Design and performance comparison of two implemented trust evaluation models for fifth generation (5G) and beyond 5G (B5G) network slicing using an interval type-2 fuzzy logic system

Abstract

Trust evaluation for fifth generation (5G) and beyond 5G (B5G) network slicing has become increasingly critical due to the complexity of multi-tenant orchestration, dynamic resource allocation, and strict quality of service (QoS) requirements. However, conventional trust evaluation methods cannot capture the uncertainty coming from measurement noise, linguistic ambiguity, and dynamic network conditions. In this paper, we propose a fuzzy-based system for slice trust evaluation (FSSTE) designed for 5G/B5G network slicing environments. We implement two models: FSSTEM1 and FSSTEM2. FSSTEM1 considers three input parameters: QoS, security posture (SP), and isolation integrity (II), while FSSTEM2 extends this framework by incorporating resource reliability (RR) as a fourth parameter. Both models use interval type-2 fuzzy logic system to decide the slice trust (ST) output value. We evaluated the implemented models by simulations and found that when QoS, SP, II, and RR values increase, the ST value increases consistently. For FSSTEM1, when all parameters reach 0.9, the ST value is 0.868, which is suitable for mission-critical applications. For FSSTEM2, the RR provides 21% trust improvement under poor QoS conditions, which is suitable for safety-critical deployments. Parameter sensitivity analysis for FSSTEM1 shows that QoS and II have the same impact on ST (0.251). While SP has a stronger impact (0.257) compared with QoS and II. For FSSTEM2, the higher maximum footprint uncertainty of FSSTEM2 (0.249 vs. 0.190) suggests that four-parameters assessment involves greater uncertainty. FSSTEM2 is more complex than FSSTEM1 but provides better trust evaluation, especially in dynamic multi-tenant environments where RR changes.

Keywords

trust computing trust evaluation network slicing 5G network fuzzy logic

1. Introduction

The evolution toward fifth generation (5G) and B5G networks represents a paradigm shift in telecommunications infrastructure. This change is driven by the rapid growth of connected devices, diverse service requirements, and the emergence of mission-critical applications.¹ In 5G environments, network services are categorized into three fundamental classes—enhanced mobile broadband (eMBB), ultra-reliable low-latency communications (URLLCs), and massive machine-type communications (mMTCs)—each designed to support specific quality of service (QoS) and reliability requirements. Recent studies in B5G show that these categories increasingly converge into hybrid domains such as ultra-broadband low-latency communications, massive ultra-low-latency communications, and ultra-massive broadband,² as illustrated in Figure 1. This convergence enables emerging applications such as extended reality, digital twins, autonomous logistics, and widespread intelligent systems, which demand simultaneous high throughput, ultra-reliability, and scalability.

Figure 1.

5G and B5G usage scenarios highlighting hybrid service domains.² 5G: fifth generation; B5G: beyond 5G.

To meet the diverse and dynamic requirements of these services, network slicing (NS) has become a key enabling technology. NS allows multiple virtual networks with different characteristics to share a physical infrastructure.^3,4 By isolating and tailoring logical network slices for different applications, NS provides customized service guarantees. However, the complexity of multi-tenant orchestration, dynamic resource allocation, and strict QoS requirements introduces significant challenges in ensuring both trustworthy operation and security isolation.^5,6

Security and trust have become critical aspects of NS. The expansion of the attack surface across orchestration, virtualization, and inter-slice communication layers exposes new vulnerabilities.^7,8 Compromised slices can violate isolation boundaries and affect coexisting tenants.⁵ Beyond direct security threats, operational reliability issues such as resource contention, QoS degradation, and isolation breaches undermine confidence in the slicing technology. Therefore, a robust trust evaluation mechanism is essential for ensuring secure, reliable, and transparent slice operation.^9,10

Trust computing in 5G/B5G environments includes multiple dimensions: reliability assessment, security evaluation, and behavioral trust based on service history. Recent frameworks use service level agreement (SLA)-driven, machine learning (ML), and deep learning (DL) models to structure trust management.¹¹ However, conventional methods struggle to capture the uncertainty coming from measurement noise, linguistic vagueness, and dynamic network conditions.¹² These limitations are particularly clear in B5G scenarios, where trust decisions must be made under incomplete and rapidly changing information.

Interval type-2 fuzzy logic systems (IT2FLSs) help model uncertainty in trust evaluation by including a footprint of uncertainty (FOU) that handles intra- and inter-expert variability.¹³ Unlike type-1 fuzzy logic systems (T1FLSs), which use fixed membership functions (MFs), IT2FLSs use upper and lower bounds to represent uncertainty ranges. This makes them suitable for trust assessment in dynamic and noisy environments. Furthermore, fuzzy-based trust reasoning has demonstrated effectiveness in secure and adaptive decision-making for distributed networks,¹⁴ leading to its use in NS trust evaluation. Despite these advantages, IT2FLSs have not yet been fully explored for multidimensional trust assessment in 5G/B5G NS, where real-time decision-making and resource dynamics impose challenges.

In this paper, we propose a fuzzy-based system for slice trust evaluation (FSSTE) designed for 5G/B5G NS environments. Two models are developed: FSSTEM1 and FSSTEM2. FSSTEM1 considers three input parameters—QoS, security posture (SP), and isolation integrity (II)—to describe slice trustworthiness. FSSTEM2 extends this framework by introducing resource reliability (RR) as an additional parameter, addressing trust in dynamic resource allocation.¹¹ Both models use IT2FLSs to manage uncertainty and linguistic ambiguity, producing a quantitative slice trust (ST) score that enables automated slice selection and management.

The main contributions of this paper are summarized as follows:

We propose a comprehensive trust evaluation framework for 5G/B5G NS.

We implement two IT2FLS-based models (FSSTEM1 and FSSTEM2).

We present simulation-based evaluations comparing both models, providing quantitative insights for 5G/B5G networks.

The remainder of this paper is organized as follows. Section 2 provides trust computing and its applications for 5G/B5G NS. Section 3 introduces the basics of IT2FLSs and their advantages for uncertainty modeling. Section 4 details the proposed FSSTE and its models. Section 5 shows simulation results and comparative analyses. Section 6 discusses limitations of the proposed FSSTE. Finally, Section 7 concludes the paper and outlines future research directions.

2. Related work on trust computing

Trust computing provides a systematic framework for quantifying and managing trustworthiness in complex networked systems. This section presents trust evaluation and examines its application for 5G/B5G NS environments, where dynamic resource allocation, multitenancy, and service heterogeneity introduce challenges.

2.1. Trust computing in 5G/B5G NS

Trust is defined as the expectation that an entity—whether a person, system, node, cluster, or organization—will act favorably or predictably, even under uncertain conditions.¹⁵ In the context of 5G/B5G NS, trust reflects the belief that a slice will deliver its promised QoS, maintain security guarantees, and preserve II even when operating in dynamic environments.⁹ Trust evaluation is often affected by incomplete monitoring data, delayed feedback, and differing evaluation criteria among mobile network operators, infrastructure providers (InPs), and vertical service providers.⁵ Trust computing in 5G/B5G NS includes three phases: trust collection, trust evaluation, and trust decision, forming a trust management process (TMP), as shown in Figure 2.

Figure 2.

Trust management process (TMP) structure.

2.1.1. Trust collection

Trust collection in NS environments involves gathering multidimensional data from diverse sources to assess slice trustworthiness comprehensively. Data sources include real-time telemetry from network function virtualization (NFV) infrastructure, performance metrics from virtual network functions, security audit logs from slice orchestration systems, and feedback from service consumers.¹⁶

Quantitative indicators include QoS measurements (latency, throughput, and packet loss), resource utilization patterns, security event frequencies, and SLA compliance rates.¹⁷ Qualitative data include reputation scores from previous slice deployments, security certification levels, and attestation reports from trusted third parties.¹¹ In zero trust (ZT) architectures, continuous verification mechanisms enhance traditional trust collection by providing real-time behavioral analytics and anomaly detection data.¹⁸

2.1.2. Trust evaluation

Trust evaluation transforms collected raw data into meaningful trust metrics through computational models that account for uncertainty, imprecision, and temporal dynamics. Below, we summarize representative approaches for trust evaluation in 5G/B5G environments.

Reputation-based models

Reputation-based models aggregate multisource feedback (SLA compliance, QoS telemetry, and tenant feedback) into quantitative trust scores with temporal decay and resistance to manipulation attacks (collusion, bad-mouthing, and on–off attacks). Valero et al.¹⁹ propose a trust-as-a-service framework that combines transaction histories and contextual evidence for automated resource brokering in 5G marketplaces, emphasizing low overhead and cross-domain portability. Jorquera et al.¹⁰ survey “trust assets” in 5G/B5G environments, highlighting design requirements including compatibility across software-defined networking (SDN)/NFV layers, explainability, and auditability. Theodorou et al.¹¹ develop an SLA-driven trust framework for distributed marketplaces, demonstrating automated evaluation for multistakeholder environments.

ML/DL-based models

ML/DL-based models infer hidden trust indicators from high-dimensional observables (traffic patterns, logs, and control-plane events) while adapting to nonstationary conditions and evolving threats. Cai et al.²⁰ employ prediction-assisted deep reinforcement learning (DRL) for radio access network slicing resource allocation. In their approach, learned policy stability and action-value uncertainty serve as real-time trust indicators for slices under load fluctuations. Andreou et al.²¹ leverage DRL to coordinate moving target defense strategies, achieving 96%–99% attack mitigation. Their value functions and policy entropy provide operational trust signals regarding slice SP. Allaw et al.¹⁶ integrate SDN/NFV telemetry with artificial intelligence (AI)-based anomaly detectors across multiple planes, enabling cross-layer trust inference that detects sophisticated threats. Sánchez et al.²² survey DRL techniques for NS, identifying how $Q$ -values and policy gradients encode trust-relevant information about slice reliability.

Blockchain-based models

Blockchain-based models provide tamper-proof recording of trust events (SLA proofs, policy changes, and brokerage transactions) with auditable execution via smart contracts. Xiao et al.²³ design a privacy-preserving SLA audit scheme using blockchain with order-revealing encryption, enabling verifiable compliance checking without exposing sensitive data. Nour et al.²⁴ propose a blockchain-based slice broker that manages multiprovider leasing through on-chain smart contracts with immutable reputation records and automated settlement. Togou et al.²⁵ present DBNS, a distributed blockchain-enabled framework that combines slice lifecycle management with transparent charging and monitoring, demonstrating 18% throughput improvement. Singh et al.²⁶ demonstrate blockchain consensus coordinating learning-based resource optimizers across infrastructure providers with accountable on-chain logs. Nowak et al.²⁷ survey blockchain applications for 5G security, examining data transmission, access control, and vertical industry use cases.

