Fuzzy logic trust management framework for Cyber Physical-Social Systems (FTM-CPSS)

Introduction

Cyber-Physical-Social Systems (CPSSs) introduces a new and exciting paradigm that merges cyber-physical and cyber-social systems. A CPSS consists of three systems (cyber, physical, and social). Within a cyber system, there are technical components such as computers and networks, physical systems (controlled entities), and social systems (human interaction) as shown in Fig. 1. Notably, these elements are highly distributed and exhibit a dynamic stochastic hybrid nature. CPSS can simplify and expedite tasks, leading to a higher level of control and accessibility. This unique framework integrates various components, including computation, communication, sensing, actuation, and social systems.

Their application can be observed in different contexts, such as smart homes, which are built on the integration of smart devices and Smart Home Technologies (SHTs). These SHTs consist of a network of sensors, actuators, monitors, interfaces, appliances, and devices. Through this interconnected system, smart homes offer personalized information and services, accommodating the diverse preferences of their users (Rahman, 2018). The emergence of new information communication technology in urban management infrastructure has led to the development of a prototype known as a smart city, aimed at enhancing the quality of life, providing better services, and promoting a clean and safe global environment (Angelidou, 2015). Smart healthcare is a distinct sector within smart cities, characterized by its unique approach and business model. It encompasses various aspects such as aiding in diagnosis and treatment, facilitating drug research, managing health, preventing diseases, monitoring risks, utilizing virtual assistants, and incorporating smart hospitals (Tian et al., 2019). The evolution of information technology has brought the concept of smart healthcare to the forefront. This innovative framework employs a new generation of information technologies, including the Internet of Things (IoT), big data, cloud computing, and artificial intelligence, to fundamentally alter the traditional healthcare system, enhancing its efficiency, convenience, and personalization. Advanced healthcare technologies can improve self-management of health. Individuals can access timely and relevant medical services as required, with these services being more customized to their specific needs. For healthcare facilities, advanced healthcare technologies can help minimize costs, ease the burden on staff, facilitate integrated management of resources and data, and enhance the patient experience. In research settings, these technologies can lead to reduced research costs, shorter timelines, and increased efficiency in research activities. On a macro level, advanced healthcare technologies can help rectify inequalities in medical resource allocation, drive healthcare reform, support preventive health strategies, and lower overall societal healthcare costs.

The social manufacturing environment aims to facilitate customer-producer interaction by providing mediators (Jiang, Ding & Leng, 2016). Intelligent transportation is a combined hybrid system designed to improve driver behavior prediction, offering potential benefits for autonomous driving (Dressler, 2018). Smart Tourism, based on the web, takes inspiration from the idea of a “Smart City”. Smart tourism aims to deliver engaging and current information including location, directions, visuals, ratings, and descriptions of tourist destinations around the clock and across various locations (Nisiotis, Alboul & Beer, 2020). Smart energy systems aim to find the most effective and economical solution through the utilization of existing infrastructure, low-temperature district sources, and renewable energy heat sources (Camtepe & Yener, 2007). Taking into account engineering and social elements, including the operational environment, social context, personnel, regulations, equipment, and information processing, the proposal for air traffic management within a CPSS has been developed (Wang et al., 2024a). Utilizing transformer-based cyber-physical social systems for the intelligent analysis of user-generated content related to urban natural gas (Wang et al., 2024b). An automated delivery model operating in parallel with the CPSS for the final leg of delivering super-chilling products, highlighting the societal benefits of logistics drone operations (Liu, Tsang & Lee, 2024). The Metaverse is a prime example that can be effectively utilized by CPSS as shown in Fig. 2. Major tech companies around the world, such as Facebook (now rebranded as “Meta”), Microsoft, Google, and Amazon, are showing a growing interest in the Metaverse. In the Metaverse, individuals are represented as avatars and can immerse themselves in a three-dimensional environment that faithfully replicates the real world. This enables users and software agents to actively participate in interactive exchanges with each other. The integration of advanced technologies in the Metaverse aims to improve service delivery and user-platform server interaction. These technologies include digital twin for replicating real-world images, virtual reality (VR) for virtual communication, augmented reality (AR) for immersive 3D experiences, and 5G for connecting devices to high-speed, low-latency networks (Kürtünlüoğlu, Akdik & Karaarslan, 2022). The Metaverse can be described as a three-dimensional virtual environment that overcomes the limitations of online services by providing immersive experiences through avatars (Ryu et al., 2022).

