Search Results (24)

From both theoretical and applied perspectives, the trapezoidal fuzzy numbers are widely relevant fuzzy sets. In this paper, we show that the four kinds of common metrics—the supremum metric, the $L_p$-type $d_p$ metrics, the sendograph metric, and the endograph metric—are equivalent on the trapezoidal fuzzy numbers. In fact, we obtain a stronger result: the convergence induced by these four kinds of metrics on the trapezoidal fuzzy numbers is equivalent to the convergence of the corresponding representation quadruples of the trapezoidal fuzzy numbers in ${\mathbb{R}}^4$. The latter convergence is very easy to verify. Our results give a fundamental understanding of these four kinds of common metrics on the trapezoidal fuzzy numbers and provide a quick judgment condition for the convergence induced by them. Full article

Ensuring reliable power system control demands innovative architectural solutions. This research introduces a fault-tolerant hybrid parallel compensator architecture for load frequency control (LFC), combining a Proportional–Integral–Derivative with Filter (PIDF) compensator with a Fuzzy Fractional-Order PI-PD (Fuzzy FOPI–FOPD) module. Particle Swarm Optimization (PSO) determines optimal PID gains, while the Catch Fish Optimization Algorithm (CFOA) tunes the Fuzzy FOPI–FOPD parameters—both minimizing the Integral Time Absolute Error (ITAE) index. The parallel compensator structure guarantees continuous operation during subsystem faults, substantially boosting grid reliability. Rigorous partial failure tests confirm uncompromised performance-controlled degradation. Benchmark comparisons against contemporary controllers reveal the proposed architecture’s superiority, quantifiable through transient metric enhancements: undershoot suppression (−9.57 × 10⁻⁵ p.u. to −1.17 × 10⁻⁷ p.u.), settling time improvement (8.8000 s to 3.1511 s), and ITAE reduction (0.0007891 to 0.0000001608), verifying precision and stability gains. Resilience analyses across parameter drift and step load scenarios, simulated in MATLAB/Simulink, demonstrate superior disturbance attenuation and operational stability. These outcomes confirm the solution’s robustness, dependability, and field readiness. Overall, this study introduces a transformative LFC strategy with high practical viability for modern power networks. Full article

In this paper, we aim to investigate a type of lattice-valued fuzzy metric within the framework of L-topology. Firstly, we present a comprehensive construction theorem for this type of metric, utilizing the concept of L-quasi metric. Secondly, we provide an equivalent characterization through the use of C-nbd clusters, which are formed from all $B_r$: one of four types of basic spheres defined herein. Thirdly, recognizing that these four types of basic spheres serve as essential tools for characterizing various metrics, we meticulously examine the relationships among them and outline a series of topological properties associated with these metrics, which include their opening and closing characteristics, symmetrical property, and more. Finally, in addressing the corresponding symmetry problem between two types of basic spheres, namely $B_r\left(a\right)$ and $Q_r\left(a\right)$, we introduce a novel fuzzy p-metric and demonstrate tht the L-real line $\mathbf{R}\left(L\right)$ satisfies this fuzzy p-metric. Full article

This paper addresses a fundamental challenge in statistical radar detection systems: optimizing the trade-off between the probability of a false alarm ($P_{FA}$) and the probability of a miss ($P_M$). These two metrics are inversely related and critical for performance evaluation. Traditional detection approaches often enhance one aspect at the expense of the other, limiting their practical applicability. To overcome this limitation, a fuzzy hypothesis testing framework is introduced that improves decision making under uncertainty by incorporating both crisp and fuzzy data representations. The methodology is divided into three phases. In the first phase, we reduce the probability of false alarm $P_{FA}$ while maintaining a constant probability of miss $P_M$ using crisp data characterized by deterministic values and classical statistical thresholds. In the second phase, the inverse scenario is considered: minimizing $P_M$ while keeping $P_{FA}$ fixed. This is achieved through parameter tuning and refined threshold calibration. In the third phase, a strategy is developed to simultaneously enhance both $P_{FA}$ and $P_M$, despite their inverse correlation, by adopting adaptive decision rules. To further strengthen system adaptability, fuzzy data are introduced, which effectively model imprecision and ambiguity. This enhances robustness, particularly in scenarios where rapid and accurate classification is essential. The proposed methods are validated through both real and synthetic simulations of radar measurements, demonstrating their ability to enhance detection reliability across diverse conditions. The findings confirm the applicability of fuzzy hypothesis testing for modern radar systems in both civilian and military contexts, providing a statistically sound and operationally applicable approach for reducing detection errors and optimizing system performance. Full article

