mathbb {E} \digamma _{2}}\right)$ $\left ({\digamma _{1} \otimes \digamma _{2}}\right)^{\mathbb {E}}=\digamma _{1}^{\mathbb {E}} \otimes \digamma _{2}^{\mathbb {E}}$ $\left ({\mathbb {E}_{1}+\mathbb {E}_{2}}\right) \digamma _{1}=\left ({\mathbb {E}_{1} \digamma _{1}}\right) \oplus \left ({\mathbb {E}_{2} \digamma _{2}}\right)$ $\digamma _{1}^{\mathbb {E}_{1}+\mathbb {E}_{2}}=\digamma _{1}^{\mathbb {E}_{1}} \otimes \digamma _{2}^{\mathbb {E}_{2}}$
Definition 2.5:
For T-SFNs \begin{equation*}\mathrm {T-SFWG}(S_{1}, TS_{2}, \ldots, S_{s}) = \prod _{j=1}^{s} S_{j}^{\omega _{j}},\end{equation*}
Theorem 2.6:
The aggregated value of a collection of \begin{align*} \mathrm {T{-}SFWG}(S_{1}, S_{2}, \ldots, S_{s}) &= \left ({\prod _{j=1}^{s} (\eta _{j}^{a} + \varrho _{j}^{a})^{\omega _{j}^{a}} - \prod _{j=1}^{s} \varrho _{j}^{a\omega _{j}^{a}}, }\right. \\ &\quad \left.{ \prod _{j=1}^{s} \varrho _{j}^{a\omega _{j}^{a}}, \sqrt [n]{1 - \prod _{j=1}^{s} (1 - \theta _{j}^{a\omega _{j}^{a}})\vphantom {\prod _{j=1}^{s}}}}\right). \tag{11}\end{align*}
Algorithm of the T-SF-Based Critic-WASPAS Model for the Evaluation of C-Its Scenarios
Step 1:
Each alternative is defined by eight linguistic terms, which are listed in Table 2. These concepts are supplemented by linguistic idioms linked with knowledge, as shown in Table 3. This broad variety of linguistic terms makes it possible to depict the information evaluation process in a thorough manner. Input the T-SPFNs data set of against the suitable alternatives
$\mathrm {A_{p}};(p=1,2,\ldots,r)$ $\mathrm {C_{q}};(q=1,2,\ldots,s)$ Step 2:
Determine the ratings of DMs according to the significance of DMs provided in T-SFNs as Table 2 provides the LTs. Assume
$\digamma _{k}=\left \langle{ {\eta _{\digamma }}_{k}, {\theta _{\digamma }}_{k}, {\varrho _{\digamma }}_{k}}\right \rangle $ $\zeta _{k}$ \begin{equation*} \zeta _{k}=\frac {\digamma _{k}}{\sum _{k=1}^{p} \digamma _{k}}, k=1,2,3, \ldots, m, \tag{12}\end{equation*} View Source\begin{equation*} \zeta _{k}=\frac {\digamma _{k}}{\sum _{k=1}^{p} \digamma _{k}}, k=1,2,3, \ldots, m, \tag{12}\end{equation*}
$\digamma _{k}={\eta ^{t}_{\digamma }}_{K} - {\varrho ^{t}_{\digamma }}_{k}$ $\sum _{k=1}^{p} \zeta _{k}=1$ Step 3:
Calculate the aggregated decision matrix (ADM)
$M=\left [{M_{ij}}\right]_{r\times s}$ Step 4:
CRITIC technique for weights.