Users in the Metaverse environment utilize different devices such as HTC VIVE and Oculus Quest, which utilize AR, VR, and XR (extended reality) to connect with various platform servers like Roblox, Minecraft, and Fortnite, providing a virtual reality experience through avatars (Park & Kim, 2022). Metaverse platforms provide various services through virtual worlds and avatars, such as educational programs, the application of Metaverse in audiovisual education are a key tool for expanding its accessibility, underscoring its importance in experiential learning (Sung et al., 2021). Games serve as the primary medium for promoting the widespread adoption of the Metaverse. Apart from catering to people’s interests, games also offer a means to simplify complex tasks. Given the extensive use of payment and personal data within the Metaverse, a blockchain-based game has been suggested as a solution (Ryskeldiev et al., 2018). The rise of the virtual domain, in conjunction with an exceptional intuitive platform that ensures a thrilling customer experience, is becoming prominent and is anticipated to result in a significant shift in the execution of marketing programs (Wasiq et al., 2024). A study was performed to assess the impact of corporate social responsibility on ethical and policy-related aspects (Papagiannidis, Bourlakis & Li, 2008). A comprehensive analysis was carried out on the operational framework of a corporation within Virtual Worlds and Second Life (Cagnina & Poian, 2007).

Table 1 presents an overview of each of these aggregation techniques, including their respective strengths and weaknesses.

• Weighted sum: This technique of aggregation is described as the weighted average mean for each value, where static or dynamic weights are assigned to each metric in order to obtain a single score (Wang et al., 2024c).

• Belief theory: This theory is frequently known as Dempster-Shafer theory or evidence theory. It synthesizes various forms of evidence to establish a degree of belief that lies within the range of 0 to 1, with 0 representing no support and 1 representing complete support for the evidence (Zhao, Chen & Wang, 2024).

• Bayesian system: Bayesian inference is a widely utilized method for trust computational modeling, wherein trust is regarded as a random variable that spans the interval [0, 1] and adheres to a beta distribution to represent the probability distribution of a data point, node, or interaction. This approach is fundamentally grounded in Bayes’ theorem (Zheng et al., 2023).

• Machine learning: Techniques for aggregation driven by machine learning typically involve a two-step process for making predictions. The first step is unsupervised learning, specifically clustering, which is utilized when the training data lacks labels. The second step involves multi-class supervised learning, or classification, which is employed to categorize the interactions or nodes into distinct classes, such as trustworthy and untrustworthy (Sousa et al., 2024).

• Regression analysis: This statistical method employs the slope of lines to consolidate various independent variables. There are two primary types of regression: (i) Linear regression, which predicts a single dependent variable using data from one independent variable, and (ii) multiple regression, which forecasts the outcome of a dependent variable based on data from multiple independent variables (Jayasinghe, Lee & Lee, 2017).

• Fuzzy logic: Fuzzy logic focuses on reasoning that is approximate rather than strictly accurate. It is characterized as a many-valued logic, which offers enhanced strength and flexibility over traditional binary logic. This approach embraces the notion of partial truth, allowing truth values to exist on a spectrum from fully true to entirely false. Moreover, these degrees can be regulated by particular membership functions, especially in the presence of linguistic factors. Reputation and trust are frequently represented as fuzzy measures, with membership functions illustrating the different levels of these qualities (Mansour et al., 2021).

This CPSS plays a pivotal role in driving the data science revolution by facilitating the integration of information resources from different spaces. However, the establishment of CPSSs also raises concerns regarding trust and security.