Multimodal freight transport systems, integrating maritime, rail, and road modes, play a vital role in modern logistics but face elevated operational, human, and environmental risks due to their complexity and interdependencies. To address the limitations of conventional risk assessment methods, this study proposes a hybrid risk modeling framework that integrates fault tree analysis (FTA), dynamic fault trees (DFTs), and fuzzy logic reasoning. This approach supports the modeling of sequential failures and captures qualitative uncertainties such as human fatigue and inadequate training. The framework incorporates reliability metrics, including Mean Time to Failure (MTTF) and Mean Time Between Failures (MTBF), enabling the quantification of system resilience and identification of critical failure pathways. Application of the model revealed human error, particularly procedural violations, insufficient training, and fatigue, as the dominant risk factor across transport modes. Road transport exhibited the highest probability of risk occurrence (p = 0.9960), followed by rail (p = 0.9937) and maritime (p = 0.9900). By integrating probabilistic reasoning with qualitative insights, the proposed model offers a flexible decision support tool for logistics operators and policymakers, enabling scenario-based risk planning and enhancing system robustness under uncertainty. Full article

This paper proposes a new approach to integrating Q learning into the fuzzy linear programming (FLP) paradigm to improve peer selection in P2P networks. Using Q learning, the proposed method employs real-time feedback to adjust and update peer selection policies. The FLP framework enriches this process by dealing with imprecise information through fuzzy logic. It is used to achieve multiple objectives, such as enhancing the throughput rate, reducing the delay, and guaranteeing a reliable connection. This integration effectively solves the problem of network uncertainty, making the network configuration more stable and flexible. It is also important to note that throughout the use of the Q-learning agent in the network, various state metric indicators, including available bandwidth, latency, packet drop rates, and connectivity of nodes, are observed and recorded. It then selects actions by choosing optimal peers for each node and updating a Q table that defines states and actions based on these performance indices. This reward system guides the agent’s learning, refining its peer selection policy over time. The FLP framework supports the Q-learning agent by providing optimized solutions that balance conflicting objectives under uncertain conditions. Fuzzy parameters capture variability in network metrics, and the FLP model solves a fuzzy linear programming problem, offering guidelines for the Q-learning agent’s decisions. The proposed method is evaluated under different experimental settings to reveal its effectiveness. The Erdos–Renyi model simulation is used, and it shows that throughput increased by 21% and latency decreased by 40%. The computational efficiency was also notably improved, with computation times diminishing by up to five orders of magnitude compared to traditional methods. Full article

The use of a static modulation coding scheme (MCS), such as 7, and resource keep probability ($P_{rk}$) value, such as 0.8, was proven to be insufficient to achieve the best packet reception ratio (PRR) performance. Various adaptation techniques have been used in the following years. This work introduces a novel optimization algorithm approach called the fuzzy inference reinforcement learning (FIRL) sequence for adaptive parameter configuration in cellular vehicle-to-everything (C-V2X) mode-4 communication networks. This innovative method combines a Sugeno-type fuzzy inference system (FIS) control system with a Q-learning reinforcement learning algorithm to optimize the PRR as the key metric for overall network performance. The FIRL sequence generates adaptive configuration parameters for $P_{rk}$ and MCS index values each time the Long-Term Evolution (LTE) packet is generated. Simulation results demonstrate the effectiveness of this optimization algorithm approach, achieving up to a 169.83% improvement in performance compared to static baseline parameters. Full article

In this study, trapezoidal-type inequalities in fuzzy settings have been investigated. The theory of fuzzy analysis has been discussed in detail. The integration by parts formula of analysis of fuzzy mathematics has been employed to establish an equality. Trapezoidal-type inequality for functions with values in the fuzzy number-valued space is proven by applying the proven equality together with the properties of a metric defined on the set of fuzzy number-valued space and Höler’s inequality. The results proved in this research provide generalizations of the results from earlier existing results in the field of mathematical inequalities. An example is designed by defining a function that has values in fuzzy number-valued space and validated the results numerically using the software Mathematica (latest v. 14.1). The p-levels of the defined fuzzy number-valued mapping have been shown graphically for different values of $p\in \left[0,1\right]$. Full article