Compute the ADM’s score by using:
\begin{equation*} {Sc}_{ij}={\eta ^{t}_{\digamma }}_{i j} - {\varrho ^{t}_{\digamma }}_{i j}, \quad i = 1, 2, \ldots, r; ~j = 1, 2, \ldots, s; \tag{13}\end{equation*} View Source\begin{equation*} {Sc}_{ij}={\eta ^{t}_{\digamma }}_{i j} - {\varrho ^{t}_{\digamma }}_{i j}, \quad i = 1, 2, \ldots, r; ~j = 1, 2, \ldots, s; \tag{13}\end{equation*}
Apply the formula to transform the Sc matrix into a standard T-SFNs matrix:
\begin{align*} \widetilde {Sc}_{i j}= \begin{cases}\displaystyle \frac {Sc_{i j}-{Sc}_{j}^{-}}{Sc_{j}^{+}-{Sc}_{j}^{-}}, & \quad i = 1, 2, \ldots, r; ~j = 1, 2, \ldots, s; \\ \displaystyle \frac {Sc_{j}^{+}-{Sc}_{i j}}{Sc_{j}^{+}-{Sc}_{j}^{-}}, & \end{cases} \tag{14}\end{align*} View Source\begin{align*} \widetilde {Sc}_{i j}= \begin{cases}\displaystyle \frac {Sc_{i j}-{Sc}_{j}^{-}}{Sc_{j}^{+}-{Sc}_{j}^{-}}, & \quad i = 1, 2, \ldots, r; ~j = 1, 2, \ldots, s; \\ \displaystyle \frac {Sc_{j}^{+}-{Sc}_{i j}}{Sc_{j}^{+}-{Sc}_{j}^{-}}, & \end{cases} \tag{14}\end{align*}
${Sc}_{j}^{+}=\displaystyle \max _{i} {Sc}_{i j}, {Sc}_{j}^{-}=\displaystyle \min _{i} {Sc}_{i j}$ Determine the criteria’ standard deviations by utilising:
\begin{equation*} \beth _{j}=\sqrt {\frac {\displaystyle \sum _{i=1}^{s}\left ({{Sc}_{i j}-\bar {Sc}_{j}}\right)^{2}}{n}} \quad j = 1, 2, \ldots, s; \tag{15}\end{equation*} View Source\begin{equation*} \beth _{j}=\sqrt {\frac {\displaystyle \sum _{i=1}^{s}\left ({{Sc}_{i j}-\bar {Sc}_{j}}\right)^{2}}{n}} \quad j = 1, 2, \ldots, s; \tag{15}\end{equation*}
$\bar {Sc}_{j}=\displaystyle \sum _{i=1}^{r} \widetilde {Sc}_{i j} / $ Find the correlation coefficient of the criterion by using:
\begin{align*} k_{ij} = \frac {\displaystyle \sum _{i=1}^{s}\left ({{Sc}_{i j}-\bar {Sc}_{j}}\right)\left ({{Sc}_{i j}-\bar {Sc_{t}}}\right)}{\sqrt {\displaystyle \sum _{i=1}^{n}\left ({{Sc}_{i j}-\bar {Sc}_{j}}\right)^{2}\left ({{Sc}_{i j}-\bar {Sc}_{t}}\right)^{2}}} \quad i = 1, 2, \ldots, r;\,\,j = 1, 2, \ldots, s;\tag{16}\end{align*} View Source\begin{align*} k_{ij} = \frac {\displaystyle \sum _{i=1}^{s}\left ({{Sc}_{i j}-\bar {Sc}_{j}}\right)\left ({{Sc}_{i j}-\bar {Sc_{t}}}\right)}{\sqrt {\displaystyle \sum _{i=1}^{n}\left ({{Sc}_{i j}-\bar {Sc}_{j}}\right)^{2}\left ({{Sc}_{i j}-\bar {Sc}_{t}}\right)^{2}}} \quad i = 1, 2, \ldots, r;\,\,j = 1, 2, \ldots, s;\tag{16}\end{align*}
Analyze the information for each criterion using:
\begin{equation*} {c_{j}}=\beth _{j} \sum _{j=1}^{s}\left ({1-k_{ij}}\right) \quad j = 1, 2, \ldots, s; \tag{17}\end{equation*} View Source\begin{equation*} {c_{j}}=\beth _{j} \sum _{j=1}^{s}\left ({1-k_{ij}}\right) \quad j = 1, 2, \ldots, s; \tag{17}\end{equation*}
${cr_{j}}$ Calculate the objective weight that every single criterion should have by using:
\begin{equation*} {\omega _{j}}=\frac {cr_{j}}{\displaystyle \sum _{j=1}^{s} {cr_{j}}} \quad j = 1, 2, \ldots, s; \tag{18}\end{equation*} View Source\begin{equation*} {\omega _{j}}=\frac {cr_{j}}{\displaystyle \sum _{j=1}^{s} {cr_{j}}} \quad j = 1, 2, \ldots, s; \tag{18}\end{equation*}
Step 5:
WASPAS method.