It is important to find a way to determine the level of trust in the Metaverse. Trust plays a crucial role in providing a solution for individuals and services to navigate uncertainty and mitigate risks when making decisions. By establishing a trust service platform, it is possible to reduce unexpected risks, enhance predictability, and ensure the smooth operation of the Metaverse environment while preventing service failures. After a lot of studies, we found that fuzzy logic is the most appropriate way to measure trust in the Metaverse environment because Fuzzy logic is akin to human reasoning, effectively functioning even when faced with ambiguous or unclear information, and fuzzy logic’s nature makes it suitable for evaluating trust in complex situations, allowing for efficient and effective decision-making. Fuzzy logic with social reputation is the most important metric to take into consideration, reputation serves as a social framework that mirrors how the public views the characteristics of an entity. The main goal of a reputation is to effectively convey details regarding the reliability of an entity (acting as a trustee) to others (as trustors), thereby encouraging trustors to engage in online transactions even without personal experience. Typically, reputation relies on feedback mechanisms to handle the evaluations of participants following transactions, encompassing both good and bad feedback. Many metrics must be added to obtain better and more accurate results such as service level agreement (SLA), processing performance (PP), security issues (SI), and violations (V). In this article, we propose a Fuzzy Logic Trust Management Framework for Cyber-Physical-Social Systems (FTM-CPSS); the framework consists of five tiers employing fuzzy logic that assesses the Metaverse as an example of CPSS. The proposed protocol consists of two parts. Part I presents the five tiers (service level agreement (SLA)—processing performance (PP)—social reputation (SR)—security issues (SI) and violations (V)). Part II integrates the five-tier and derives an overall trust value and status for the platform server, using a MATLAB-based trust fuzzy inference system (FIS). We compared the proposed protocol (FTM-CPSS) to other protocols by analyzing various platform server properties. The structure of this article is as follows. ‘Literature Review and Related Work’ introduces the literature review and related work; the proposed FTM-CPSS described in ‘Proposed Fuzzy Logic Trust Management Framework for Cyber-Physical-Social Systems (FTM-CPSS)’; ‘Simulation Results, Security Analysis and limitations of the Proposed System’ displays the simulation results, discusses security analysis and limitations of the proposed system; finally, the conclusion is conducted in ‘Conclusion and Future Work’.

Literature review and related work

An integrated inspection method for CPSSs has been proposed, which incorporates artificial systems, computational experiments, and parallel execution to facilitate smart manufacturing by Wang et al. (2023). Mustafa (2023) introduced an investigation which focuses on identifying and classifying the sources of personal data creation in CPSSs. Its findings are crucial for future studies dedicated to enhancing personal data security in CPSS. The proposed framework will significantly improve the functionality of CPSSs by facilitating automatic knowledge acquisition, continuous updating and iteration, as well as reasoning and decision-making processes utilizing extensive, diverse data from multiple sources. This advancement aims to establish a knowledge-driven semantic cognition and an autonomous decision-making system for industrial processes was introduced by Wang & Cheng (2021). Qian, Tang & Yu (2024) outline the current state of the process industry, utilizing a CPSS framework. The article examines the latest advancements within the sector, alongside the primary challenges and opportunities that arise. A forward-looking vision for the process industry, grounded in CPSS principles, is articulated, emphasizing three key areas: environmental sustainability and low carbon initiatives, high-value and premium production, as well as the digitalization and intellectualization of process manufacturing. The discussion concludes with an overview of advanced technologies and methodologies in CPSS, particularly those propelled by artificial intelligence and industrial digitalization, which are crucial for fostering sustainable development in the process industry. Furthermore, the evolution of comprehensive digital technologies including virtual reality, digital twins, blockchain, and big data will catalyze the realization of an innovative concept within the CPSS framework known as the industrial metaverse. Valinejad & Mili (2023) outlines a strategy for optimizing community resilience in accordance with power flow constraints in cyber-physical systems associated with power engineering, which is tackled using a multi agent-based algorithm. Abed, Abdelkader & Hashem (2023) outline the key characteristics of CPSS, examine their vulnerabilities, and identify associated challenges. Furthermore, it emphasizes the primary attacks directed at CPSS and the suggested security measures. To illustrate the concept of CPSS, a case study on its application in smart agriculture is presented.

A dynamic trust model was introduced by Li & Gui (2010) to precisely measure and forecast users’ cognitive behavior. For effective service matching in the cloud, they presented the T-broker trust-aware service brokering scheme in 2015 (Li et al., 2015). To assess user behavior, Tan & Wang (2015) suggested a combination-weighted technique based on relative entropy. Evolutionary algorithms paired with trust mechanisms have been proposed by several academics (Sanadhya & Singh, 2015). The trust evaluation approach based on the cloud model was proposed by Wang, Zhang & Li (2010). The twice excitation and deceit detection-based trust model was created by Xie, Liu & Zhao (2012). For multi-agent societies, Ahmadi & Allan (2016) presented a trust-based decision-making paradigm. For cloud-based applications, AbdAllah et al. (2017) proposed the mechanisms of trust evaluation methodologies. A trust-based probabilistic recommendation model for social networks was introduced by Wang et al. (2015). Deng et al.’s (2017) creatively proposed a two-phase recommendation process that effectively combines the interests of users and their reliable friends to initialize deep learning and synthesize user interests. This significantly increased recommendation accuracy and effectiveness. To ensure the credibility of the entities Saleh, Hamed & Hashem (2014) proposed a hybrid model to build, evaluate, and expose trust. To effectively assess the competence of cloud services based on the various trust attributes, Li & Du (2013) introduced an adaptive trust management model. Das & Islam (2012) proposed a dynamic trust model based on feedback and a new load-balancing algorithm to deal with the hostile actors’ strategically changing behavior and distribute the burden as evenly as feasible among service providers.