Machine learning and response surface methods for predicting the compressive strength of high-strength concrete have not been adequately compared. Therefore, this research aimed to predict the compressive strength of high-strength concrete (HSC) using different methods. To achieve this purpose, neuro-fuzzy inference systems (ANFISs), artificial neural networks (ANNs), and response surface methodology (RSM) were used as ensemble methods. Using an ANN and ANFIS, high-strength concrete (HSC) output was modeled and optimized as a function of five independent variables. The RSM was designed with three input variables: cement, and fine and coarse aggregate. To facilitate data entry into Design Expert, the RSM model was divided into six groups, with p-values of responses 1 to 6 of 0.027, 0.010, 0.003, 0.023, 0.002, and 0.026. The following metrics were used to evaluate model compressive strength projection: R, R², and MSE for ANN and ANFIS modeling; R², Adj. R², and Pred. R² for RSM modeling. Based on the data, it can be concluded that the ANN model (R = 0.999, R² = 0.998, and MSE = 0.417), RSM model (R = 0.981 and R² = 0.963), and ANFIS model (R = 0.962, R² = 0.926, and MSE = 0.655) have a good chance of accurately predicting the compressive strength of high-strength concrete (HSC). Furthermore, there is a strong correlation between the ANN, RSM, and ANFIS models and the experimental data. Nevertheless, the artificial neural network model demonstrates exceptional accuracy. The sensitivity analysis of the ANN model shows that cement and fine aggregate have the most significant effect on predicting compressive strength (45.29% and 35.87%, respectively), while superplasticizer has the least effect (0.227%). RSME values for cement and fine aggregate in the ANFIS model were 0.313 and 0.453 during the test process and 0.733 and 0.563 during the training process. Thus, it was found that both ANN and RSM models presented better results with higher accuracy and can be used for predicting the compressive strength of construction materials. Full article

We consider the concept of fuzzy $\mathcal{H}$-quasi-contraction ($\mathcal{F}\mathcal{H}$-$\mathcal{Q}\mathcal{C}$ for short) initiated by Ćirić in tripled fuzzy metric spaces ($\mathcal{T}$-$\mathcal{F}\mathcal{M}\mathcal{S}$s for short) and present a new fixed point theorem ($\mathcal{F}\mathcal{P}\mathcal{T}$ for short) for $\mathcal{F}\mathcal{H}$-$\mathcal{Q}\mathcal{C}$ in complete $\mathcal{T}$-$\mathcal{F}\mathcal{M}\mathcal{S}$s. As an application, we prove the corresponding results of the previous literature in setting fuzzy metric spaces ($\mathcal{F}\mathcal{M}\mathcal{S}$s for short). Moreover, we obtain theorems of sufficient and necessary conditions which can be used to demonstrate the existence of fixed points. In addition, we construct relevant examples to illustrate the corresponding results. Finally, we show the existence and uniqueness of solutions for integral equations by applying our new results. Full article

A flying ad hoc network (FANET) is formed from a swarm of drones also known as unmanned aerial vehicles (UAVs) and is currently a popular research subject because of its ability to carry out complicated missions. However, the specific features of UAVs such as mobility, restricted energy, and dynamic topology have led to vital challenges for making reliable communications between drones, especially when designing routing methods. In this paper, a novel optimized link-state routing scheme with a greedy and perimeter forwarding capability called OLSR+GPSR is proposed in flying ad hoc networks. In OLSR+GPSR, optimized link-state routing (OLSR) and greedy perimeter stateless routing (GPSR) are merged together. The proposed method employs a fuzzy system to regulate the broadcast period of hello messages based on two inputs, namely the velocity of UAVs and position prediction error so that high-speed UAVs have a shorter hello broadcast period than low-speed UAVs. In OLSR+GPSR, unlike OLSR, MPR nodes are determined based on several metrics, especially neighbor degree, node stability (based on velocity, direction, and distance), the occupied buffer capacity, and residual energy. In the last step, the proposed method deletes two phases in OLSR, i.e., the TC message dissemination and the calculation of all routing paths to reduce routing overhead. Finally, OLSR+GPSR is run on an NS3 simulator, and its performance is evaluated in terms of delay, packet delivery ratio, throughput, and overhead in comparison with Gangopadhyay et al., P-OLSR, and OLSR-ETX. This evaluation shows the superiority of OLSR+GPSR. Full article