Normalize the benefit criteria and cost criteria using:
\begin{align*} {WS}_{i j}\!= \!\begin{cases}\displaystyle \frac {s_{(ij)}}{\displaystyle \max _{i}{s_{(ij)}}}, & i \!=\! 1, 2, \ldots, r; ~j = 1, 2, \ldots, s;\\ \displaystyle \frac {\displaystyle \max _{i}{s_{(ij)}}}{s_{(ij)}}, \end{cases} \tag{19}\end{align*} View Source\begin{align*} {WS}_{i j}\!= \!\begin{cases}\displaystyle \frac {s_{(ij)}}{\displaystyle \max _{i}{s_{(ij)}}}, & i \!=\! 1, 2, \ldots, r; ~j = 1, 2, \ldots, s;\\ \displaystyle \frac {\displaystyle \max _{i}{s_{(ij)}}}{s_{(ij)}}, \end{cases} \tag{19}\end{align*}
Utilize Equation (20) to ascertain the additive relative importance in the weighted normalized data for each alternative:
\begin{equation*} {Q^{1}}_{i}=\sum _{j=1}^{n}{WS}_{i j}\cdot \omega _{j} \quad i = 1, 2, \ldots, r; \tag{20}\end{equation*} View Source\begin{equation*} {Q^{1}}_{i}=\sum _{j=1}^{n}{WS}_{i j}\cdot \omega _{j} \quad i = 1, 2, \ldots, r; \tag{20}\end{equation*}
${Q^{1}}_{i}$ Apply Equation (21) to calculate the multiplicative relative importance of the weighted normalized data for each alternative:
\begin{equation*} {Q^{2}}_{i}=\prod _{j=1}^{n} {WS}_{i j}^ {\omega _{j}} \quad i = 1, 2, \ldots, r; \tag{21}\end{equation*} View Source\begin{equation*} {Q^{2}}_{i}=\prod _{j=1}^{n} {WS}_{i j}^ {\omega _{j}} \quad i = 1, 2, \ldots, r; \tag{21}\end{equation*}
Introduce the joint generalized criterion (Q), formulated to generalize and integrate additive and multiplicative methods, as:
\begin{equation*} {Q}_{i}=\frac {1}{2}\left ({\sum _{j=1}^{n}{WS}_{i j}\cdot \omega _{j}+\prod _{j=1}^{n} {WS}_{i j}^ {\omega _{j}}}\right) \quad i = 1, 2, \ldots, r; \tag{22}\end{equation*} View Source\begin{equation*} {Q}_{i}=\frac {1}{2}\left ({\sum _{j=1}^{n}{WS}_{i j}\cdot \omega _{j}+\prod _{j=1}^{n} {WS}_{i j}^ {\omega _{j}}}\right) \quad i = 1, 2, \ldots, r; \tag{22}\end{equation*}
$\lambda \in [{0,1}]$ \begin{align*} {Q}_{i}=\lambda \sum _{j=1}^{n}{WS}_{i j}\cdot \omega _{j}+(1-\lambda)\prod _{j=1}^{n} {WS}_{i j}^ {\omega _{j}}\quad i = 1, 2, \ldots, r; \tag{23}\end{align*} View Source\begin{align*} {Q}_{i}=\lambda \sum _{j=1}^{n}{WS}_{i j}\cdot \omega _{j}+(1-\lambda)\prod _{j=1}^{n} {WS}_{i j}^ {\omega _{j}}\quad i = 1, 2, \ldots, r; \tag{23}\end{align*}
Applications of the Proposed Framework
The incorporation of self-powered sensors into C-ITS marks a new age in transportation dynamics, promising unparalleled levels of robustness. The transformative potential is envisioned in countries at the vanguard of sensor technology investments, where traffic management surpasses conventional bounds. The core innovation is the incorporation of self-powered sensors into the C-ITS framework, a strategic move that has the potential to rethink traffic optimization, improve safety criteria, and instill a sustainable mindset. The autonomy of these sensors distinguishes them, reducing the need for periodic recharging and opening up possibilities for utilizing renewable energy sources. Within the C-ITS paradigm, this study methodically dissects five various infrastructure possibilities. For starters, the use of self-powered sensors in road construction and alerts for slow or stalled cars promises to improve the system’s adaptability. Second, self-powered sensors enable the integration of in-vehicle signage, speed limits, and real-time weather condition information, which is a critical dimension for informed and safe driving experiences. Finally, the use of self-powered sensors in C-ITS traffic management, as demonstrated by the green light best speed advice, represents a comprehensive strategy to simplifying traffic flow and improving overall efficiency.