In order to evaluate the dependability of the provider, Wang et al. (2011) first offered a platform for service level agreements and then a reputation system was suggested based on the platform. An SLA template pool was also suggested to facilitate SLA negotiations between cloud providers and customers. However, there were no mathematical formulas and simulation tests. Manuel (2015) built a novel trust model and determined the values of four linked factors using the prior credentials and current capabilities of a cloud resource provider. To create a trust model based on fuzzy mathematics in the cloud computing environment, Mohsenzadeh & Motameni (2015) took into account success and failure interactions between cloud entities. Noor et al. (2016) discussed various trust management philosophies and methods. A brand-new distributed trust model was presented by Tan et al. (2010). In order to calculate the value of trust, they created a communication multi-dimension history vector and its distributed storage structure. The most recent evidence was added to the iterative calculations in Tan, Wang & Wang (2016) dynamic and iterative trust model. Combining Bayesian notions into the trust model, Wang & Vassileva (2003) suggested a Bayesian network-based trust model but did not provide the methodology for calculation. Reviewing previous collusion assaults by Saini, Sihag & Yadav (2014) suggested a preventative defense mechanism against them and offered a reduction mechanism to punish colluding peers. An SLA framework with negotiation, a secure monitoring system, and a third party was proposed by Binu & Gangadhar (2014). A framework for trust evaluation systems was built by Li et al. (2014), who also proposed a model of trust evaluation tailored to the field of mechanical manufacturing. According to Chiregi & Navimipour (2016), the trust value is assessed using five characteristics (availability, dependability, data integrity, identity, and capability) while taking into account the influence of opinion leaders on other entities and removing the effect of troll entities in the cloud environment.

Nitti et al. (2014) describe the trustworthiness management paradigm for the Internet of Things (IoT), which makes use of both an object’s subjective and objective attributes. The calculation of objective trustworthiness takes into account centrality as well as the long- and short-term perspectives of all networked objects. In order to calculate the single trust score, the static weighted sum aggregation is used. In their REK trust model, presented by Truong et al. (2017), the experience and reputation of an object are used as indicators of its reliability. Experience is calculated based on three variables: three factors: (1) interaction intensity; (2) interaction values (cooperative, uncooperative, or neutral); and (3) relationship status at the moment. In a mutual context-aware trust evaluation approach presented by Khani et al. (2018), the trustworthiness of an object is assessed using three social trust metrics and two QoS metrics. The three social measures are similar in relationships, communities of interest, and friendships, whereas the QoS metrics are expected and announced QoS. The status of a device (energy and computing capacity), environment (location), and task type are merged for trust metrics computation in context awareness. The static weighted sum aggregation approach is used to separate these independent trust indicators at the conclusion. Jayasinghe et al. (2019) offer a data-centric machine learning-based trust evaluation mode that incorporates social trust measures to assess the trustworthiness of nodes and uses machine learning-based trust aggregation to produce a single trust score. Chen, Bao & Guo (2016) introduce the adaptive trust model, suitable for the dynamic changing environment in SIoT, to separate the misbehaving nodes committing trust-related attacks. Two trust metrics, similarity trust and familiarity trust are used by Xia et al. (2019) to define a framework for context-aware trustworthiness inference. To calculate direct and indirect trust, the familiarity trust uses a kernel-based nonlinear multivariate grey prediction model. An ideal credit and reputation-based trust model for the Internet of Things is proposed by Xiao, Sidhu & Christianson (2015). An integrated three-tier trust management framework that evaluates cloud service providers in three main domains is proposed by Mansour et al. (2021). Abed, Abdelkader & Hashem (2024) provides a comprehensive examination of trustworthiness management in the context of CPSS. Create an innovative B-DTM framework for EC networks that incorporates off-chain trust verification alongside on-chain trust-based consensus mechanisms is proposed by Shi et al. (2024). Approaches to trust computation are shown in Table 2.