ZT-based models

ZT-based models treat every access request as untrusted, requiring continuous verification and policy-driven authorization considering identity, device posture, and behavioral patterns. Alnaim²⁸ proposes SecureChain-ZT, an adaptive framework that dynamically updates enforcement rules using federated learning and blockchain attestations, achieving 98.6% authentication accuracy with 3.1 ms latency overhead. Liu et al.²⁹ systematically analyze ZT architectures for IoT, identifying practical controls—micro-segmentation, attribute-based access control, continuous multifactor authentication—that extend to slice-level trust enforcement in multi-tenant 5G networks. Dhiman et al.³⁰ conduct a comparative analysis of ZT models, examining latency and scalability tradeoffs for 5G/industrial internet of things deployments and providing guidance on allocating verification checkpoints without violating QoS requirements of URLLCs.

Fuzzy-based models

Fuzzy-based models capture imprecision in operational judgments and combine linguistically expressed trust indicators into numerically interpretable scores through rule-based reasoning. Taleghani et al.¹² survey trust evaluation techniques for 6G networks, emphasizing fuzzy algorithms, outlining rule-based design, MF tuning, and integration with probabilistic evidence from monitoring systems. Higashi et al.³¹ develop a fuzzy system for relational trust in IoT contexts, transferable to multi-tenant slicing where inter-slice social signals (tenant reputation and historical interactions) complement technical key performance indicators (KPIs). Kholidy et al.³² combine dynamic hexagonal fuzzy numbers with attack-graph analysis at the 5G edge for risk-aware trust updates accounting for evolving multistep threats, achieving 37.84% higher accuracy versus conventional scoring. Yang et al.³³ propose generative adversarial learning-enabled trust management for 6G networks, applying AI-based evaluation to secure clustering for reliable communications. Table 1 provides a systematic summary of the five trust evaluation approaches for 5G/B5G environments.

Table 1.
Summary of trust evaluation approaches for 5G/B5G.

References Approach Advantages Limitations

Jorquera Valero et al.,¹⁰ Theodorou et al.,¹¹ and Valero et al.¹⁹ Reputation-based Leverages historical behavior; transparent and interpretable; low overhead ( $O (n)$ updates); and established defenses against manipulation Cold-start problem; vulnerable to coordinated attacks; and limited real-time adaptivity

Allaw et al.,¹⁶ Cai et al.,²⁰ Andreou et al.,²¹ and Sánchez et al.²² ML/DL-based Adapts to non-stationary environments; high-dimensional learning; 95%–99% attack detection; and scalable via distributed training Requires large datasets; black-box explainability; adversarial vulnerability; and inference latency 10–100 ms

Xiao et al.,²³ Nour et al.,²⁴ Togou et al.,²⁵ Singh et al.,²⁶ and Nowak et al.²⁷ Blockchain-based Cryptographically verifiable audit trails; strong accountability without TTP; transparent multioperator coordination; and automated smart contracts High latency (seconds to minutes); limited throughput; interoperability challenges; and privacy-transparency tradeoffs

Alnaim,²⁸ Liu et al.,²⁹ and Dhiman et al.³⁰ ZT-based No implicit trust assumptions; fine-grained per-slice scoring; 98.6% authentication accuracy with 3.1 ms latency; and continuous risk assessment High verification overhead; complex policy management; and PEP placement versus URLLCs latency constraints

Taleghani et al.,¹² Higashi et al.,³¹ Kholidy et al.,³² and Yang et al.³³ Fuzzy-based Handles measurement uncertainty; human-interpretable linguistic rules; and graceful degradation with incomplete data Requires domain expertise; limited high-dimensional scalability; and few studies

Proposed FSSTE Uncertainty modeling via FOU; real-time evaluation (sub-millisecond latency); interpretable linguistic rules; no training data required; and multi-dimensional assessment Simulation-based evaluation; and adaptation to temporal dynamics and trust evolution

References	Approach	Advantages	Limitations
Jorquera Valero et al.,¹⁰ Theodorou et al.,¹¹ and Valero et al.¹⁹	Reputation-based	Leverages historical behavior; transparent and interpretable; low overhead ( $O (n)$ updates); and established defenses against manipulation	Cold-start problem; vulnerable to coordinated attacks; and limited real-time adaptivity
Allaw et al.,¹⁶ Cai et al.,²⁰ Andreou et al.,²¹ and Sánchez et al.²²	ML/DL-based	Adapts to non-stationary environments; high-dimensional learning; 95%–99% attack detection; and scalable via distributed training	Requires large datasets; black-box explainability; adversarial vulnerability; and inference latency 10–100 ms
Xiao et al.,²³ Nour et al.,²⁴ Togou et al.,²⁵ Singh et al.,²⁶ and Nowak et al.²⁷	Blockchain-based	Cryptographically verifiable audit trails; strong accountability without TTP; transparent multioperator coordination; and automated smart contracts	High latency (seconds to minutes); limited throughput; interoperability challenges; and privacy-transparency tradeoffs
Alnaim,²⁸ Liu et al.,²⁹ and Dhiman et al.³⁰	ZT-based	No implicit trust assumptions; fine-grained per-slice scoring; 98.6% authentication accuracy with 3.1 ms latency; and continuous risk assessment	High verification overhead; complex policy management; and PEP placement versus URLLCs latency constraints
Taleghani et al.,¹² Higashi et al.,³¹ Kholidy et al.,³² and Yang et al.³³	Fuzzy-based	Handles measurement uncertainty; human-interpretable linguistic rules; and graceful degradation with incomplete data	Requires domain expertise; limited high-dimensional scalability; and few studies
Proposed FSSTE		Uncertainty modeling via FOU; real-time evaluation (sub-millisecond latency); interpretable linguistic rules; no training data required; and multi-dimensional assessment	Simulation-based evaluation; and adaptation to temporal dynamics and trust evolution

5G: fifth generation; B5G: beyond 5G; ML: machine learning; DL: deep learning; TTP: trusted third party; PEP: policy enforcement point; URLLC: ultra-reliable low-latency communication; ZT: zero trust; FSSTE: fuzzy-based system for slice trust evaluation; FOU: footprint of uncertainty.

While existing approaches demonstrate effectiveness in specific scenarios, they exhibit inherent tradeoffs that limit their applicability for real-time trust evaluation in 5G/B5G NS environments. Reputation-based models offer transparent and interpretable trust scoring with low-computational overhead, but lack mechanisms to quantify measurement uncertainty inherent in heterogeneous monitoring infrastructures. ML/DL-based models achieve high accuracy and adaptability to evolving threats but require large training datasets and suffer from black-box explainability, making trust decisions difficult to audit. Blockchain-based models provide strong accountability and tamper-proof audit trails, but introduce high latency (seconds to minutes) that is fatal for latency-sensitive services such as URLLCs. ZT-based models offer continuous verification and fine-grained access control but impose high overhead on PEPs, potentially violating QoS guarantees for real-time slice operations. Existing fuzzy-based models provide interpretable reasoning but cannot capture uncertainty about MFs themselves, limiting robustness under noisy or ambiguous conditions. On the other hand, the proposed FSSTE framework uses IT2FLSs to explicitly model uncertainty through FOU, enabling trust evaluation with incomplete data while maintaining real-time evaluation capability. Unlike ML/DL approaches, the proposed trust models provide human-interpretable linguistic rules that facilitate auditing and cross-stakeholder consensus without requiring large training datasets. Furthermore, compared to blockchain and ZT approaches, FSSTE achieves a low-latency trust assessment suitable for dynamic slice lifecycle management.

2.1.3. Trust decision

Trust decision is the final phase where evaluated trust information guides operational actions through three mechanisms: thresholds, ranking, and policy rules.

In contexts of NS, threshold-based decisions enforce minimum trust levels for critical operations. For example, admitting new slice tenants only when trust scores exceed 0.8, or dynamically isolating slices whose trust falls below 0.3. Ranking-based decisions prioritize resource allocation, directing premium bandwidth to higher-trust slices during congestion. Policy-based decisions encode complex rules such as “if trust<0.5 AND anomaly detected, then trigger micro-segmentation and alert operator.” This ensures automated and audited risk mitigation aligned with SLA guarantees.

Figure 2 illustrates the TMP, highlighting the iterative feedback loop where trust decisions inform data collection and evaluation refinements. This closed-loop enables dynamic trust management that responds to evolving network conditions, emerging threats, and tenant behavior patterns in real-time multistakeholder 5G/B5G environments.

3. Outline of fuzzy logic (FL)

FL provides a mathematical framework for reasoning with imprecise, uncertain, and vague information, reflecting human cognitive processes in decision-making under uncertainty. Unlike classical Boolean logic, which operates on binary truth values, FL allows for partial truth values between true and false. This enables more detailed representations of real-world phenomena.¹³ This capability makes FL suitable for trust evaluation in complex network environments where measurements are inherently uncertain and linguistic assessments are subjective.

3.1. T1FLS and T2FLS

T1FLS represents the foundation of fuzzy computing. In T1FLS, each element in a fuzzy set is defined by a crisp MF $μ_{A} (x)$ that maps input values to membership degrees in the interval $[0, 1]$ . For a linguistic variable $x$ with universe of discourse $U$ , a type-1 fuzzy set $A$ is defined as:

\begin{aligned} A = {(x, μ_{A} (x)) ∣ x \in U, μ_{A} (x) \in [0, 1]} . \end{aligned}

(1)

While T1FLS has proved effective in numerous applications, with fundamental limitations when dealing with high levels of uncertainty. The primary limitation lies in its inability to directly model uncertainty about MFs themselves. In real-world network environments, particularly in 5G/B5G NS scenarios, there are multiple sources of uncertainty as shown in the following.

Measurement noise: Network monitoring tools produce measurements with varying accuracy and temporal granularity.

Subjective variations: Expert opinions differ when defining linguistic terms.

Temporal variations: Network conditions change dynamically, causing fluctuations in parameter assessments.

T1FLS MFs are represented by crisp mathematical functions. This means there is no uncertainty about the membership grade once the MF is specified. This limitation becomes problematic when the meaning of linguistic terms varies among different stakeholders or changes dynamically with network conditions.