A. Definition of Alternatives
Utilization of self-powered sensors in C-ITS road works, slow or stationary vehicle warnings
$({A_{1}})$ Integration of self-powered sensors in C-ITS vehicle signage, speed limits, and weather condition information
$({A_{2}})$ Deployment of self-powered sensors in C-ITS traffic management, including green light optimum speed advice
$({A_{3}})$ Self-powered sensors for predictive maintenance in C-ITS infrastructure
$({A_{4}})$ Autonomous traffic flow management through self-powered sensors
$({A_{5}})$
B. Definition of Criteria
Improved traffic flow (benefit)
$({C_{1}})$ Positive impact on traffic flow (benefit)
$({C_{2}})$ Advanced hardware requirement (cost)
$({C_{3}})$ Need for cybersecurity (cost)
$({C_{4}})$ Competence in implementation activities planning (cost)
$({C_{5}})$ Competence in control, inspection, and maintenance (cost)
$({C_{6}})$ Better protocol for communication (benefit)
$({C_{7}})$ Implementation standardization (cost)
$({C_{8}})$
C. Experimental Results
The T-SF-based CRITIC-WASPAS application procedure can be divided into the stages that follow:
Step 1:
For each alternative, the DMs used the T-SFNs dataset and several criteria, as described in Table 4, including linguistic terms from Table 2.
Step 2:
The weights of the DMs were established through the application of the scoring function delineated in Equation 2. The resulting values are showcased in Table 5.
Step 3:
Equation (11) was used to build the ADM
$M=\left [{M_{ij}}\right]_{r\times s}$ Step 4.1:
Equation (13) was used to get the decision matrix’s aggregated score.
\begin{align*} &\hspace {-.4pc} Sc_{ij} \\ & = \begin{bmatrix} 0.0275 &\, 0.2365 &\, 0.0652 &\, 0.1011 &\, 0.5898 &\, 0.4363 &\, 0.3272 &\, 0.2221 \\ 0.5904 &\, 0.0223 &\, 0.1102 &\, 0.2343 &\, 0.3209 &\, 0.0739 &\, 0.2366 &\, -0.0084 \\ 0.0637 &\, 0.2365 &\, 0.0045 &\, 0.3198 &\, 0.5903 &\, 0.1056 &\, 0.0216 &\, 0.3101 \\ 0.1136 &\, 0.3176 &\, 0.5778 &\, 0.0272 &\, 0.0678 &\, 0.4331 &\, 0.2237 &\, 0.0569 \\ 0.2283 &\, 0.5684 &\, 0.1109 &\, 0.0625 &\, -0.0216 &\, 0.3153 &\, 0.0287 &\, -0.0223 \\ \end{bmatrix}\end{align*} View Source\begin{align*} &\hspace {-.4pc} Sc_{ij} \\ & = \begin{bmatrix} 0.0275 &\, 0.2365 &\, 0.0652 &\, 0.1011 &\, 0.5898 &\, 0.4363 &\, 0.3272 &\, 0.2221 \\ 0.5904 &\, 0.0223 &\, 0.1102 &\, 0.2343 &\, 0.3209 &\, 0.0739 &\, 0.2366 &\, -0.0084 \\ 0.0637 &\, 0.2365 &\, 0.0045 &\, 0.3198 &\, 0.5903 &\, 0.1056 &\, 0.0216 &\, 0.3101 \\ 0.1136 &\, 0.3176 &\, 0.5778 &\, 0.0272 &\, 0.0678 &\, 0.4331 &\, 0.2237 &\, 0.0569 \\ 0.2283 &\, 0.5684 &\, 0.1109 &\, 0.0625 &\, -0.0216 &\, 0.3153 &\, 0.0287 &\, -0.0223 \\ \end{bmatrix}\end{align*}
Step 4.2:
Equation (14) was used to convert the matrix
$\bar {Sc}$ \begin{align*} &\hspace {-.4pc} \bar {Sc_{i j}} \\ & =\begin{bmatrix} 1.0000 &\, 0.6203 &\, 0.1040 &\, 0.2543 &\, 0.9993 &\, 0.9810 &\, 0 &\, 0.7272 \\ 0 &\, 1.0000 &\, 0.1809 &\, 0.7086 &\, 0.5524 &\, 0 &\, 0.2965 &\, 0.0121 \\ 0.9357 &\, 0.6202 &\, 0 &\, 1.0000 &\, 1.0000 &\, 0.0859 &\, 1.0000 &\, 1.0000 \\ 0.8471 &\, 0.4658 &\, 1.0000 &\, 0 &\, 0.1303 &\, 1.0000 &\, 0.3090 &\, 0.2176 \\ 0.6434 &\, 0 &\, 0.1752 &\, 0.1160 &\, 0 &\, 0.6804 &\, 0.9800 &\, 0 \\ \end{bmatrix}\end{align*} View Source\begin{align*} &\hspace {-.4pc} \bar {Sc_{i j}} \\ & =\begin{bmatrix} 1.0000 &\, 0.6203 &\, 0.1040 &\, 0.2543 &\, 0.9993 &\, 0.9810 &\, 0 &\, 0.7272 \\ 0 &\, 1.0000 &\, 0.1809 &\, 0.7086 &\, 0.5524 &\, 0 &\, 0.2965 &\, 0.0121 \\ 0.9357 &\, 0.6202 &\, 0 &\, 1.0000 &\, 1.0000 &\, 0.0859 &\, 1.0000 &\, 1.0000 \\ 0.8471 &\, 0.4658 &\, 1.0000 &\, 0 &\, 0.1303 &\, 1.0000 &\, 0.3090 &\, 0.2176 \\ 0.6434 &\, 0 &\, 0.1752 &\, 0.1160 &\, 0 &\, 0.6804 &\, 0.9800 &\, 0 \\ \end{bmatrix}\end{align*}
Step 4.3:
Equation (15) was used to approximate the standard deviations for the criteria.