Wei et al. (2021) proposes a socio-cognitive-based trust model that is context-aware for the purpose of service delegation in service-oriented SIoT. Abdelghani et al. (2022) Presents a scalable multi-level trustworthiness management model designed to detect and mitigate malicious objects capable of conducting a range of attacks. As a result, a variety of trust metrics are employed, including, but not limited to, direct experience, ratings, the credibility of raters, frequency of ratings, and social similarity. Xiao, Sidhu & Christianson (2015) presents an ideal credit and reputation-based trust model for SIoT, which incorporates two parameters: credit (identified as the guarantor) to ascertain whether the object is capable of communication, and reputation to assess trustworthiness and identify any misbehaving nodes. A security model based on policy, referred to as Real Alert, is proposed by Li, Song & Zeng (2018) To determine the trust level of a node and the data it holds. The model specifies the policies grounded in contextual data to pinpoint the nodes that are compromised and the misleading information by assessing the model through different trust attack methodologies. Comparisons between schemes that rely on the reputation-based trust model are shown in Table 3.

Proposed fuzzy logic trust management framework for cyber-physical-social systems

Extensive analysis has revealed that fuzzy logic is the most suitable approach for gauging trust in the Metaverse environment. Fuzzy logic, resembling human reasoning, operates effectively in the presence of ambiguous or unclear data, making it well-suited for evaluating trust in complex situations and enabling efficient decision-making. Social reputation, when integrated with fuzzy logic, emerges as a key metric, as it mirrors public perceptions of an entity’s characteristics. The primary objective of a reputation is to efficiently communicate information about the trustworthiness of an entity (in the role of a trustee) to others (as trustors), in turn fostering trustors to participate in online transactions even in the absence of direct experience. Reputation commonly utilizes feedback mechanisms to manage assessments from participants’ post-transactions, encompassing good and bad feedback. Additionally, various metrics like service level agreement (SLA), processing performance (PP), security issues (SI), and violations (V) must be incorporated to enhance the quality and accuracy of results. We proposed (an FTM-CPSS) protocol that aims to establish trust in CPSS by employing fuzzy logic within a comprehensive five-tier trust management framework that evaluates trust in Metaverse as an example of CPSS. The framework comprises five main tiers:

• Tier I, SLA functions as a contract signed between a virtual service provider (VSP) and a user, establishing the conditions for service processing execution. The VSP bears full responsibility for creating the SLA and must clearly define all processing terms for the user. These terms encompass aspects such as computational cost, storage, execution time, and QoS (SC_ib_R, SS_ib_R, ST_ib_R, SQ_ib_R).

• Tier II in which the processing performance of VSP is calculated, such as average processing success ratio (APSU_i), The number of processes that the platform servers accepted but failed to complete (PIN_i), and average user termination ratio (AUTE_i).

• Tier III in which the social reputations of VSP is measured, such as good reputation (GR_ib) and bad reputation (BR_ib).

• Tier IV in which the security issues of VSP is checked.

• Tier V in which the violations committed by VSP in Tier I, II, III, and IV are monitored. Examples of violations include the amount of cost dissatisfaction exceeded the limit (War 1_Sr_i issue), the amount of time dissatisfaction exceeded the limit (War 2_Sr_i issue), the amount of storage dissatisfaction exceeded the limit (War 3_Sr_i issue), VSP is below the quality of service threshold (War 4_Sr_i issue), VSP exceeds the processing incompliance threshold (War 5_Sr_i issue), VSP exceeds the processing user termination threshold (War 6_Sr_i issue), VSP is below the social reputation threshold (War 7_Sr_i issue) and VSP undergoes security privacy problem (War 8_Sr_i issue).

The notations used in the proposed framework are detailed in Table 4.

System model

The suggested protocol is made up of a user, an avatar, a virtual service provider, Metaverse Service Manager, decentralized storage, and a network provider as shown in Fig. 3.

• •

  Service User (“SUj”:j^th): The Metaverse is accessed by users, who are the individuals responsible for creating their avatars. Once inside this virtual world, users are granted the opportunity to customize their avatars to accurately represent their preferences, personality traits, and distinctive styles. Furthermore, users possess the ability to create, share, and trade content through their avatars, actively engaging in the content-driven economy and playing a pivotal role in shaping the dynamic ecosystem of the metaverse.