T2FLSs address these limitations by introducing a third dimension to represent uncertainty about MFs. In T2FLS, the MF itself is fuzzy, defined by both primary and secondary MFs. A type-2 fuzzy set $\tilde{A}$ is defined by a type-2 MF $μ_{\tilde{A}} (x, u)$ , where $x \in U$ is the primary variable and $u \in J_{x} \subseteq [0, 1]$ is the secondary variable:

\begin{aligned} \tilde{A} = {((x, u), μ_{\tilde{A}} (x, u)) ∣ x \in U, u \in J_{x} \subseteq [0, 1]} . \end{aligned}

(2)

The secondary MF $μ_{\tilde{A}} (x, u)$ assigns membership grades to primary membership grades. This enables the representation of uncertainty about the MF itself. This two-level structure provides significantly enhanced capability for modeling linguistic and measurement uncertainties compared to T1FLS. As shown in Figure 3, the fuzzy logic controller of T2FLS introduces an additional type-reduction component between the inference engine and the defuzzifier to handle the conversion from type-2 to type-1 fuzzy sets.

Figure 3.

Fuzzy logic controller structure.

3.2. Interval type-2 fuzzy logic systems (IT2FLSs)

While T2FLS offers powerful modeling capabilities, its computational complexity poses challenges for real-time applications. IT2FLSs provide a practical compromise by limiting all secondary MFs to equal unity across their domain. This simplification, introduced by Liang and Mendel,³⁴ maintains most of the uncertainty-handling benefits while significantly reducing computational requirements.

An interval type-2 fuzzy set $\tilde{A}$ is defined by:

\begin{aligned} \tilde{A} = \int_{x \in U} \int_{u \in J_{x}} 1 / (x, u) = \int_{x \in U} [J_{x} / x], \end{aligned}

(3)

where

J_{x}

is called the primary membership of

x

, and

\int

denotes union over all admissible

x

and

u

The concept in IT2FLS is the FOU, which is the union of all primary memberships and represents the uncertainty in the MF. The FOU is bounded by an upper MF (UMF) ${\bar{μ}}_{\tilde{A}} (x)$ and a lower MF (LMF) ${\underline{μ}}_{\tilde{A}} (x)$ :

\begin{aligned} FOU (\tilde{A}) = ⋃_{x \in U} [{\underline{μ}}_{\tilde{A}} (x), {\bar{μ}}_{\tilde{A}} (x)] . \end{aligned}

(4)

The FOU represents the entire uncertainty band, visualized as the shaded region between the UMF and LMF. This uncertainty representation is particularly valuable for trust evaluation.

A T1FLS (Figure 3) comprises four modules (fuzzifier, rule base, inference engine, and defuzzifier), whereas an IT2FLS adds a type reducer between inference engine and defuzzifier, totaling five modules.

Fuzzifier: The fuzzifier transforms crisp input values into fuzzy sets using predefined MFs.

Rule base: The rule base contains a collection of fuzzy IF–THEN rules of the form “IF $X$ is $A$ THEN $Y$ is $B$ ,” where $A$ and $B$ are fuzzy sets.

Inference engine: The inference engine processes fuzzy rules using the combined rule of inference to produce fuzzy output sets.

Type reducer: The type reducer converts the interval type-2 output set into a type-1 set using algorithms such as the Karnik–Mendel (KM) iterative procedure, center-of-sets, or enhanced KM (EKM) variants optimized for real-time processing.

Defuzzifier: The defuzzifier maps the type-1 fuzzy output to a crisp value using, for example, the centroid (center of gravity), center of sums, or mean of maxima. In IT2FLS, defuzzification is applied to the type-reduced set; a common choice is the average of its left and right endpoints.

IT2FLS offers several critical advantages for trust evaluation in 5G/B5G NS environments. First, the FOU explicitly models measurement noise from network monitoring systems, variations in subjective linguistic assessments by network administrators, and temporal fluctuations in network parameters. Second, IT2FLS demonstrates superior robustness to parameter variations and noisy measurements compared to T1FLS. This translates to more stable trust evaluations in heterogeneous monitoring environments. Third, the uncertainty bands allow for different interpretations of trust-related linguistic terms across network operators and service providers, enabling consensus-based decision-making across multiple stakeholders. Finally, the uncertainty representation reduces sensitivity to precise MF parameters, minimizing the need for extensive rule base tuning during deployment.³⁵

4. Proposed fuzzy-based trust models

This section presents the FSSTE, designed specifically for trust assessment in 5G and B5G NS environments. Figure 4 illustrates the system structure. We implement two models: FSSTEM1 and FSSTEM2. FSSTEM1 considers three input parameters (QoS, SP, and II) and outputs ST. FSSTEM2 extends this by incorporating RR as a fourth parameter to capture dynamic resource allocation trustworthiness—a critical dimension to NS. Both models evaluate trust at the network slice level by considering service-level performance and infrastructure-level guarantees.

Figure 4.

Proposed system structure.

QoS: QoS measures the service-level performance delivered to tenants, including end-to-end latency, throughput, packet loss rate, and availability.¹⁷ Different slice types (eMBB, URLLCs, and mMTCs) impose distinct QoS requirements that must be continuously monitored.¹ The QoS parameter is normalized to $[0, 1]$ by aggregating KPI relative to SLA targets. QoS degradation below SLA thresholds erodes tenant trust, potentially triggering service migration or contract violations. Higher QoS values directly enhance ST, serving as a primary indicator of operational reliability.

SP: SP measures security strength and protection against attack vectors covering virtualization infrastructure, inter-slice communication, and orchestration planes.^6,7 This parameter evaluates authentication and authorization mechanisms, encryption coverage for control and user planes, intrusion detection/prevention capabilities, vulnerability management, and attack surface minimization.^5,16 Higher SP values indicate stronger security measures and lower vulnerability exposure, directly enhancing slice trustworthiness and tenant confidence.

II: II measures the effectiveness of resource and traffic separation between coexisting slices in multitenant environments.^36,37 This includes computing of resource isolation via containerization and hypervisor-based virtualization, network resource isolation through bandwidth guarantees and traffic segregation, control-plane isolation preventing unauthorized management access, data plane isolation using multiprotocol label switching or virtual extensible large area network, and fault isolation containing failures within slice boundaries.^6,38 Higher II values indicate stronger isolation guarantees, reducing inter-slice interference and security violations. Compromised II renders service guarantees unreliable and significantly diminishes tenant trust.

RR: RR evaluates the consistency and reliability of physical resource allocation over time, focusing on infrastructure-level ability to maintain promised allocations.^20,22 Unlike QoS which measures service-level outcomes, RR assesses resource allocation stability (variance in central processing unit, graphics processing unit, memory, and bandwidth availability), allocation latency for provisioning and scaling, hardware reliability through mean time between failures metrics, resource contention handling during peak demand, and geographic distribution consistency for multisite deployments. High RR values indicate predictable and stable allocation essential for URLLCs slices requiring stringent guarantees. Low RR values signal potential SLA violations that erode trust and directly reduce ST.

ST: ST represents the overall trustworthiness assessment based on input parameters. The ST output is normalized to $[0, 1]$ . ST values guide network operators in slice selection for tenant requests, dynamic slice reallocation or migration decisions, SLA violation prediction and preventive actions, and resource allocation prioritization.

Figure 5 illustrates the MFs for all parameters. We employ IT2FLS to handle inherent uncertainties in network measurements and dynamic slicing environments. Table 2 summarizes the term sets. The three-level linguistic terms for each input parameter are designed to balance interpretability and computational efficiency. While finer levels (e.g., five or seven levels) could theoretically increase precision, it would exponentially increase the rule base size. Similarly, coarser levels (e.g., two levels) would oversimplify trust evaluation, failing to distinguish between moderate and best operating conditions critical for dynamic slice management. For the output parameter, FSSTEM1 uses seven levels, and FSSTEM2 uses nine levels to maintain interpretability for operational decision-making. The additional two levels in FSSTEM2 reflect the increased expressiveness, enabling finer trust decisions.

Figure 5.

MFs for FSSTEM. (a) Quality of service, (b) security posture, (c) isolation integrity, (d) resource reliability, (e) slice trust (FSSTEM1), and (f) slice trust (FSSTEM2). MF: membership function; FSSTEM: fuzzy-based system for slice trust evaluation model.

Table 2.

Parameters and their term sets for FSSTEM1 and FSSTEM2.

Parameters	Term sets
QoS	Bad (Bd), good (Gd), excellent (Ex)
SP	Weak (We), moderate (Mo), strong (St)
II	Low (Lo), medium (Me), high (Hi)
RR	Low (Lw), medium (Md), high (Hg)
ST (FSSTEM1)	ST1, ST2, ST3, ST4, ST5, ST6, ST7
ST (FSSTEM2)	ST1, ST2, ST3, ST4, ST5, ST6, ST7, ST8, ST9

FSSTEM1: fuzzy-based system for slice trust evaluation model 1; FSSTEM2: fuzzy-based system for slice trust evaluation model 2; QoS: quality of service; SP: security posture; II: isolation integrity; RR: resource reliability; ST: slice trust.

4.1. MF and fuzzy rule base (FRB) design

We design MFs for all input and output parameters using interval type-2 triangular and trapezoidal shapes, which are computationally efficient for real-time network operations. The FOU is visualized as the shaded region between the UMF and LMF, as illustrated in Figure 6.

Figure 6.

Interval type-2 triangular and trapezoidal MFs with FOU. MF: membership function; FOU: footprint of uncertainty.

We define interval type-2 triangular $f$ and trapezoidal $g$ MFs. For the triangular function $f (x; x_{0}, {\bar{w}}_{0}, {\underline{w}}_{0}, {\bar{w}}_{1}, {\underline{w}}_{1})$ , the UMF support is $[x_{0} - x_{{\bar{w}}_{0}}, x_{0} + x_{{\bar{w}}_{1}}]$ and the LMF support is $[x_{0} - x_{{\underline{w}}_{0}}, x_{0} + x_{{\underline{w}}_{1}}]$ . For the trapezoidal function $g (x; x_{0}, x_{1}, {\bar{w}}_{0}, {\underline{w}}_{0}, {\bar{w}}_{1}, {\underline{w}}_{1})$ , the plateau is $[x_{0}, x_{1}]$ , with UMF support $[x_{0} - x_{{\bar{w}}_{0}}, x_{1} + x_{{\bar{w}}_{1}}]$ and LMF support $[x_{0} - x_{{\underline{w}}_{0}}, x_{1} + x_{{\underline{w}}_{1}}]$ .

