This paper presents the design and implementation of interval type-2 fuzzy logic PID controller for an uncertain twin-rotor multi-variable system. Twin-rotor multi-input multi-output system (TRMS) is a benchmark control problem that resembles helicopter dynamics. In practice, a conventional type-1 fuzzy logic controller (FLC) can be used to identify the behavior of this highly nonlinear system with various types of uncertainties. However, it cannot fully capture the uncertainties in the system due to membership functions and improper knowledge base information. Additionally, the computational complexity of operations on fuzzy sets increases as the type of fuzzy set becomes more complex. Moreover, the lack of data may affect the decision-making process in many problem-solving situations. To address the issues with type-1 FL PID, this paper aims to design and analyze an interval type-2 fuzzy logic PID controller for controlling the pitch and yaw angles of the main and tail rotors of the TRMS, Furthermore, we demonstrate the stability of the proposed controller by utilizing Kharitonov rectangles and the zero-exclusion theorem. We compare the performance of the proposed controller with the conventional type-1 fuzzy logic PID controller. The results indicate that the proposed interval type-2 FL PID controller offers satisfactory response compared to the traditional type 1 fuzzy logic PID controller.
High-dimensional data in agriculture and remote sensing suffer from the curse of dimensionality, leading to poor model performance and high computational cost. Feature selection mitigates this by removing irrelevant and redundant features while preserving discriminative power. We propose Fuzzy Hypergraph Feature Association Map (FH-FAM), a novel supervised feature selection method that uses fuzzy hypergraphs to model higher-order feature interactions and uncertainty. It computes multi-way normalized mutual information for relevance, multi-way correlation for redundancy, applies sigmoidal and gamma fuzzy membership functions, constructs weighted fuzzy hypergraphs, and selects an optimized subset via maximal independent set after three-stage refinement. FH-FAM was evaluated on 15 public datasets (food/agriculture and remote sensing domains) using Random Forest classification (80:20 train–test split). Compared to FFAMFS, CFS, DSCA, FCFB, FROT, and ABESS, FH-FAM achieved the highest mean accuracy (81.43
Sustainable water resource management has become a pressing challenge for Saudi Arabia due to rising demand, groundwater depletion, and environmental constraints. To evaluate and prioritize effective strategies under such complex conditions, this study develops an advanced multi-criteria decision-making (MCDM) framework. Interval-valued q-rung orthopair hesitant fuzzy (IV-qRHF) sets are adopted to capture uncertainty, hesitancy, and incomplete information in expert evaluations. A family of Hamacher-based operational laws tailored to the IV-qRHF environment is introduced. Building upon these laws, novel aggregation operators—namely the IV-qRHF Hamacher weighted averaging (IV-qRHFHWA) and IV-qRHF Hamacher weighted geometric (IV-qRHFHWG) operators—are proposed and their mathematical properties are examined. Several special cases of these operators are discussed to highlight their flexibility. In addition, an entropy measure is formulated and proven to satisfy the required axioms, serving as an objective tool for determining criteria weights when prior information is unavailable. By integrating the entropy measure with the proposed operators, a systematic MCDM framework is established. Its practicality is demonstrated via an applied analysis addressing long-term water sustainability challenges in Saudi Arabia. Sensitivity analysis confirms the stability of the model, while comparative experiments show its superiority over existing approaches, particularly in highly uncertain decision environments.