This paper is devoted to showing the relevance of the notion of completeness used to establish a fixed point theorem in fuzzy metric spaces introduced by Kramosil and Michalek. Specifically, we show that demanding a stronger notion of completeness, called p-completeness, it is possible to relax some extra conditions on the space to obtain a fixed point theorem in this framework. To this end, we focus on a fixed point result, proved by Mihet for complete non-Archimedean fuzzy metric spaces (Theorem 1). So, we define a weaker concept than the non-Archimedean fuzzy metric, called t-strong, and we establish an alternative version of Miheţ’s theorem for p-complete t-strong fuzzy metrics (Theorem 2). In addition, an example of t-strong fuzzy metric spaces that are not non-Archimedean is provided. Full article

The aim of this paper is to focus on the metrization question in L-fuzzy sets. Firstly, we put forward an L-quasi (pseudo)-metric on the completely distributive lattice $L^X$ by comparing some existing lattice-valued metrics with the classical metric and show a series of its related properties. Secondly, we present two topologies: ${\psi }_p$ and ${\zeta }_p$, generated by an L-quasi-metric p with different spherical mappings, and prove ${\psi }_p={\zeta }_p^{\prime }$ if p is further an L-pseudo-metric on $L^X$. Thirdly, we characterize an equivalent form of L-pseudo-metric in terms of a class of mapping clusters and acquire several satisfactory results. Finally, based on this kind of L-metric, we assert that, on $L^X$, a Yang–Shi metric topology is $Q-C_I$, but an Erceg metric topology is not always so. Full article

In this writing, first, we disclose the first and second category of a ${\Gamma }_{\tau }\mathcal{F}$-fuzzy proximal contraction for a mapping $\mathcal{O}:\mathfrak{U}\to \mathfrak{V}$ which is nonself and also declare a fuzzy q-property to confirm the existence of the best proximity point for nonself function $\mathcal{O}$. Then, we discover a few results using the ${\Gamma }_{\tau }\mathcal{F}$-fuzzy proximal contraction of the first category for a continuous and discontinuous nonself function $\mathcal{O}$ in a non-Archimedean fuzzy metric space. Later, we discuss another result for the ${\Gamma }_{\tau }\mathcal{F}$-fuzzy proximal contraction of the second category as well. In between the fuzzy proximal theorems, many examples are presented in support of the definitions and theorems proved in this writing. Full article

In the current era of e-mobility and for the planning of sustainable grid infrastructures, developing new efficient tools for real-time grid performance monitoring is essential. Thus, this paper presents the prediction of the voltage stability margin (VSM) of power systems by the critical boundary index (CBI) approach using the machine learning technique. Prediction models are based on an adaptive neuro-fuzzy inference system (ANFIS) and its enhanced model with particle swarm optimization (PSO). Standalone ANFIS and PSO-ANFIS models are implemented using the fuzzy ‘c-means’ clustering method (FCM) to predict the expected values of CBI as a veritable tool for measuring the VSM of power systems under different loading conditions. Six vital power system parameters, including the transmission line and bus parameters, the power injection, and the system voltage derived from load flow analysis, are used as the ANFIS model implementation input. The performances of the two ANFIS models on the standard IEEE 30-bus and the Nigerian 28-bus systems are evaluated using error and regression analysis metrics. The performance metrics are the root mean square error ($RMSE$), mean absolute percentage error ($MAPE$), and Pearson correlation coefficient (R) analyses. For the IEEE 30-bus system, $RMSE$ is estimated to be 0.5833 for standalone ANFIS and 0.1795 for PSO-ANFIS; $MAPE$ is estimated to be 13.6002% for ANFIS and 5.5876% for PSO-ANFIS; and R is estimated to be 0.9518 and 0.9829 for ANFIS and PSO-ANFIS, respectively. For the NIGERIAN 28-bus system, the $RMSE$ values for ANFIS and PSO-ANFIS are 5.5024 and 2.3247, respectively; $MAPE$ is 19.9504% and 8.1705% for both ANFIS and PSO-ANFIS variants, respectively, and the R is estimated to be 0.9277 for ANFIS and 0.9519 for ANFIS-PSO, respectively. Thus, the PSO-ANFIS model shows a superior performance for both test cases, as indicated by the percentage reduction in prediction error, although at the cost of a higher simulation time. Full article