For FSSTEM, the input parameters are defined as follows:

\begin{aligned} T (QoS) & = {Bad (Bd), Good (Gd), Excellent (Ex)}, \\ T (SP) & = {Weak (We), Moderate (Mo), Strong (St)}, \\ T (II) & = {Low (Lo), Medium (Me), High (Hi)}, \\ T (RR) & = {Low (Lw), Medium (Md), High (Hg)} . \end{aligned}

The MFs for input parameters are defined using interval type-2 representations.

\begin{aligned} μ_{Bd} (QoS) & = g (QoS; {Bd}_{0}, {Bd}_{1}, {Bd}_{{\bar{w}}_{0}}, {Bd}_{{\underline{w}}_{0}}, {Bd}_{{\bar{w}}_{1}}, {Bd}_{{\underline{w}}_{1}}), \\ μ_{Gd} (QoS) & = f (QoS; {Gd}_{0}, {Gd}_{{\bar{w}}_{0}}, {Gd}_{{\underline{w}}_{0}}, {Gd}_{{\bar{w}}_{1}}, {Gd}_{{\underline{w}}_{1}}), \\ μ_{Ex} (QoS) & = g (QoS; {Ex}_{0}, {Ex}_{1}, {Ex}_{{\bar{w}}_{0}}, {Ex}_{{\underline{w}}_{0}}, {Ex}_{{\bar{w}}_{1}}, {Ex}_{{\underline{w}}_{1}}), \\ μ_{We} (SP) & = g (SP; {We}_{0}, {We}_{1}, {We}_{{\bar{w}}_{0}}, {We}_{{\underline{w}}_{0}}, {We}_{{\bar{w}}_{1}}, {We}_{{\underline{w}}_{1}}), \\ μ_{Mo} (SP) & = f (SP; {Mo}_{0}, {Mo}_{{\bar{w}}_{0}}, {Mo}_{{\underline{w}}_{0}}, {Mo}_{{\bar{w}}_{1}}, {Mo}_{{\underline{w}}_{1}}), \\ μ_{St} (SP) & = g (SP; {St}_{0}, {St}_{1}, {St}_{{\bar{w}}_{0}}, {St}_{{\underline{w}}_{0}}, {St}_{{\bar{w}}_{1}}, {St}_{{\underline{w}}_{1}}), \\ μ_{Lo} (II) & = g (II; {Lo}_{0}, {Lo}_{1}, {Lo}_{{\bar{w}}_{0}}, {Lo}_{{\underline{w}}_{0}}, {Lo}_{{\bar{w}}_{1}}, {Lo}_{{\underline{w}}_{1}}), \\ μ_{Me} (II) & = f (II; {Me}_{0}, {Me}_{{\bar{w}}_{0}}, {Me}_{{\underline{w}}_{0}}, {Me}_{{\bar{w}}_{1}}, {Me}_{{\underline{w}}_{1}}), \\ μ_{Hi} (II) & = g (II; {Hi}_{0}, {Hi}_{1}, {Hi}_{{\bar{w}}_{0}}, {Hi}_{{\underline{w}}_{0}}, {Hi}_{{\bar{w}}_{1}}, {Hi}_{{\underline{w}}_{1}}), \\ μ_{Lw} (RR) & = g (RR; {Lw}_{0}, {Lw}_{1}, {Lw}_{{\bar{w}}_{0}}, {Lw}_{{\underline{w}}_{0}}, {Lw}_{{\bar{w}}_{1}}, {Lw}_{{\underline{w}}_{1}}), \\ μ_{Md} (RR) & = f (RR; {Md}_{0}, {Md}_{{\bar{w}}_{0}}, {Md}_{{\underline{w}}_{0}}, {Md}_{{\bar{w}}_{1}}, {Md}_{{\underline{w}}_{1}}), \\ μ_{Hg} (RR) & = g (RR; {Hg}_{0}, {Hg}_{1}, {Hg}_{{\bar{w}}_{0}}, {Hg}_{{\underline{w}}_{0}}, {Hg}_{{\bar{w}}_{1}}, {Hg}_{{\underline{w}}_{1}}), \end{aligned}

where the parameters with overline (

\bar{w}

) represent the UMF bounds, while those with underline (

\underline{w}

) represent the LMF bounds, together defining the FOU.

The output linguistic parameter is ST. The term set for ST is defined as follows:

\begin{aligned} T (ST) = [\begin{matrix} Slice Trust 1 \\ Slice Trust 2 \\ ⋮ \\ Slice Trust 9 \end{matrix}] = [\begin{matrix} ST 1 \\ ST 2 \\ ⋮ \\ ST 9 \end{matrix}] . \end{aligned}

(5)

The MFs of ST for FSSTEM1 are defined as follows:

\begin{aligned} μ_{ST1} (ST) & = g (ST; {ST1}_{0}, {ST1}_{1}, {ST1}_{{\bar{w}}_{0}}, {ST1}_{{\underline{w}}_{0}}, {ST1}_{{\bar{w}}_{1}}, {ST1}_{{\underline{w}}_{1}}), \\ μ_{ST2} (ST) & = f (ST; {ST2}_{0}, {ST2}_{{\bar{w}}_{0}}, {ST2}_{{\underline{w}}_{0}}, {ST2}_{{\bar{w}}_{1}}, {ST2}_{{\underline{w}}_{1}}), \\ μ_{ST3} (ST) & = f (ST; {ST3}_{0}, {ST3}_{{\bar{w}}_{0}}, {ST3}_{{\underline{w}}_{0}}, {ST3}_{{\bar{w}}_{1}}, {ST3}_{{\underline{w}}_{1}}), \\ μ_{ST4} (ST) & = f (ST; {ST4}_{0}, {ST4}_{{\bar{w}}_{0}}, {ST4}_{{\underline{w}}_{0}}, {ST4}_{{\bar{w}}_{1}}, {ST4}_{{\underline{w}}_{1}}), \\ μ_{ST5} (ST) & = f (ST; {ST5}_{0}, {ST5}_{{\bar{w}}_{0}}, {ST5}_{{\underline{w}}_{0}}, {ST5}_{{\bar{w}}_{1}}, {ST5}_{{\underline{w}}_{1}}), \\ μ_{ST6} (ST) & = f (ST; {ST6}_{0}, {ST6}_{{\bar{w}}_{0}}, {ST6}_{{\underline{w}}_{0}}, {ST6}_{{\bar{w}}_{1}}, {ST6}_{{\underline{w}}_{1}}), \\ μ_{ST7} (ST) & = g (ST; {ST7}_{0}, {ST7}_{1}, {ST7}_{{\bar{w}}_{0}}, {ST7}_{{\underline{w}}_{0}}, {ST7}_{{\bar{w}}_{1}}, {ST7}_{{\underline{w}}_{1}}) . \end{aligned}

While for FSSTEM2, we consider nine MFs.

\begin{aligned} μ_{ST1} (ST) & = g (ST; {ST1}_{0}, {ST1}_{1}, {ST1}_{{\bar{w}}_{0}}, {ST1}_{{\underline{w}}_{0}}, {ST1}_{{\bar{w}}_{1}}, {ST1}_{{\underline{w}}_{1}}), \\ μ_{ST2} (ST) & = f (ST; {ST2}_{0}, {ST2}_{{\bar{w}}_{0}}, {ST2}_{{\underline{w}}_{0}}, {ST2}_{{\bar{w}}_{1}}, {ST2}_{{\underline{w}}_{1}}), \\ μ_{ST3} (ST) & = f (ST; {ST3}_{0}, {ST3}_{{\bar{w}}_{0}}, {ST3}_{{\underline{w}}_{0}}, {ST3}_{{\bar{w}}_{1}}, {ST3}_{{\underline{w}}_{1}}), \\ μ_{ST4} (ST) & = f (ST; {ST4}_{0}, {ST4}_{{\bar{w}}_{0}}, {ST4}_{{\underline{w}}_{0}}, {ST4}_{{\bar{w}}_{1}}, {ST4}_{{\underline{w}}_{1}}), \\ μ_{ST5} (ST) & = f (ST; {ST5}_{0}, {ST5}_{{\bar{w}}_{0}}, {ST5}_{{\underline{w}}_{0}}, {ST5}_{{\bar{w}}_{1}}, {ST5}_{{\underline{w}}_{1}}), \\ μ_{ST6} (ST) & = f (ST; {ST6}_{0}, {ST6}_{{\bar{w}}_{0}}, {ST6}_{{\underline{w}}_{0}}, {ST6}_{{\bar{w}}_{1}}, {ST6}_{{\underline{w}}_{1}}), \\ μ_{ST7} (ST) & = f (ST; {ST7}_{0}, {ST7}_{{\bar{w}}_{0}}, {ST7}_{{\underline{w}}_{0}}, {ST7}_{{\bar{w}}_{1}}, {ST7}_{{\underline{w}}_{1}}), \\ μ_{ST8} (ST) & = f (ST; {ST8}_{0}, {ST8}_{{\bar{w}}_{0}}, {ST8}_{{\underline{w}}_{0}}, {ST8}_{{\bar{w}}_{1}}, {ST8}_{{\underline{w}}_{1}}), \\ μ_{ST9} (ST) & = g (ST; {ST9}_{0}, {ST9}_{1}, {ST9}_{{\bar{w}}_{0}}, {ST9}_{{\underline{w}}_{0}}, {ST9}_{{\bar{w}}_{1}}, {ST9}_{{\underline{w}}_{1}}), \end{aligned}

The FOU width in each MF is designed based on the expected measurement uncertainty and linguistic ambiguity for each parameter in 5G/B5G network environments. For parameters with higher measurement variability (QoS and RR) are assigned wider FOUs, while more stable parameters (SP, II, and ST) have narrower FOUs.

The FRB encodes expert knowledge about the relationship between input parameters (QoS, SP, II, and optionally RR) and the output ST parameter. The FRB for FSSTEM1 and FSSTEM2 is shown in Tables 3 and 4, respectively. For FSSTEM1, the FRB consists of 27 rules derived from the Cartesian product of three input parameters with three linguistic terms each: $| T (ST) | = | T (QoS) | \times | T (SP) | \times | T (II) | = 3 \times 3 \times 3 = 27$ . Each rule follows the standard fuzzy IF–THEN structure. For example, Rule 27 represents the highest trust scenario: “IF QoS is Excellent AND SP is Strong AND II is High, THEN ST is ST7,” where all critical parameters achieve best levels suitable for mission-critical applications. Conversely, Rule 1 captures the worst-case scenario: “IF QoS is Bad AND SP is Weak AND II is Low, THEN ST is ST1,” indicating an untrustworthy slice unsuitable for any deployment. For FSSTEM2, the FRB expands to 81 rules by incorporating the additional RR parameter.