Dual hesitant q-rung orthopair fuzzy (DHq-ROF) numbers exhibit superior performance in characterizing complex uncertain and ambiguous information compared to q-rung orthopair fuzzy (q-ROF) numbers and dual hesitant fuzzy (DHF) numbers. Nevertheless, existing studies on DHq-ROF-based MADM still have some research gaps that require resolution: first, most existing entropy measures for DHq-ROF numbers suffer from inadequate discrimination capability and low computational efficiency, failing to accurately quantify the uncertainty inherent in DHq-ROF information; second, conventional similarity measures for DHq-ROF numbers do not incorporate the influence of entropy (i.e., the degree of uncertainty), leading to imprecise characterization of the similarity between DHq-ROF numbers; third, the traditional multiplicative multi-objective optimization approach by ratio analysis (MULTIMOORA) method has not been effectively extended to the DHq-ROF context, and weight-determining methods in existing DHq-ROF-based MADM methods typically neglect the integration of subjective and objective preferences, potentially resulting in biased decision outcomes. To bridge these research gaps and effectively tackle MADM problems evaluated by DHq-ROF numbers, this study proposes a novel MADM method, namely the DHq-ROF-MULTIMOORA method. Specifically, a new entropy measure for DHq-ROF numbers is initially developed to accurately characterize the uncertainty of DHq-ROF information, which outperforms existing entropy measures in discrimination capability and computational efficiency. Subsequently, considering the influence of the proposed entropy measure, a novel cosine similarity measure between two DHq-ROF numbers is constructed to precisely depict their similarity relationship, and its advantages and applicability are validated through comparisons with existing similarity measures. Based on the proposed entropy and cosine similarity measures, the DHq-ROF-MULTIMOORA method is established by extending the traditional MULTIMOORA to the DHq-ROF environment. In detail, a novel weight-determining method is designed to integrate both subjective and objective weight assignment approaches, ensuring the rationality and reliability of attribute weights. A practical case study is conducted to demonstrate the practicality and effectiveness of the proposed DHq-ROF-MULTIMOORA method. Finally, sensitivity and comparison analysis are performed, and the results confirm the flexibility, effectiveness, and superiority of the proposed method in solving DHq-ROF-based MADM problems.
The increasing complexity of modern communication networks and medical imaging demands robust mathematical tools capable of handling both high-dimensional structures and uncertainty. This paper introduces a novel framework based on complex fuzzy tensors (CFTs), which integrate the descriptive power of tensor algebra with the uncertainty modeling ability of complex fuzzy sets. Building on this foundation, we develop a CFT–TOPSIS methodology for multicriteria decision-making that simultaneously incorporates magnitude and phase information, offering a richer and more reliable evaluation of alternatives. The proposed framework is applied to two representative case studies: beam selection in next-generation wireless MIMO systems and the assessment of medical image processing techniques. In both domains, the approach demonstrates superior performance in terms of robustness, interpretability, and accuracy when compared with traditional methods. The results confirm that CFT–TOPSIS not only provides theoretical advances in uncertainty modeling but also offers practical benefits for real-world decision problems where high-dimensionality and phase-sensitive information play a crucial role.
Low-frequency oscillations (LFOs) in interconnected power systems threaten stability, and various damping devices such as Power System Stabilizers (PSSs) often fail to mitigate inter-area modes effectively. High-Voltage Direct Current (HVDC) transmission systems, with independent control of active and reactive power at both converter ends, provide a flexible platform for damping oscillations. This research introduces a hybrid Neuro-Fuzzy Wavelet Controller (NFWC) optimized via the Levenberg–Marquardt Algorithm (LMA) to enhance HVDC system stability. The NFWC combines fuzzy inference with Wavelet Neural Networks (WNNs) to provide a damping current signal to the master control of the HVDC control system. The proposed algorithm utilizes the LMA rather than conventional optimization techniques, thereby avoiding the issue of getting stuck in local minima and effectively damping LFOs. Simulation results on single-machine and multi-machine power systems under varied loading and fault scenarios demonstrate superior transient and steady-state damping performance of the proposed controller. Based on qualitative and quantitative results, it is found that the proposed NFWC significantly improves performance in both transient and steady-state regions.