• •

  Avatar: Avatars act as virtual representations of users, playing different roles such as interacting with other avatars and digital entities, accessing a wide array of Metaverse services, and participating in content-related activities. They are essential in content creation, curation, and trading, empowering users to actively engage in the content-driven economy of the Metaverse.

• •

  Virtual Server Provider (VSP): (“VSri”:i^th): VSPs are pivotal entities within the content trading ecosystem of the Metaverse. They provide a range of services related to content, including uploading, downloading, and facilitating user interfaces for external content searches. By ensuring transparency and trustworthiness in content transactions, VSPs actively contribute to establishing a safer and more efficient Metaverse environment.

• •

  Metaverse Service Manager (MSM): The responsibility of MSM includes carrying out, monitoring, and evaluating the trust computation process for virtual service providers in the Metaverse. Upon request, MSM can share the computed trust values of virtual service providers with other MSM within its operational scope. Furthermore, MSM ensures the secure storage of trust calculation results for virtual service providers.

• •

  Decentralized storage (DS) is responsible for storing content uploaded by VSPs. It offers a search function that allows VSPs to easily access the content they need. By utilizing this distributed storage method, data availability and resilience are improved, guaranteeing that Metaverse users can access and engage with their preferred content without interruptions. The communication flow can be characterized as follows (Oh et al., 2023):

  • (1)

    When users wish to register for their specific virtual world, they begin by sending a registration request query to VSP. VSP then proceeds to verify the user’s identity and generates an Avatar and a content upload key for the user.

  • (2)

    Within the virtual environment, Avatar₁ creates content that is later shared with VSP_X. VSP_X validates the legality of Avatar₁ and proceeds to upload the content to DS, providing detailed information. Additionally, VSP_X uploads verification values to 1, 2.

  • (3)

    Avatar₂ utilizes the search user interface (UI) offered by VSP_Y to access DS and explore the content that is accessible. It subsequently verifies the information pertaining to the content via DS.

  • (4)

    After receiving the necessary details, Avatar2 makes a selection of the desired content and requests access to it. VSP_Y initiates an automatic payment process through a smart contract upon receiving the corresponding content from DS. Once the smart contract is executed, VSP_Y delivers the requested content to Avatar₂.

• •

  Network provider: It also handles network communications between all of the above entities.

The suggested proposal evaluates the virtual server provider’s trustworthiness while taking numerous factors into account. As depicted in Fig. 4, the protocol is constructed from two components. Part I is composed of five major tires: Tier I assesses the platform server’s compliance, Tier II calculates the platform server’s processing performance value, and Tier III presents the social reputation. Calculate the security issues at tier IV. Tier V checks the Metaverse platform server violations. In Part II, a MATLAB-based overall trust fuzzy inference system (FIS) is developed to integrate the evaluated results of Tier I, II, III, IV, and V, to gain an overall trust value and status for platform servers in Metaverse.

Part II: five–tier integration using fuzzy logic

The trustworthiness of the i^th virtual service provider is determined by combining the results from five different tiers: SLA evaluation, processing performance computation, social reputation, security issues, and violations measurement. This overall trust value is calculated using a fuzzy inference system (FIS) called “Overall Trust”, as illustrated in Fig. 4 and explained in the articles “Using Fuzzy Logic for Trust Computation in Metaverse” and “Integration of Tiers I, II, III, IV and V Results using Fuzzy Logic”.

Trust computation using fuzzy logic in metaverse environments

Fuzzy logic, as a branch of artificial intelligence, involves the utilization of input parameters in a fuzzy inference system, where these parameters are presented as unclear or uncertain data, indicating the partial truth of a parameter (Nagarajan, Selvamuthukumaran & Thirunavukarasu, 2017). Unlike Boolean logic which operates on discrete numbers of 0 or 1, this method involves input values that span from 0 to 1. These values are subsequently utilized in membership functions to differentiate between distinct values ranges, a process commonly referred to as fuzzification (Sule et al., 2017). The fuzzy inference rule base editor in MATLAB is programmed with if-then-else rules to assign specific output decisions to input value ranges. The defuzzification process converts the output result into a clear value. Fuzzy logic offers various advantages, such as flexibility, quick response time, affordability, and logical reasoning. Therefore, fuzzy logic was employed to calculate the overall trust value and status of virtual service providers in this framework, given the dynamic nature of the Metaverse environment. The computation of trust for virtual service providers aids users in selecting the most suitable provider while maintaining a balance between services offered and price.