Table 3.

FRB for FSSTEM1.

Rule	QoS	SP	II	ST
1	Bd	We	Lo	ST1
2	Bd	We	Me	ST1
3	Bd	We	Hi	ST2
4	Bd	Mo	Lo	ST1
5	Bd	Mo	Me	ST2
6	Bd	Mo	Hi	ST3
7	Bd	St	Lo	ST2
8	Bd	St	Me	ST3
9	Bd	St	Hi	ST4
10	Gd	We	Lo	ST1
11	Gd	We	Me	ST2
12	Gd	We	Hi	ST3
13	Gd	Mo	Lo	ST2
14	Gd	Mo	Me	ST3
15	Gd	Mo	Hi	ST4
16	Gd	St	Lo	ST3
17	Gd	St	Me	ST4
18	Gd	St	Hi	ST5
19	Ex	We	Lo	ST2
20	Ex	We	Me	ST3
21	Ex	We	Hi	ST4
22	Ex	Mo	Lo	ST3
23	Ex	Mo	Me	ST4
24	Ex	Mo	Hi	ST5
25	Ex	St	Lo	ST4
26	Ex	St	Me	ST6
27	Ex	St	Hi	ST7

FRB: fuzzy rule base; FSSTEM1: fuzzy-based system for slice trust evaluation model 1; QoS: quality of service; SP: security posture; II: isolation integrity; ST: slice trust; Bd: bad; Gd: good; Ex: excellent; We: weak; Mo: moderate; St: strong; Lo: low; Me: medium; Hi: high.

Table 4.

FRB for FSSTEM2.

Rule	QoS	SP	II	RR	ST	Rule	QoS	SP	II	RR	ST
1	Bd	We	Lo	Lw	ST1	41	Gd	Mo	Me	Md	ST4
2	Bd	We	Lo	Md	ST1	42	Gd	Mo	Me	Hg	ST5
3	Bd	We	Lo	Hg	ST2	43	Gd	Mo	Hi	Lw	ST4
4	Bd	We	Me	Lw	ST1	44	Gd	Mo	Hi	Md	ST5
5	Bd	We	Me	Md	ST2	45	Gd	Mo	Hi	Hg	ST6
6	Bd	We	Me	Hg	ST3	46	Gd	St	Lo	Lw	ST3
7	Bd	We	Hi	Lw	ST2	47	Gd	St	Lo	Md	ST4
8	Bd	We	Hi	Md	ST3	48	Gd	St	Lo	Hg	ST5
9	Bd	We	Hi	Hg	ST4	49	Gd	St	Me	Lw	ST4
10	Bd	Mo	Lo	Lw	ST1	50	Gd	St	Me	Md	ST5
11	Bd	Mo	Lo	Md	ST2	51	Gd	St	Me	Hg	ST6
12	Bd	Mo	Lo	Hg	ST3	52	Gd	St	Hi	Lw	ST5
13	Bd	Mo	Me	Lw	ST2	53	Gd	St	Hi	Md	ST6
14	Bd	Mo	Me	Md	ST3	54	Gd	St	Hi	Hg	ST7
15	Bd	Mo	Me	Hg	ST4	55	Ex	We	Lo	Lw	ST1
16	Bd	Mo	Hi	Lw	ST3	56	Ex	We	Lo	Md	ST2
17	Bd	Mo	Hi	Md	ST4	57	Ex	We	Lo	Hg	ST3
18	Bd	Mo	Hi	Hg	ST5	58	Ex	We	Me	Lw	ST2
19	Bd	St	Lo	Lw	ST2	59	Ex	We	Me	Md	ST3
20	Bd	St	Lo	Md	ST3	60	Ex	We	Me	Hg	ST4
21	Bd	St	Lo	Hg	ST4	61	Ex	We	Hi	Lw	ST3
22	Bd	St	Me	Lw	ST3	62	Ex	We	Hi	Md	ST4
23	Bd	St	Me	Md	ST4	63	Ex	We	Hi	Hg	ST5
24	Bd	St	Me	Hg	ST5	64	Ex	Mo	Lo	Lw	ST2
25	Bd	St	Hi	Lw	ST4	65	Ex	Mo	Lo	Md	ST3
26	Bd	St	Hi	Md	ST5	66	Ex	Mo	Lo	Hg	ST4
27	Bd	St	Hi	Hg	ST6	67	Ex	Mo	Me	Lw	ST3
28	Gd	We	Lo	Lw	ST1	68	Ex	Mo	Me	Md	ST4
29	Gd	We	Lo	Md	ST2	69	Ex	Mo	Me	Hg	ST5
30	Gd	We	Lo	Hg	ST3	70	Ex	Mo	Hi	Lw	ST4
31	Gd	We	Me	Lw	ST2	71	Ex	Mo	Hi	Md	ST5
32	Gd	We	Me	Md	ST3	72	Ex	Mo	Hi	Hg	ST6
33	Gd	We	Me	Hg	ST4	73	Ex	St	Lo	Lw	ST3
34	Gd	We	Hi	Lw	ST3	74	Ex	St	Lo	Md	ST4
35	Gd	We	Hi	Md	ST4	75	Ex	St	Lo	Hg	ST5
36	Gd	We	Hi	Hg	ST5	76	Ex	St	Me	Lw	ST4
37	Gd	Mo	Lo	Lw	ST2	77	Ex	St	Me	Md	ST6
38	Gd	Mo	Lo	Md	ST3	78	Ex	St	Me	Hg	ST7
39	Gd	Mo	Lo	Hg	ST4	79	Ex	St	Hi	Lw	ST6
40	Gd	Mo	Me	Lw	ST3	80	Ex	St	Hi	Md	ST8
						81	Ex	St	Hi	Hg	ST9

FRB: fuzzy rule base; FSSTEM2: fuzzy-based system for slice trust evaluation model 2; QoS: quality of service; SP: security posture; II: isolation integrity; ST: slice trust; Bd: bad; Gd: good; Ex: excellent; We: weak; Mo: moderate; St: strong; Lo: low; Lw; low; Me: medium; Md: medium; Hi: high; Hg: high.

For type reduction, we use the EKM algorithm,³⁹ which computes the type-reduced interval $[y_{l}, y_{u}]$ with improved efficiency over the original KM method. The final crisp output is obtained as $ST = (y_{l} + y_{u}) / 2$ . The EKM algorithm’s fast convergence ensures real-time trust evaluation suitable for 5G/B5G NS environments.

5. Simulation results

In this section, we present simulation results for the proposed FSSTE models. The simulations are performed on a computer running Ubuntu 24.04 LTS with the following specifications: 8 GB of RAM and AMD Ryzen 9 7950X3D $\times$ 8 processor. For simulations, we used our developed FuzzyC system.⁴⁰ Trust categories are defined as: untrusted (ST $\in$ [0.00, 0.50]), trusted (ST $\in$ [0.51, 0.70]), and high trust (ST $\in$ [0.71, 1.00]). The threshold $ST >$ 0.7 indicates slices suitable for mission-critical applications. We decided the MFs and their terms through many simulations.

5.1. Simulation results for FSSTEM1

Figure 7 shows the relationship between ST and II for different SP values with constant QoS. Shaded regions represent the FOU, demonstrating the uncertainty-handling capability of IT2FLS. Table 5 presents quantitative results with FOU widths.

Figure 7.

Simulation results for FSSTEM1: (a) $QoS = 0.1$ , (b) $QoS = 0.5$ and (c) $QoS = 0.9$ . FSSTEM1: fuzzy-based system for slice trust evaluation model 1; QoS: quality of service.

Table 5.

ST values for FSSTEM1 under varying parameter combinations.

		QoS $=$ 0.1			QoS $=$ 0.5			QoS $=$ 0.9
SP	II	ST	FOU	Cat.	ST	FOU	Cat.	ST	FOU	Cat.
0.1	0.1	0.088	0.036	Untrusted	0.111	0.081	Untrusted	0.214	0.054	Untrusted
0.1	0.5	0.111	0.081	Untrusted	0.230	0.123	Untrusted	0.349	0.084	Untrusted
0.1	0.9	0.218	0.053	Untrusted	0.351	0.088	Untrusted	0.483	0.054	Untrusted
0.5	0.1	0.111	0.081	Untrusted	0.233	0.129	Untrusted	0.353	0.092	Untrusted
0.5	0.5	0.232	0.120	Untrusted	0.360	0.190	Untrusted	0.483	0.147	Untrusted
0.5	0.9	0.352	0.084	Untrusted	0.484	0.150	Untrusted	0.619	0.115	Trusted
0.9	0.1	0.218	0.053	Untrusted	0.354	0.096	Untrusted	0.488	0.064	Untrusted
0.9	0.5	0.352	0.084	Untrusted	0.487	0.154	Untrusted	0.731	0.154	High Trust
0.9	0.9	0.487	0.056	Untrusted	0.623	0.124	Trusted	0.868	0.124	High Trust

ST: slice trust; FSSTEM1: fuzzy-based system for slice trust evaluation model 1; QoS: quality of service; SP: security posture; II: isolation integrity; FOU: footprint of uncertainty; Cat.: category.

At $QoS = 0.1$ , the model shows conservative behavior. For $SP = 0.9$ , increasing II from 0.1 to 0.9 raises ST from 0.218 to 0.487 (123% gain), but it remains untrusted. This reflects the dominant influence of QoS. Poor service quality seriously reduces trust regardless of strong security and isolation. FOU widths remain modest (0.036–0.120), indicating confident low-trust assessments.

At $QoS = 0.5$ , trust improvements become clearer. With $(SP, II) = (0.9, 0.9)$ , ST reaches 0.623 (trusted category), representing a 28% increase from $QoS = 0.1$ . Maximum FOU (0.190) occurs at (0.5, 0.5, 0.5), reflecting uncertainty when all parameters show mixed characteristics. The nonlinear ST progression suggests synergistic effects between isolation and moderate security under medium QoS.

At $Q o S = 0.9$ , ST values increase substantially. For $SP = 0.9$ , raising II from 0.1 to 0.5 yields a 50% improvement (0.488 to 0.731), bypassing trusted to reach high trust directly. At high values configuration (0.9, 0.9, 0.9), ST is 0.868, which is suitable for mission-critical URLLCs applications. However, weak security ( $SP = 0.1$ ) limits ST to 0.483 even with maximum QoS and II, confirming the essential role of security.