This paper presents a comprehensive framework for reliability and availability analysis of multi-state k-out-of-n:G systems in star topology, with application to weather monitoring infrastructure. The proposed model integrates performance sharing and copula-based repair strategies to capture dependencies between component failures and repairs. A Markov process formulation, solved using the Sumudu transform, evaluates time-dependent reliability and availability metrics. To address uncertainty in failure parameters, the model incorporates Fermatean fuzzy set theory via Triangular Fermatean Fuzzy Numbers (TFFNs) and (α ,β ) -cuts, enabling robust fuzzy reliability and sensitivity analyses. A comparative study demonstrates that the copula-based approach yields more accurate long-run reliability forecasts than traditional Markov models by considering repair dependencies. The framework also includes a cost analysis module for evaluating maintenance strategies under uncertainty, supported by a structured failure–repair flowchart for intuitive system representation. The results reveal that while inherent reliability declines over time, proper maintenance sustains high system availability, with Fermatean fuzzy modeling providing realistic performance bounds. This study offers a novel integration of copula theory and Fermatean fuzzy sets for analyzing complex multi-state systems, providing a vital decision-support tool for long-run infrastructure planning and maintenance optimization.
In the field of affective product design, accurately aggregating preferences from diverse groups is critical for decision-making. However, traditional multi-subgroup decision models often treat user preferences as static inputs, overlooking the structural cognitive bias introduced by sequential sample presentation. This theoretical limitation frequently leads to data distortion and fails to capture genuine consensus within complex design spaces. To address this, this paper proposes a novel decision-making framework based on probability linguistic term sets oriented toward simultaneous lineups. Methodologically, it proposes a Repeated Random Simultaneous Lineups experimental protocol to replace single-sequence evaluation, transforming subjective rankings into stable probability distributions and thereby eliminating order-induced bias. Theoretically, a Choquet-Integrated Borda operator is constructed to quantify nonlinear synergistic effects among evaluation criteria and resolve conflicts across different subgroups. Comparative experiments with three baseline methods confirm the superiority of this paradigm. Traditional sequential and non-repeated methods, affected by random noise, yielded consensus indices of merely 65.5 to 74.66
Probabilistic dual hesitant fuzzy sets effectively characterize hesitant fuzzy information alongside its associated probability distribution, serving as a robust tool for managing uncertainty. Addressing the research void concerning group decision-making with probabilistic dual hesitant fuzzy sets within social network contexts, this paper proposes a group decision-making method grounded in probabilistic dual hesitant fuzzy preference relations. The concept and assessment approach for geometric consistency are introduced, and an optimization model is subsequently formulated to enhance consistency levels. Furthermore, a consensus-reaching framework leveraging dynamic social network trust is developed. This framework guides experts toward consensus by supplementing trust relationships, computing expert trust weights, conducting multi-level consensus evaluations, and iteratively adjusting both trust relationships and preferences. Additionally, a methodology for dynamically determining experts’ comprehensive weights is proposed, integrating social network trust with group consensus levels and employing the BrowseRank algorithm. Finally, the effectiveness and practicality of the proposed method are validated through numerical case studies.
The automation of pilot tasks is a critical factor in enhancing flight safety, particularly during takeoff and landing, where improper management of high-lift devices may lead to unsafe conditions. The timing of flap and slat deployment is especially sensitive: delayed actuation increases safety risks, whereas premature deployment reduces fuel efficiency. This paper proposes an intelligent automatic management system for aircraft high-lift devices based on fuzzy logic and inspired by pilot operating procedures. The proposed system estimates the flight phase through a fuzzy inference mechanism and generates control commands for flap and slat positioning as a function of speed, ensuring safe and efficient maneuvering. The main contribution lies in the formulation of two indices, K and T, which formalize pilot safety and efficiency criteria into quantitative metrics. These indices are embedded within a particle swarm optimization (PSO) framework to tune the membership functions of the fuzzy controller, enabling the simultaneous maximization of safety margins and operational efficiency during critical flight phases. The proposed methodology is validated through simulation using Airbus flap configurations and a real flight speed profile. Quantitative results indicate that the system maintains safety margins under the tested disturbance scenarios while ensuring appropriate configuration transitions, thereby demonstrating the feasibility and potential effectiveness of the proposed intelligent control strategy.