Integration of tier I, II, III, IV, and V results using fuzzy logic

To obtain an overall trust value for the i^th virtual service provider during the computation of section II, the fuzzy logic concept is utilized to integrate the results of Tiers I, II, III, IV, and V from section I. This integration process is illustrated in Fig. 4. The development of the “overall trust” system was facilitated by the fuzzy logic toolbox in MATLAB (The MathWorks, Natick, MA, USA). The five fuzzy inputs of the five tiers (SLA evaluation, processing performance computation, social reputation, and violations measurement) were represented using trapezoid-curve shapes, accompanied by their corresponding fuzzy membership functions, as demonstrated in Fig. 5A. The input values for membership functions are limited to the range of [0, 100], and are converted into fuzzy linguistic input variables, SLA evaluation and processing performance computation choose one value of (low–medium-high), but the social reputation takes one value of (low-high) because the reputation can be good or bad it cannot be average.

The security issues and violations measurement determine yes or no because these two properties require (yes) or (no) and do not include any other options. As well as their respective fuzzy membership functions were represented using a trapezoidal shape. Centroid defuzzification was utilized to obtain a precise overall trust value for the i^th virtual service provider as illustrated in Table 11.

Table 11:

System design and structure.

The five fuzzy inputs (SLA evaluation, processing performance computation, social reputation, and violations measurement) were represented using trapezoid-curve shapes, accompanied by their corresponding fuzzy membership functions, as demonstrated in Fig. 5A. The input values for membership functions are limited to the range of [0, 100], and are converted into fuzzy linguistic input variables, SLA evaluation and processing performance computation choose one value of (low-medium-high), but the social reputation takes one value of (low-high) because the reputation can be good or bad it cannot be average. The security issues and violations measurement determine yes or no because these two properties require (yes) or (no) and do not include any other options. As well as their respective fuzzy membership functions were represented using a trapezoidal shape. Centroid defuzzification was utilized to obtain a precise overall trust value for the i^th virtual service provider as illustrated in this table.

FIS type: Mamdani	Rules: 72	Defuzzification Type: Centroid
	Input	Output
No	5	1
Name	I-SLA, II-PP, III-SR, IV-SI, V-VM	Overall trust
No. of membership functions	SLA :3 & PP:3 & SR:2 & SI:2 & VM:2	4
Membership function type	Trapezoidal	Trapezoidal
Membership function name and Rang for each tier.	I-SLA, II-PP (Low-Medium-High) (0–40) (30–70) (60–100)	Low-Medium-High-Excellent (0–30) (30–60) (60–90) (90–100)
	III-SR (low-high) (0–60) (40–100)
	IV-SI, V-VM (yes-no) (0–60) (40–100)

DOI: 10.7717/peerj-cs.3164/table-11

As illustrated in Fig. 5B, the Trapezoid-shaped curve denotes the output value membership functions (low, medium, high, excellent). The overall trust value of the i^th virtual service provider belongs to one of the four fuzzy output sets. In order to calculate the overall trust status of the i^th virtual service provider, seventy-two inference rules were incorporated into the Mamdani inference system. These rules take into account the SLA evaluation, processing performance computation, social reputation, security issues, and violation measurement. Each rule employs the AND logical operator to establish a correlation between the input and output variables. The integration of the five-tier values contributes to the formulation of the overall trust fuzzy inference system, which calculates the overall trust of the virtual service provider in the Metaverse, as shown in Fig. 5C. A smooth surface between processing performance and SLA evaluations illustrated in Fig. 6A. Smooth surface between security issues and violation measurement shown in Fig. 6B. The main goal of ‘Literature Review and Related Work’ is to determine the overall trustworthiness of virtual service providers in the Metaverse. This is accomplished by evaluating the success of interactions and the level of violations of virtual service providers, while also taking into account service user’s opinions of the SLA. Through the application of fuzzy logic, the results from the five tiers are integrated to calculate the overall trust value and status of i^th virtual service provider. Virtual service providers in the simulation were constrained to specific value ranges to verify the system equations and 72 fuzzy inference system rules under different circumstances as shown in Table 12.

Table 12:

Fuzzy inference system rules.

Virtual service providers in the simulation were constrained to specific value ranges to verify the system equations and 72 fuzzy inference system rules under different circumstances as shown in this table.