Figure 8 visualizes the trust landscape through 3D surfaces. At $QoS = 0.1$ , the surface remains mostly low (blue region), creating a trust valley. At $QoS = 0.5$ , gradient transitions from blue to green emerge as SP and II increase. At $QoS = 0.9$ , a clear ridge appears at high SP and II (red/orange region), with gradients along the SP axis when II is high.

Figure 8.

Three-dimensional trust surface visualization for FSSTEM1. (a) $QoS = 0.1$ , (b) $QoS = 0.5$ , and (c) $QoS = 0.9$ . FSSTEM1: fuzzy-based system for slice trust evaluation model 1; QoS: quality of service.

Table 6 shows parameter sensitivity analysis. QoS and II have the same impact on ST (0.251). While SP has a stronger impact (0.257) compared with QoS and II. At 0.9 value, $ST = 0.868$ exceeds linear prediction, showing a positive effect. In contrast, at 0.1 value, $ST = 0.088$ shows combined degradation.

Table 6.

Parameter sensitivity analysis for FSSTEM1.

Parameter	ST at Min (0.1)	ST at Max (0.9)	Absolute change (Min–Max)
QoS	0.232	0.483	0.251
SP	0.230	0.487	0.257
II	0.233	0.484	0.251

FSSTEM1: fuzzy-based system for slice trust evaluation model 1; ST: slice trust; QoS: quality of service; SP: security posture; II: isolation integrity.

5.2. Simulation results for FSSTEM2

Figures 9 to 11 show ST versus RR for different II values with constant QoS and SP. Table 7 presents results at $RR = 1.0$ .

Figure 9.

Simulation results for FSSTEM2 ( $QoS = 0.1$ ). (a) $SP = 0.1$ , (b) $SP = 0.5$ , and (c) $SP = 0.9$ . FSSTEM2: fuzzy-based system for slice trust evaluation model 2; QoS: quality of service; SP: security posture.

Figure 10.

Simulation results for FSSTEM2 ( $QoS = 0.5$ ). (a) $SP = 0.1$ , (b) $SP = 0.5$ , and (c) $SP = 0.9$ . FSSTEM2: fuzzy-based system for slice trust evaluation model 2; QoS: quality of service; SP: security posture.

Figure 11.

Simulation results for FSSTEM2 ( $QoS = 0.9$ ). (a) $SP = 0.1$ , (b) $SP = 0.5$ , and (c) $SP = 0.9$ . FSSTEM2: fuzzy-based system for slice trust evaluation model 2; QoS: quality of service; SP: security posture.

Table 7.

ST values for FSSTEM2 under varying parameter combinations ( $RR = 1.0$ ).

		QoS $=$ 0.1			QoS $=$ 0.5			QoS $=$ 0.9
SP	II	ST	FOU	Cat.	ST	FOU	Cat.	ST	FOU	Cat.
0.1	0.1	0.229	0.057	Untrusted	0.316	0.052	Untrusted	0.320	0.039	Untrusted
0.1	0.5	0.326	0.066	Untrusted	0.405	0.075	Untrusted	0.414	0.052	Untrusted
0.1	0.9	0.412	0.036	Untrusted	0.490	0.045	Untrusted	0.500	0.024	Untrusted
0.5	0.1	0.326	0.066	Untrusted	0.405	0.075	Untrusted	0.416	0.057	Untrusted
0.5	0.5	0.417	0.088	Untrusted	0.497	0.126	Untrusted	0.508	0.095	Trusted
0.5	0.9	0.501	0.057	Trusted	0.582	0.081	Trusted	0.595	0.069	Trusted
0.9	0.1	0.412	0.036	Untrusted	0.493	0.051	Untrusted	0.503	0.031	Trusted
0.9	0.5	0.501	0.057	Trusted	0.582	0.100	Trusted	0.670	0.088	Trusted
0.9	0.9	0.591	0.037	Trusted	0.679	0.087	Trusted	0.868	0.109	High Trust

ST: slice trust; FSSTEM2: fuzzy-based system for slice trust evaluation model 2; RR: resource reliability; QoS: quality of service; SP: security posture; II: isolation integrity; FOU: footprint of uncertainty; Cat.: category.

At $QoS = 0.1$ (see Figure 9) when $RR = 1.0$ and $(SP, II) = (0.9, 0.9)$ , ST reaches 0.591, which is a 21% improvement over FSSTEM1 (0.487), crossing into trusted category. RR enables category transitions even under poor QoS, though high trust remains unachievable. FOU widths increase at mid-RR ranges, especially when $II = 0.5$ .

At $QoS = 0.5$ (see Figure 10), RR becomes very important for operation. With $(SP, II) = (0.9, 0.9)$ , increasing RR from 0.0 to 1.0 yields 44% improvement (0.472 to 0.679). Compared to FSSTEM1 (0.623), this represents 9% higher trust. Maximum FOU (0.249) at (0.5, 0.5, 0.5, 0.5) exceeds the maximum FOU of FSSTEM1 (0.190), reflecting greater uncertainty with the additional parameter dimension.

At $QoS = 0.9$ (see Figure 11) when $RR = 1.0$ and $(SP, II) = (0.9, 0.9)$ , $ST = 0.868$ , matching FSSTEM1 (0% difference). Increasing II from 0.1 to 0.9 improves ST by 72% (0.503 to 0.868). Even with moderate security ( $SP = 0.5$ ) and high isolation ( $II = 0.9$ ), $ST = 0.595$ remains trusted, confirming the necessary role of security. FOU width of 0.109 reflects the combined uncertainty from multiple factors.

Table 8 shows the progressive contribution of RR at moderate parameter levels. Gains increase rapidly between $RR = 0.5$ and $RR = 1.0$ (0.391 to 0.494), indicating that operators should prioritize high RR values.

Table 8.

Impact of RR on ST at moderate parameter levels.

RR	ST (FSSTEM2)	$Δ$ ST from RR $=$ 0.0
0.0	0.289	—
0.3	0.339	$+$ 17%
0.5	0.391	$+$ 35%
0.7	0.443	$+$ 54%
1.0	0.494	$+$ 71%

RR: resource reliability; ST: slice trust; FSSTEM2: fuzzy-based system for slice trust evaluation model 2.

Table 9 compares both models. FSSTEM2 provides the greatest improvement (21%) when QoS is poor, but other parameters are strong. Under moderate configurations, improvements range from 9% to 20%.

Table 9.

Comparison of FSSTEM1 and FSSTEM2 under equivalent parameter configurations.

QoS	SP	II	ST (M1)	ST (M2, $RR = 1.0$ )	$Δ$ ST (%)	Category change
0.1	0.9	0.9	0.487	0.591	$+$ 21%	Untrusted $\to$ trusted
0.5	0.5	0.9	0.484	0.581	$+$ 20%	Untrusted $\to$ trusted
0.5	0.9	0.9	0.623	0.679	$+$ 9%	Trusted $\to$ trusted
0.9	0.5	0.9	0.619	0.595	$-$ 4%	Trusted $\to$ trusted
0.9	0.9	0.9	0.868	0.868	$+$ 0%	High trust $\to$ high trust

5.3. Applications of FSSTEM

Trust-based admission control: Reject slices with $ST < 0.5$ . Admit ST $\in$ [0.5, 0.7] for noncritical services. Require $ST > 0.7$ for mission-critical applications and $ST > 0.85$ for URLLCs. FSSTEM2 enables finer distinction based on RR, which is beneficial when QoS degrades but infrastructure remains reliable.

Parameter prioritization: For FSSTEM1, QoS and II have the same impact on ST (0.251). While SP has a stronger impact (0.257) compared with QoS and II. For FSSTEM2, RR contributes progressively, with gains increasing at higher values. However, even $RR = 0.7$ under moderate conditions (0.5, 0.5, 0.5) fails to reach the trusted category. Operators should target high RR while improving other parameters.

Uncertainty-aware decision-making: FOU widths exceeding 0.10 require additional verification through extended monitoring, multisource verification, or redundant measurement. The higher maximum FOU of FSSTEM2 (0.249 vs. 0.190) suggests that four-parameter assessment involves greater uncertainty, requiring conservative protocols.

5.4. Discussion on simulation results

Comparative analysis of FSSTEM1 and FSSTEM2: The three-parameter formulation of FSSTEM1 suits contractually enforced infrastructure guarantees, while FSSTEM2 explicitly models RR for dynamic environments. FSSTEM2 provides substantial improvements under degraded QoS (21% at 0.1, 0.9, 0.9) but matches FSSTEM1 (0% difference), reflecting conservative evaluation. FOU analysis reveals that the higher maximum uncertainty of FSSTEM2 signals occurs when additional verification is needed.

Effectiveness of IT2FLS: IT2FLS proves essential through three key advantages. First, FOU bands explicitly quantify uncertainty near category boundaries where T1FLS would produce potentially misleading single-valued outputs. Second, 3D visualizations reveal complex nonlinear interactions, such as the trust valley at low QoS and trust ridge at high QoS that linear approaches cannot capture. Third, linguistic scales provide easy-to-understand interpretability while maintaining mathematical rigor through EKM-type reduction and demonstrate computational feasibility for real-time deployment.

Validation with operational data: The simulation-based evaluation demonstrates logical consistency, parameter sensitivity, and systematic trust evaluation under diverse operational scenarios. While these results provide strong evidence of the models’ theoretical soundness and computational feasibility, practical deployment will require calibration of trust thresholds to operator-specific risk tolerance and validation using telemetry data from operational 5G NS environments.

Extensibility to B5G networks: The evolution toward B5G and 6G networks will introduce additional trust dimensions beyond the four parameters considered in FSSTEM2. These include satellite reliability for nonterrestrial networks, edge AI trustworthiness for distributed inference, quantum-safe compliance for post-quantum cryptography readiness, and energy efficiency for sustainable operation.⁴¹ Incorporating these parameters using the current rule-based structure would yield more complexity.

6. Discussion and limitations

While the proposed FSSTE framework demonstrates effectiveness through simulation-based analysis, several fundamental limitations must be addressed for practical deployment and future scalability. This section presents these limitations and outlines directions for addressing them.