This paper presents a design of a multi-layered control scheme for mobile robots operating under a leader–follower formation strategy. The proposed methodology combines three interconnected control layers: the first layer introduced a nonlinear body-frame kinematic controller for leader trajectory tracking; the second layer proposed a dynamic-level adaptive fuzzy type two mechanism that copes with system uncertainties for each robot; and the third layer developed a kinematic control algorithm to maintain an accurate formation of follower robots. In the first control layer, a smooth bounded function is introduced to eliminate singularities near zero orientation errors. In the second layer, self-adjusting Gaussian membership functions are included within a novel fuzzy logic mechanism to address and solve the problem of model nonlinearities and uncertainties. The third layer is devoted to improving the followers’ tracking at the kinematic level by developing an adaptive sliding mode control law. A Lyapunov-based stability is strictly analyzed to prove a global bounded convergence of tracking errors. Numerical simulations have been conducted to show the effectiveness of the proposed controllers. Compared to relevant works in the literature, the proposed control formation framework showed better performance and improvement in terms of tracking, formation precision, and robustness against model uncertainties.
The three-way decision-making method in hesitant fuzzy environments is widely recognized as a powerful tool for addressing uncertainties and ambiguities in the decision-making process. Moreover, prospect theory objectively depicts the effect of decision-makers’ psychological behavior on the decision-making process. Therefore, this article intends to establish a novel multi-attribute three-way decision-making method in a hesitant fuzzy environment by incorporating prospect theory to account for decision-makers’ irrational behaviors. Specifically, to overcome the limitations of existing distance formulas for hesitant fuzzy elements, we introduce a novel formula for computing the distance between hesitant fuzzy elements at first. On this basis, a novel method for computing the conditional probability in hesitant fuzzy environments is proposed. Concurrently, a relative loss function is developed for each scheme by integrating the hesitant fuzzy TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) method with prospect theory, which is utilized to address real-life multi-attribute decision-making problems. Finally, through case and comparative analysis, we demonstrate scientific validity and superior performance of the proposed method, and prove the reliability and robustness of the proposed method through parametric sensitivity analysis. The successful implementation of these methods has fully demonstrated the tremendous potential and advantages of artificial intelligence technology in dealing with complex decision-making problems.
As one of the effective techniques of image segmentation, fuzzy C-means clustering (FCM) algorithm can perform well in image segmentation for noiseless images, but it is sensitive to outliers. In order to overcome this shortcoming, scholars have proposed various improved methods. The previous ideas of fuzzy clustering are to initialize the membership, and then calculate the cluster center further. Due to the randomness of initialization, the objective functions of some algorithms may oscillate or become larger before converging during the first few iterations, which affects the segmentation speed ultimately. In order to solve this problem, we proposed the cluster center initialization with fast convergence based on FCM (FCM-CCI). Firstly, the pixels of image are evenly divided into groups equal to the number of clusters according to the histogram statistics of the image. Then, the algorithm uses each group of pixels and its corresponding number to calculate the value of the corresponding central pixel, which is the initial clustering of the image. In addition, this algorithm combines the pixels of the original image and the filtered image on the basis of the original FCM algorithm and takes the local density function as the correction weight. Finally, the final segmentation result is obtained by the membership filtering idea. The experiments of performance evaluation on synthetic and real images show that the algorithm has better effect of segmentation and faster convergence. In addition, the convergence speed of some FCM algorithms is further improved by integrating the proposed algorithm into these algorithms.
The promotion of sustainability in the port shipping industry is crucial for improving production efficiency and accelerating the modernization of port shipping equipment (PSE). The latter process necessitates selecting an optimal PSE supplier. However, due to the uncertainty of supplier evaluation, supplier selection of PSE becomes a complicated fuzzy multiple criteria decision-making (MCDM) problem, which includes the fuzzy criteria and stochastic criteria (FCSC). While the application of MCDM approaches to PSE supplier selection has been widely reported in recent years, most studies only consider either stochastic criteria or fuzzy criteria based on stochastic dominance rules or interval-valued intuitionistic fuzzy set (IVIFS) theory. Consequently, the complexity of supplier selection under the mixed uncertainty of FCSC trade-offs remains unresolved. This paper presents an improved multi-criteria optimization and compromise solution (VIKOR) method that integrates FCSC. In this method, the theories of IVIFS and of stochastic dominance rules are applied to address the FCSC, a nonlinear consistency optimization model is constructed to derive the criteria weights for FCSC, and the superiority ranking of alternative PSE suppliers is conducted based on an improved VIKOR framework. Moreover, method comparisons and sensitivity analyses are elaborated through a real-world case study of PSE supplier selection. Finally, comparative analysis with traditional methods reveals the effectiveness of the proposed approach.