Rule no.	SLA	PP	SR	SI	VM	Overall trust
1	L	L	L	N	N	M
2	L	L	L	N	Y	L
3	L	L	L	Y	N	L
4	L	L	L	Y	Y	L
5	L	L	H	N	N	H
6	L	L	H	N	Y	M
7	L	L	H	Y	N	M
8	L	L	H	Y	Y	M
9	L	M	L	N	N	M
10	L	M	L	N	Y	M
11	L	M	L	Y	N	M
12	L	M	L	Y	Y	L
13	L	M	H	N	N	H
14	L	M	H	N	Y	M
15	L	M	H	Y	N	M
16	L	M	H	Y	Y	M
17	L	H	L	N	N	H
18	L	H	L	N	Y	M
19	L	H	L	Y	N	M
20	L	H	L	Y	Y	L
21	L	H	H	N	N	H
22	L	H	H	N	Y	M
23	L	H	H	Y	N	M
24	L	H	H	Y	Y	L
25	M	L	L	N	N	M
26	M	L	L	N	Y	L
27	M	L	L	Y	N	L
28	M	L	L	Y	Y	L
29	M	L	H	N	N	H
30	M	L	H	N	Y	M
31	M	L	H	Y	N	M
32	M	L	H	Y	Y	M
33	M	M	L	N	N	M
34	M	M	L	N	Y	M
35	M	M	L	Y	N	M
36	M	M	L	Y	Y	L
37	M	M	H	N	N	H
38	M	M	H	N	Y	M
39	M	M	H	Y	N	M
40	M	M	H	Y	Y	M
41	M	H	L	N	N	H
42	M	H	L	N	Y	M
43	M	H	L	Y	N	M
44	M	H	L	Y	Y	L
45	M	H	H	N	N	H
46	M	H	H	N	Y	M
47	M	H	H	Y	N	M
48	M	H	H	Y	Y	L
49	H	L	L	N	N	H
50	H	L	L	N	Y	M
51	H	L	L	Y	N	M
52	H	L	L	Y	Y	L
53	H	L	H	N	N	H
54	H	L	H	N	Y	M
55	H	L	H	Y	N	M
56	H	L	H	Y	Y	L
57	H	M	L	N	N	H
58	H	M	L	N	Y	M
59	H	M	L	Y	N	M
60	H	M	L	Y	Y	L
61	H	M	H	N	N	H
62	H	M	H	N	Y	H
63	H	M	H	Y	N	H
64	H	M	H	Y	Y	M
65	H	H	L	N	N	H
66	H	H	L	N	Y	M
67	H	H	L	Y	N	M
68	H	H	L	Y	Y	M
69	H	H	H	N	Y	H
70	H	H	H	Y	N	H
71	H	H	H	Y	Y	M
72	H	H	H	N	N	Excellent

DOI: 10.7717/peerj-cs.3164/table-12

Simulation results, security analysis and limitations of the proposed system

Conclusion and future work

In this article, we proposed a five-tier architecture for CPSS that evaluates trust using fuzzy logic (FTM-CPSS) to increase the efficiency, dependability, and overall satisfaction of the services. Fuzzy logic is highly effective in synthesizing various criteria and inputs, allowing for the assignment of different weights based on their significance through the application of fuzzy rules and Demonstrates exceptional proficiency in managing ambiguous or uncertain data. The first tier involves assessing the compliance of virtual service providers with the agreed service level agreement to gauge their performance, the second tier calculates the processing performance of VSP based on the successful tasks completed, the third tier measures the social reputations of VSP, the fourth tier checks the security issues of VSP, the fifth tier monitors the violations committed by VSP during specific computational periods while operating in the Metaverse. The computation in Section I consists of a five-tier evaluation process. By integrating these tiers with the overall trust fuzzy inference system developed in the Literature Review and Related Work, the total trust value is obtained. We show that the suggested protocol (FTM-CPSS) is resistant to a number of security attacks through this informal security analysis, including Self-promotion attacks (SPA), Bad-mouthing attacks (BMA), Opportunistic service attacks (OSA), On-off attacks (OOA), Whitewashing attacks (WA), Discriminatory attacks, and Ballot Stuffing attacks (BSA).

This work can be extended to measure the mutual trust between VSPs and service users, which could potentially impact both trust values. Furthermore, the trust value of service users can act as a filter against falsified ratings. It is important to consider the transaction cost as a factor influencing trust computation, as high-cost transactions are typically authentic. Additionally, the active work time of a virtual service provider should be assessed in relation to its total subscription lifespan in the Metaverse environment, reflecting the commitment of operational virtual service providers.

Supplemental Information