6.1. FRB scalability challenges

The exponential growth of fuzzy rules with increasing input parameters poses a fundamental scalability challenge. The exponential complexity increases computational burden during inference, complicates rule consistency maintenance, and challenges expert knowledge elicitation for rule definition. Three approaches can address these scalability constraints. First, hierarchical IT2FLS architectures can decompose trust evaluation into multiple stages. For example, a two-layer hierarchy could evaluate each parameter (QoS, SP, II, and RR) in the first layer and then integrate their output values for comprehensive evaluation at the second layer, reducing the exponential growth in rule base size.⁴² Second, integrating neural network and fuzzy logic can automatically learn optimal MF parameters and rule weights from operational data, reducing reliance on manual tuning while preserving interpretability.⁴³ Third, computational optimization of type reduction through advanced algorithms can reduce inference latency, enabling real-time evaluation even with larger rule bases.⁴⁴

6.2. Temporal dynamics and trust evolution

FSSTE models evaluate trust based on the network slice parameters without incorporating temporal dynamics, limiting their ability to detect gradual trust degradation or emerging threats. This static approach cannot distinguish between temporary performance anomalies and sustained degradation patterns, nor can it account for trust decay when slices remain inactive or monitoring data becomes stale. In dynamic 5G/B5G environments, where slice behaviors evolve continuously due to traffic fluctuations, resource contention, and security incidents, the lack of temporal trust modeling prevents proactive threat detection and may lead to delayed response to slow-moving attacks or service quality decline.³³

Extending FSSTE with temporal trust mechanisms would enable the detection of behavioral trends and adaptive trust evaluation. Niu et al.⁴⁵ propose a three-component temporal model for 5G network slices combining historical trust aggregation, subjective evaluation, and dynamic reward/punishment mechanisms with temporal forgiveness, demonstrating how trust scores can evolve based on slice lifecycle events. Yang et al.³³ integrate T2FLS with temporal trust vectors and time-based decay functions, where trust from recent interactions receives higher weights through exponential decay, enabling systems to adapt to dynamic network conditions while maintaining uncertainty-handling capabilities. Patel et al.⁴⁶ formalize exponential decay mechanisms with dynamically adjustable windows, where window lengths adapt based on current trust levels—longer windows for trusted entities and shorter windows for suspicious ones—providing mathematical foundations for trust decay computation. Incorporating such temporal mechanisms into FSSTE would require extending IT2FLS with time-indexed trust histories as additional input parameters, implementing sliding window aggregation for historical ST values, and designing fuzzy rules that consider trust evolution patterns (e.g., “IF trust declining rapidly THEN increase verification frequency”).

6.3. MF adaptation

The proposed models employ fixed MFs designed based on domain expertise and expected operational ranges. While this ensures stability and interpretability, it limits adaptability to operator-specific requirements and evolving network conditions. Different operators may interpret linguistic terms differently, and the interpretation of parameters may shift as network infrastructure evolves.

Adaptive MF tuning mechanisms can address this limitation while preserving IT2FLS interpretability. Intelligent algorithms can adjust FOU widths based on operator feedback, narrowing FOU after successful deployments and expanding it after SLA violations. The adaptation must incorporate safeguards against adversarial manipulation. Additionally, clustering techniques applied to historical operational data can identify natural groupings of parameter values, enabling data-driven MF design that reflects actual network behavior.⁴⁷

7. Conclusions and future work

In this paper, we proposed two FSSTE models for 5G/B5G NS. FSSTEM1 considers three parameters (QoS, SP, and II), while FSSTEM2 adds RR. Both implementations of IT2FLS can handle measurement uncertainty and linguistic ambiguity. Through simulations, we draw the following conclusions:

ST increases consistently as QoS, SP, and II increase, with the greatest improvements when all parameters rise at the same time from 0.1 to 0.9, showing positive combined effects.

FSSTEM1 achieves $ST = 0.868$ , suitable for mission-critical URLLC applications. However, poor QoS limits ST to 0.487 even with maximum SP and II, confirming the essential role of QoS in trust.

FSSTEM2 provides 21% improvement under poor QoS.

Parameter sensitivity analysis for FSSTEM1 shows that QoS and II have the same impact on ST (0.251). While SP has a stronger impact (0.257) compared with QoS and II. For FSSTEM2, RR increases gradually with faster improvements at higher values. FOU analysis reveals the higher maximum uncertainty of FSSTEM2 (0.249 vs. 0.190), showing when additional verification is needed.

FSSTEM2 offers superior discrimination in dynamic multitenant environments where RR fluctuates, owing to its higher complexity compared to FSSTEM1.

Future work will focus on five main areas. First, we will test the proposed models using real network telemetry from operational 5G testbeds to confirm effectiveness in practice and adjust trust thresholds. Second, we will extend FSSTE with temporal IT2FLS architectures to model trust evolution and detect slow decline patterns. Third, we will develop hierarchical fuzzy inference systems to allow scaling beyond four parameters without exponential growth of rules. Fourth, we will develop adaptive MF tuning methods based on historical slice behavior with protections against attacks. Finally, we will create a complete trust-aware slice management framework combining FSSTE with dynamic resource allocation, SLA enforcement, and admission control for autonomous B5G network management.

Footnotes

Acknowledgement

The authors would like to thank JSPS for the financial support.

ORCID iDs

Shunya Higashi

Paboth Kraikritayakul

Yi Liu

Makoto Ikeda

Keita Matsuo

Leonard Barolli

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research work is supported by Japan Society for the Promotion of Science (JSPS), Number 25KJ2239.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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Rule	QoS	SP	II	ST
1	Bd	We	Lo	ST1
2	Bd	We	Me	ST1
3	Bd	We	Hi	ST2
4	Bd	Mo	Lo	ST1
5	Bd	Mo	Me	ST2
6	Bd	Mo	Hi	ST3
7	Bd	St	Lo	ST2
8	Bd	St	Me	ST3
9	Bd	St	Hi	ST4
10	Gd	We	Lo	ST1
11	Gd	We	Me	ST2
12	Gd	We	Hi	ST3
13	Gd	Mo	Lo	ST2
14	Gd	Mo	Me	ST3
15	Gd	Mo	Hi	ST4
16	Gd	St	Lo	ST3
17	Gd	St	Me	ST4
18	Gd	St	Hi	ST5
19	Ex	We	Lo	ST2
20	Ex	We	Me	ST3
21	Ex	We	Hi	ST4
22	Ex	Mo	Lo	ST3
23	Ex	Mo	Me	ST4
24	Ex	Mo	Hi	ST5
25	Ex	St	Lo	ST4
26	Ex	St	Me	ST6
27	Ex	St	Hi	ST7

Rule	QoS	SP	II	RR	ST	Rule	QoS	SP	II	RR	ST
1	Bd	We	Lo	Lw	ST1	41	Gd	Mo	Me	Md	ST4
2	Bd	We	Lo	Md	ST1	42	Gd	Mo	Me	Hg	ST5
3	Bd	We	Lo	Hg	ST2	43	Gd	Mo	Hi	Lw	ST4
4	Bd	We	Me	Lw	ST1	44	Gd	Mo	Hi	Md	ST5
5	Bd	We	Me	Md	ST2	45	Gd	Mo	Hi	Hg	ST6
6	Bd	We	Me	Hg	ST3	46	Gd	St	Lo	Lw	ST3
7	Bd	We	Hi	Lw	ST2	47	Gd	St	Lo	Md	ST4
8	Bd	We	Hi	Md	ST3	48	Gd	St	Lo	Hg	ST5
9	Bd	We	Hi	Hg	ST4	49	Gd	St	Me	Lw	ST4
10	Bd	Mo	Lo	Lw	ST1	50	Gd	St	Me	Md	ST5
11	Bd	Mo	Lo	Md	ST2	51	Gd	St	Me	Hg	ST6
12	Bd	Mo	Lo	Hg	ST3	52	Gd	St	Hi	Lw	ST5
13	Bd	Mo	Me	Lw	ST2	53	Gd	St	Hi	Md	ST6
14	Bd	Mo	Me	Md	ST3	54	Gd	St	Hi	Hg	ST7
15	Bd	Mo	Me	Hg	ST4	55	Ex	We	Lo	Lw	ST1
16	Bd	Mo	Hi	Lw	ST3	56	Ex	We	Lo	Md	ST2
17	Bd	Mo	Hi	Md	ST4	57	Ex	We	Lo	Hg	ST3
18	Bd	Mo	Hi	Hg	ST5	58	Ex	We	Me	Lw	ST2
19	Bd	St	Lo	Lw	ST2	59	Ex	We	Me	Md	ST3
20	Bd	St	Lo	Md	ST3	60	Ex	We	Me	Hg	ST4
21	Bd	St	Lo	Hg	ST4	61	Ex	We	Hi	Lw	ST3
22	Bd	St	Me	Lw	ST3	62	Ex	We	Hi	Md	ST4
23	Bd	St	Me	Md	ST4	63	Ex	We	Hi	Hg	ST5
24	Bd	St	Me	Hg	ST5	64	Ex	Mo	Lo	Lw	ST2
25	Bd	St	Hi	Lw	ST4	65	Ex	Mo	Lo	Md	ST3
26	Bd	St	Hi	Md	ST5	66	Ex	Mo	Lo	Hg	ST4
27	Bd	St	Hi	Hg	ST6	67	Ex	Mo	Me	Lw	ST3
28	Gd	We	Lo	Lw	ST1	68	Ex	Mo	Me	Md	ST4
29	Gd	We	Lo	Md	ST2	69	Ex	Mo	Me	Hg	ST5
30	Gd	We	Lo	Hg	ST3	70	Ex	Mo	Hi	Lw	ST4
31	Gd	We	Me	Lw	ST2	71	Ex	Mo	Hi	Md	ST5
32	Gd	We	Me	Md	ST3	72	Ex	Mo	Hi	Hg	ST6
33	Gd	We	Me	Hg	ST4	73	Ex	St	Lo	Lw	ST3
34	Gd	We	Hi	Lw	ST3	74	Ex	St	Lo	Md	ST4
35	Gd	We	Hi	Md	ST4	75	Ex	St	Lo	Hg	ST5
36	Gd	We	Hi	Hg	ST5	76	Ex	St	Me	Lw	ST4
37	Gd	Mo	Lo	Lw	ST2	77	Ex	St	Me	Md	ST6
38	Gd	Mo	Lo	Md	ST3	78	Ex	St	Me	Hg	ST7
39	Gd	Mo	Lo	Hg	ST4	79	Ex	St	Hi	Lw	ST6
40	Gd	Mo	Me	Lw	ST3	80	Ex	St	Hi	Md	ST8
						81	Ex	St	Hi	Hg	ST9