Vocational colleges must practically integrate innovation and entrepreneurship education (IAEE) with skill training, leveraging their strengths to build tailored talent systems. However, current setups remain underdeveloped and uniform—student engagement is low, teaching lacks coherence, competition entries lack feasibility, and even rising participation yields few impactful results. Assessing IAEE quality in vocational education is a complex multiple-attribute decision-making (MADM) challenge. Recent studies have adopted Exponential TODIM (ExpTODIM) and EDAS for MADM, but IAEE evaluations involve inherent uncertainty (e.g., vague feedback on teaching effectiveness or ambiguous judging criteria). Z-numbers address this by pairing numerical values with reliability measures, making them ideal for capturing unclear assessment data. This study introduces an integrated Z-number-based Exponential TODIM-EDAS (ZN-ExpTODIM-EDAS) approach. First, it uses Z-numbers to quantify uncertain IAEE quality indicators (e.g., curriculum relevance, student innovation output). Then, ExpTODIM calculates the dominance degree of each assessment object by considering decision-makers’ risk preferences, while EDAS evaluates alternatives via positive/negative distance from the average solution. The combination mitigates limitations of single methods—ExpTODIM’s sensitivity to risk and EDAS’s reliance on average values. To validate this methodology, a practical case study on IAEE quality assessment in three vocational colleges is presented. It collects data from educators, industry experts, and student projects, applies ZN-ExpTODIM-EDAS to rank IAEE quality, and compares results with traditional ExpTODIM/EDAS. The consistency and accuracy of the integrated method confirm its applicability and effectiveness for IAEE quality evaluation.
Many nonlinear systems in practical engineering encounter random noises and contain unmodeled dynamics and dead-zone inputs, which increase the challenges of system control and lead to poor tracking responses. Considering this problem, in this work, we study the tracking control issue of high-order stochastic nonlinear systems (SNSs) and aim to find a solution. By developing a direct fuzzy control method, proposing a new adaptive control strategy, and utilizing the small gain theorem, a new adaptive tracking controller is constructed to address the difficulties raised by unmodeled dynamics and dead-zone input. By constructing an integral-type Lyapunov function, it is shown that the considered SNSs are input-to-state stable in probability (ISSP) and all system signals are bounded in probability. Numerical and practical examples show the effectiveness of the theory.
The development of multi-label feature selection aims to alleviate the curse of dimensionality that is intrinsic to multi-label learning contexts. Nevertheless, the majority of existing feature selection methods adopt a uniform treatment of all labels, failing to fully account for the similarity existing between labels. However, in practical scenarios, inherent similarities exist between labels—highly similar labels tend to form label groups, which is primarily characterized by their co-occurrence across a large number of samples. This phenomenon leads to a critical limitation: when evaluating feature significance, conventional methods are more inclined to select features strongly correlated with large-scale label groups, while neglecting those that exhibit high relevance to small-scale label groups. Consequently, the performance of such methods is compromised to a certain extent. Additionally, existing methods rarely comprehensively integrate feature–label correlation, label–label correlation, and feature–feature redundancy. Moreover, the adoption of fixed fuzzy neighborhood radius further hinders the performance. To tackle these aforementioned issues, this paper designs a feature selection method that combines the label grouping strategy and the fuzzy multi-neighborhood information measures. Specifically, highly similar labels are first clustered into distinct label groups, and different fuzzy neighborhood radii are assigned to individual features. Subsequently, the comprehensive performance of features on all label groups evaluated through the fuzzy multi-neighborhood information measures. Finally, experimental results obtained from 15 datasets demonstrate that the proposed method delivers better performance than 9 representative multi-label feature selection methods.