\begin{equation*} \beth _{j} = \begin{bmatrix} 0.4160 & 0.3521 & 0.4024 & 0.4230 & 0.4696 & 0.4784 & 0.4492 & 0.4501 \end{bmatrix}\end{equation*} View Source\begin{equation*} \beth _{j} = \begin{bmatrix} 0.4160 & 0.3521 & 0.4024 & 0.4230 & 0.4696 & 0.4784 & 0.4492 & 0.4501 \end{bmatrix}\end{equation*}
Step 4.4:
The Equation (16) was used to calculate the correlation coefficients of the criterion.
\begin{align*} &\hspace {-.3pc} k_{ij} \\ & =\begin{bmatrix} 1 & -0.4421 & 0.0968 & -0.2327 & 0.2722 & 0.5944 & 0.0772 & 0.6926 \\ -0.4421 & 1 & -0.1360 & 0.5913 & 0.5919 & -0.5180 & -0.5223 & 0.1931 \\ 0.0968 & -0.1360 & 1 & -0.6345 & -0.5940 & 0.5418 & -0.3052 & -0.3810 \\ -0.2327 & 0.5913 & -0.6345 & 1 & 0.6675 & -0.8955 & 0.3273 & 0.4987 \\ 0.2722 & 0.5919 & -0.5940 & 0.6675 & 1 & -0.3072 & -0.2167 & 0.8422 \\ 0.5944 & -0.5180 & 0.5418 & -0.8955 & -0.3072 & 1 & -0.4158 & -0.0674 \\ 0.0772 & -0.5223 & -0.3052 & 0.3273 & -0.2167 & -0.4158 & 1 & 0.0729 \\ 0.6926 & 0.1931 & -0.3810 & 0.4987 & 0.8422 & -0.0674 & 0.0729 & 1 \\ \end{bmatrix}\end{align*} View Source\begin{align*} &\hspace {-.3pc} k_{ij} \\ & =\begin{bmatrix} 1 & -0.4421 & 0.0968 & -0.2327 & 0.2722 & 0.5944 & 0.0772 & 0.6926 \\ -0.4421 & 1 & -0.1360 & 0.5913 & 0.5919 & -0.5180 & -0.5223 & 0.1931 \\ 0.0968 & -0.1360 & 1 & -0.6345 & -0.5940 & 0.5418 & -0.3052 & -0.3810 \\ -0.2327 & 0.5913 & -0.6345 & 1 & 0.6675 & -0.8955 & 0.3273 & 0.4987 \\ 0.2722 & 0.5919 & -0.5940 & 0.6675 & 1 & -0.3072 & -0.2167 & 0.8422 \\ 0.5944 & -0.5180 & 0.5418 & -0.8955 & -0.3072 & 1 & -0.4158 & -0.0674 \\ 0.0772 & -0.5223 & -0.3052 & 0.3273 & -0.2167 & -0.4158 & 1 & 0.0729 \\ 0.6926 & 0.1931 & -0.3810 & 0.4987 & 0.8422 & -0.0674 & 0.0729 & 1 \\ \end{bmatrix}\end{align*}
Step 4.5:
Used Equation (17) to analyse the details for each criterion.:
\begin{align*} {c_{j}}=\begin{bmatrix} 2.4122 & 2.6151 & 3.3754 & 2.8350 & 2.6974 & 3.8757 & 3.5851 & 2.3177 \\ \end{bmatrix}\end{align*} View Source\begin{align*} {c_{j}}=\begin{bmatrix} 2.4122 & 2.6151 & 3.3754 & 2.8350 & 2.6974 & 3.8757 & 3.5851 & 2.3177 \\ \end{bmatrix}\end{align*}
Step 4.6:
Equation (18) was used to calculate the objective weight allocated to each criterion:
\begin{align*} {w_{j}}=\begin{bmatrix} 0.1017 & 0.1103 & 0.1428 & 0.1191 & 0.1137 & 0.1634 & 0.1512 & 0.0977 \\ \end{bmatrix}\end{align*} View Source\begin{align*} {w_{j}}=\begin{bmatrix} 0.1017 & 0.1103 & 0.1428 & 0.1191 & 0.1137 & 0.1634 & 0.1512 & 0.0977 \\ \end{bmatrix}\end{align*}
Step 5.1:
The use of Equation (19) allowed for the normalization of the two benefit and cost criteria. The computed values are displayed in Table 7.