Rule	QoS	SP	II	ST
1	Bd	We	Lo	ST1
2	Bd	We	Me	ST1
3	Bd	We	Hi	ST2
4	Bd	Mo	Lo	ST1
5	Bd	Mo	Me	ST2
6	Bd	Mo	Hi	ST3
7	Bd	St	Lo	ST2
8	Bd	St	Me	ST3
9	Bd	St	Hi	ST4
10	Gd	We	Lo	ST1
11	Gd	We	Me	ST2
12	Gd	We	Hi	ST3
13	Gd	Mo	Lo	ST2
14	Gd	Mo	Me	ST3
15	Gd	Mo	Hi	ST4
16	Gd	St	Lo	ST3
17	Gd	St	Me	ST4
18	Gd	St	Hi	ST5
19	Ex	We	Lo	ST2
20	Ex	We	Me	ST3
21	Ex	We	Hi	ST4
22	Ex	Mo	Lo	ST3
23	Ex	Mo	Me	ST4
24	Ex	Mo	Hi	ST5
25	Ex	St	Lo	ST4
26	Ex	St	Me	ST6
27	Ex	St	Hi	ST7

Rule	QoS	SP	II	RR	ST	Rule	QoS	SP	II	RR	ST
1	Bd	We	Lo	Lw	ST1	41	Gd	Mo	Me	Md	ST4
2	Bd	We	Lo	Md	ST1	42	Gd	Mo	Me	Hg	ST5
3	Bd	We	Lo	Hg	ST2	43	Gd	Mo	Hi	Lw	ST4
4	Bd	We	Me	Lw	ST1	44	Gd	Mo	Hi	Md	ST5
5	Bd	We	Me	Md	ST2	45	Gd	Mo	Hi	Hg	ST6
6	Bd	We	Me	Hg	ST3	46	Gd	St	Lo	Lw	ST3
7	Bd	We	Hi	Lw	ST2	47	Gd	St	Lo	Md	ST4
8	Bd	We	Hi	Md	ST3	48	Gd	St	Lo	Hg	ST5
9	Bd	We	Hi	Hg	ST4	49	Gd	St	Me	Lw	ST4
10	Bd	Mo	Lo	Lw	ST1	50	Gd	St	Me	Md	ST5
11	Bd	Mo	Lo	Md	ST2	51	Gd	St	Me	Hg	ST6
12	Bd	Mo	Lo	Hg	ST3	52	Gd	St	Hi	Lw	ST5
13	Bd	Mo	Me	Lw	ST2	53	Gd	St	Hi	Md	ST6
14	Bd	Mo	Me	Md	ST3	54	Gd	St	Hi	Hg	ST7
15	Bd	Mo	Me	Hg	ST4	55	Ex	We	Lo	Lw	ST1
16	Bd	Mo	Hi	Lw	ST3	56	Ex	We	Lo	Md	ST2
17	Bd	Mo	Hi	Md	ST4	57	Ex	We	Lo	Hg	ST3
18	Bd	Mo	Hi	Hg	ST5	58	Ex	We	Me	Lw	ST2
19	Bd	St	Lo	Lw	ST2	59	Ex	We	Me	Md	ST3
20	Bd	St	Lo	Md	ST3	60	Ex	We	Me	Hg	ST4
21	Bd	St	Lo	Hg	ST4	61	Ex	We	Hi	Lw	ST3
22	Bd	St	Me	Lw	ST3	62	Ex	We	Hi	Md	ST4
23	Bd	St	Me	Md	ST4	63	Ex	We	Hi	Hg	ST5
24	Bd	St	Me	Hg	ST5	64	Ex	Mo	Lo	Lw	ST2
25	Bd	St	Hi	Lw	ST4	65	Ex	Mo	Lo	Md	ST3
26	Bd	St	Hi	Md	ST5	66	Ex	Mo	Lo	Hg	ST4
27	Bd	St	Hi	Hg	ST6	67	Ex	Mo	Me	Lw	ST3
28	Gd	We	Lo	Lw	ST1	68	Ex	Mo	Me	Md	ST4
29	Gd	We	Lo	Md	ST2	69	Ex	Mo	Me	Hg	ST5
30	Gd	We	Lo	Hg	ST3	70	Ex	Mo	Hi	Lw	ST4
31	Gd	We	Me	Lw	ST2	71	Ex	Mo	Hi	Md	ST5
32	Gd	We	Me	Md	ST3	72	Ex	Mo	Hi	Hg	ST6
33	Gd	We	Me	Hg	ST4	73	Ex	St	Lo	Lw	ST3
34	Gd	We	Hi	Lw	ST3	74	Ex	St	Lo	Md	ST4
35	Gd	We	Hi	Md	ST4	75	Ex	St	Lo	Hg	ST5
36	Gd	We	Hi	Hg	ST5	76	Ex	St	Me	Lw	ST4
37	Gd	Mo	Lo	Lw	ST2	77	Ex	St	Me	Md	ST6
38	Gd	Mo	Lo	Md	ST3	78	Ex	St	Me	Hg	ST7
39	Gd	Mo	Lo	Hg	ST4	79	Ex	St	Hi	Lw	ST6
40	Gd	Mo	Me	Lw	ST3	80	Ex	St	Hi	Md	ST8
						81	Ex	St	Hi	Hg	ST9

Rule	QoS	SP	II	ST
1	Bd	We	Lo	ST1
2	Bd	We	Me	ST1
3	Bd	We	Hi	ST2
4	Bd	Mo	Lo	ST1
5	Bd	Mo	Me	ST2
6	Bd	Mo	Hi	ST3
7	Bd	St	Lo	ST2
8	Bd	St	Me	ST3
9	Bd	St	Hi	ST4
10	Gd	We	Lo	ST1
11	Gd	We	Me	ST2
12	Gd	We	Hi	ST3
13	Gd	Mo	Lo	ST2
14	Gd	Mo	Me	ST3
15	Gd	Mo	Hi	ST4
16	Gd	St	Lo	ST3
17	Gd	St	Me	ST4
18	Gd	St	Hi	ST5
19	Ex	We	Lo	ST2
20	Ex	We	Me	ST3
21	Ex	We	Hi	ST4
22	Ex	Mo	Lo	ST3
23	Ex	Mo	Me	ST4
24	Ex	Mo	Hi	ST5
25	Ex	St	Lo	ST4
26	Ex	St	Me	ST6
27	Ex	St	Hi	ST7

Rule	QoS	SP	II	RR	ST	Rule	QoS	SP	II	RR	ST
1	Bd	We	Lo	Lw	ST1	41	Gd	Mo	Me	Md	ST4
2	Bd	We	Lo	Md	ST1	42	Gd	Mo	Me	Hg	ST5
3	Bd	We	Lo	Hg	ST2	43	Gd	Mo	Hi	Lw	ST4
4	Bd	We	Me	Lw	ST1	44	Gd	Mo	Hi	Md	ST5
5	Bd	We	Me	Md	ST2	45	Gd	Mo	Hi	Hg	ST6
6	Bd	We	Me	Hg	ST3	46	Gd	St	Lo	Lw	ST3
7	Bd	We	Hi	Lw	ST2	47	Gd	St	Lo	Md	ST4
8	Bd	We	Hi	Md	ST3	48	Gd	St	Lo	Hg	ST5
9	Bd	We	Hi	Hg	ST4	49	Gd	St	Me	Lw	ST4
10	Bd	Mo	Lo	Lw	ST1	50	Gd	St	Me	Md	ST5
11	Bd	Mo	Lo	Md	ST2	51	Gd	St	Me	Hg	ST6
12	Bd	Mo	Lo	Hg	ST3	52	Gd	St	Hi	Lw	ST5
13	Bd	Mo	Me	Lw	ST2	53	Gd	St	Hi	Md	ST6
14	Bd	Mo	Me	Md	ST3	54	Gd	St	Hi	Hg	ST7
15	Bd	Mo	Me	Hg	ST4	55	Ex	We	Lo	Lw	ST1
16	Bd	Mo	Hi	Lw	ST3	56	Ex	We	Lo	Md	ST2
17	Bd	Mo	Hi	Md	ST4	57	Ex	We	Lo	Hg	ST3
18	Bd	Mo	Hi	Hg	ST5	58	Ex	We	Me	Lw	ST2
19	Bd	St	Lo	Lw	ST2	59	Ex	We	Me	Md	ST3
20	Bd	St	Lo	Md	ST3	60	Ex	We	Me	Hg	ST4
21	Bd	St	Lo	Hg	ST4	61	Ex	We	Hi	Lw	ST3
22	Bd	St	Me	Lw	ST3	62	Ex	We	Hi	Md	ST4
23	Bd	St	Me	Md	ST4	63	Ex	We	Hi	Hg	ST5
24	Bd	St	Me	Hg	ST5	64	Ex	Mo	Lo	Lw	ST2
25	Bd	St	Hi	Lw	ST4	65	Ex	Mo	Lo	Md	ST3
26	Bd	St	Hi	Md	ST5	66	Ex	Mo	Lo	Hg	ST4
27	Bd	St	Hi	Hg	ST6	67	Ex	Mo	Me	Lw	ST3
28	Gd	We	Lo	Lw	ST1	68	Ex	Mo	Me	Md	ST4
29	Gd	We	Lo	Md	ST2	69	Ex	Mo	Me	Hg	ST5
30	Gd	We	Lo	Hg	ST3	70	Ex	Mo	Hi	Lw	ST4
31	Gd	We	Me	Lw	ST2	71	Ex	Mo	Hi	Md	ST5
32	Gd	We	Me	Md	ST3	72	Ex	Mo	Hi	Hg	ST6
33	Gd	We	Me	Hg	ST4	73	Ex	St	Lo	Lw	ST3
34	Gd	We	Hi	Lw	ST3	74	Ex	St	Lo	Md	ST4
35	Gd	We	Hi	Md	ST4	75	Ex	St	Lo	Hg	ST5
36	Gd	We	Hi	Hg	ST5	76	Ex	St	Me	Lw	ST4
37	Gd	Mo	Lo	Lw	ST2	77	Ex	St	Me	Md	ST6
38	Gd	Mo	Lo	Md	ST3	78	Ex	St	Me	Hg	ST7
39	Gd	Mo	Lo	Hg	ST4	79	Ex	St	Hi	Lw	ST6
40	Gd	Mo	Me	Lw	ST3	80	Ex	St	Hi	Md	ST8
						81	Ex	St	Hi	Hg	ST9