This study develops an enhanced GoogLeNet model integrated with an intuitionistic fuzzy Gaussian membership function preprocessing mechanism (GoogLeNet_IF) for classifying COVID-19 computed tomography (CT) images. The approach introduces a novel combination of Intuitionistic Fuzzy Sets (IFs) and Gaussian membership functions. It enables adaptive adjustment of pixel-level membership degrees to achieve more accurate and discriminative image feature representation. The intuitionistic fuzzy Gaussian-based preprocessing framework enhances the clarity and detail of medical images before feature extraction. By synergistically integrating the powerful feature learning capability of GoogLeNet with the robustness to uncertainty of IFs, the proposed GoogLeNet_IF model exhibits superior classification robustness. Particle Swarm Optimization (PSO) is employed to jointly optimize intuitionistic fuzzy parameters and the GoogLeNet hyperparameters while ensuring optimal model performance. Six variants are evaluated: (1) the baseline GoogLeNet, (2) a fuzzy Gaussian—enhanced GoogLeNet, (3) an intuitionistic fuzzy GoogLeNet with fuzzy parameter optimization, (4) a fully optimized GoogLeNet_IF model, (5) U-Net, and (6) ResNet. Experiments on the COVID-19 CT datasets demonstrate that the proposed models achieve remarkable performance, with mean accuracies of 99.20
Traditional multi-criteria decision-making (MCDM) methods in blended textiles always may face difficulties in reconciling expert judgments with data-driven uncertainty arising from nonlinear fiber interactions. To address these issues, a hybrid blended yarn assessment framework, integrating Fuzzy Analytic Hierarchy Process with nonlinear dynamic Fuzzy TOPSIS (FAHP-ND-FTOPSIS), is introduced to mitigate fuzzy uncertainty and dynamic variations. In our method, nonlinear penalties with dynamic parameterization are first merged to amplify informative deviations while diminishing cluster adhesion, achieving elevated coefficient of variation and enhanced tier robustness. Subsequently, dynamic adjustment of distribution parameters is further utilized to reduce score clustering and improve sample differentiation. Experimental results are demonstrated that our framework could enhance the discriminative capability, achieving a 79.5
Efficient logistics management is essential for improving operational efficiency and gaining a competitive edge in dynamic business behavior. To achieve this, it is necessary to evaluate the performance by adopting digital technologies that enable rapid, innovative, and green delivery while optimizing costs and reducing delivery faults. Previous studies have examined performance evaluation in supply chain and logistics, but no study has explicitly focused on logistics operations in the digital technology domain. This study uses a hybrid multi-criteria decision-making (MCDM) methodology to explore the impact of digital technology on logistics operations. We identified twenty-five key performance indicators (KPIs) from the literature and expert input, classified into four parameters: sustainability, accountability, quality, and operational. Later, the proposed study uses the Fuzzy Delphi method (FDM), which eliminates five KPIs from the initially identified KPIs. Subsequently, the fuzzy full consistency method (FUCOM) estimated the weights of the finalized KPIs. The validity of the hybrid approach was confirmed through sensitivity and comparison analyses. The results conclude that the sustainability (P1) parameter got the highest ranking, followed by quality (P3). Moreover, “cost reduction (L4)” is ranked first and nominated as a critical KPI having a weightage of 0.0773, which is subsequently followed by “rapid delivery (L11),” “green delivery (L2),” and “regulations and legislation (L1)” having a weightage of 0.075, 0.0695, and 0.0694, respectively. The results of comparative analyses show that the ranking of the first three prime factors remains constant across F-DEMATEL, F-BWM, and F-AHP. However, the ranking for the KPI “Regulations and legislation” deviates slightly; this might be due to the F-AHP approach. In addition, the sensitivity analysis shows that the factor rankings for “cost reduction” and “rapid delivery” are insensitive to the first seven tests. The outcomes of this study will provide significant information regarding a digital technology-based KPI framework for researchers and policymakers to optimize operations and enhance logistics efficiency.