Steps 5.2-5.4:
Used equations (20), (21), and (22) to calculate the relative importance of each alternative in the weighted normalised data: (
$Q^{1}$ $Q^{2}$
The supplied table summarises the results of a thorough study of many alternatives, marked as
D. Sensitivity Analysis
The sensitivity analysis of the decision outcomes of the impact of the parameter
E. Comparative Analysis
We extensively studied the viability and efficacy of various decision-making methods inside the introduced T-SFS frame in our comprehensive comparison research. The results were more reliable and consistent because we did extensive investigations and used major validation and robustness checks all over the study. Table 10 provides a persuasive synopsis of the main results of our study. An in-depth comprehension of the pros and cons of alternative decision-making techniques is achieved through the examination of each component, which together lead to the discovery of subtle insights. To summarise, our research provides reliable insights for integrating T-SFSs strategically, which enhances our understanding of decision-making within the T-SFS environment.
When compared to existing techniques, the CRITIC-WASPAS methodology regularly outperforms VIKOR, COPRAS, TODIM, D-CRITIC and CPT–CoCoSo, and CRITIC-MARCOS in a comprehensive comparison involving numerous methodologies. CRITIC-WASPAS consistently identifies
F. Discussion
The CRITIC-WASPAS model’s real-world applicability, as studied through a case study focused on integrating self-powered sensors into C-ITS, reveals a transformational component in transportation dynamics. Examining five distinct infrastructure options within the C-ITS paradigm, this study evaluates the revolutionary power of autonomous sensors to enhance traffic optimisation, safety metrics, and sustainability. The autonomous nature of these sensors puts them in a prime position for innovation since it uses renewable energy sources and does away with the need for regular charging. It becomes clear that the CRITIC-WASPAS framework is an innovative and powerful hybrid of the CRITIC method and the WASPAS procedure. Together, the strengths of the CRITIC method and the adaptive features of the WASPAS methodology make CRITIC-WASPAS an effective and versatile tool for handling decision scenarios with multiple criteria. This partnership enhances the model’s capacity to offer DMs with thorough and reliable insights, empowering them to tackle challenging decision-making tasks with greater ease.
A real-world case study demonstrates the applicability of the CRITIC-WASPAS model. Not only does the model consistently choose
In a thorough comparison with recognized approaches such as VIKOR, TOP-DEMATEL, TODIM, CPT-CoCoSo, COPRAS, D-CRITIC, CRITIC-WASPAS, and CRITIC-MARCOS consistently selects
Conclusion and Implications
This study presents the novel CRITIC-WASPAS model, a strong and efficient decision-making solution within the T-SFS framework. By integrating the T-SF-CRITIC and T-SF-WASPAS methods, DMs are able to gain thorough and trustworthy understanding of complex MCDM situations. The developed T-SF-based CRITIC-WASPAS model is demonstrated to have substantial practical applicability in the real-world case study that incorporates self-powered sensors into C-ITS.
Integrating the T-SF-based CRITIC-WASPAS model to handle multiple decision contexts and completing additional validations in various real-world scenarios should be beneficial in future studies. Exploring the model’s scalability for bigger choice landscapes, as well as implementing additional improvements to handle diverse decision-making challenges, may contribute to its wider applicability and efficacy.
Declarations: Conflict of Interest None.
Data Availability: The data supporting the study’s conclusions are accessible from the corresponding author upon reasonable request.