This paper introduces and studies various modes of statistical convergence for sequences of complex uncertain random variables-a mathematical framework designed to model hybrid phenomena involving both randomness and uncertainty in complex-valued settings. The primary contribution is the formulation of statistical convergence concepts with respect to the chance measure, including almost sure convergence, convergence in measure, convergence in mean, and convergence in distribution. Key relationships among these convergence types are established through rigorous theorems, and their distinctions are illustrated with carefully constructed examples and counterexamples. Notably, we prove that statistical convergence in measure implies convergence in chance measure, but not vice versa, and demonstrate that convergence in distribution does not generally entail convergence in measure. The results extend and unify existing theories of statistical convergence for uncertain and random variables, offering a comprehensive analytical toolkit for sequences where both probabilistic and epistemic uncertainties coexist. This work lays a foundational basis for further research in double and triple sequences of complex uncertain random variables, with potential applications in signal processing, financial modeling, and complex systems analysis under hybrid uncertainty.

Dynamic analysis of multiple response patterns in a flexible multibody system with hybrid uncertainties

Efficient hybrid uncertainty propagation in mechanical structures via low-rank approximation

Static reliability analysis of structures with probability-interval hybrid uncertainties using direct probability integration method and genetic algorithms

With the rapid advancement of green aviation technologies, electrically driven ducted fans have seen widespread adoption in electric vertical takeoff and landing aircraft due to their high hover efficiency and low noise. However, uncertainties in manufacturing process and operation parameters can significantly affect thrust performance and introduce operational risks. Stochastic uncertain parameter and interval uncertain parameter are considered in this paper. The Polynomial Chaos Expansion integrated with the Legendre inclusion function is employed to analyze the aerodynamic performance of a ducted fan under hybrid uncertainty. The tip clearance is treated as a stochastic uncertain parameter, modeled as a normal distribution N (3.5, 0.12 2 ). The rotational speed is considered an interval uncertain parameter within the range of [2350, 2450] rpm. The hybrid uncertainty analysis shows that the lower and upper bound mean of the total thrust is [92.71 N, 100.96 N], and the lower and upper bound standard deviation is [0.666 N, 0.745 N], demonstrating noticeable performance deviation under hybrid uncertainty. In addition, statistical characteristics of the lower and upper bounds of total thrust are presented. The bound relative variance (BRV) of the overall performance is 5%, whereas the BRV of the ducted thrust increased to about 8% due to pressure variations near the lip region. Additionally, a hybrid uncertainty analysis for cruise condition has also been conducted.

In order to tackle resilient supplier selection (RSS) of high uncertainty in resilient supply chain management, an effective correlation coefficients-based multicriteria group decision-making (MCGDM) methodology has been constructed. The major contribution of the present study is twofold. Firstly, in view of that extant criteria systems are all in lack of theoretical rationality, this paper establishes a capabilities-based analytical framework for intensive evaluation of supplier resilience by taking processual viewpoints of dynamic capabilities theory and risk management theory. Secondly, to empower the proposed correlation coefficients-based MCGDM methodology, probabilistic dual hesitant fuzzy uncertain unbalanced linguistic set (PDHF_UUBLS) is employed to capture hybrid uncertainties in decision processes of RSS. Then, theoretically compliant correlation coefficients (CCs) for PDHF_UUBLS are developed, including statistics-based CC, information energy-based CC and their weighted versions. Especially, information energy-based CCs overcome limitations of statistics-based CCs in special cases, thus exhibiting general applicability. In addition, a compatibility-based programming model has also been developed to objectively derive an unknown weighting vector for DMUs. Furthermore, illustrative case studies and comparative experiments have been carried out to verify effectiveness and stability of the proposed methodology. Taken together, this paper satisfies the new normal demand of resilience building in supply chain management and presents an effective MCGDM methodology for handling the key problems of RSS.

This paper proposes a hybrid uncertainty propagation analysis method for problems involving both random and interval variables by synergistically integrating arbitrary Polynomial Chaos (aPC) with Chebyshev polynomials. In this method, the aPC method is adopted to handle random uncertainties, and an interval method based on Chebyshev is proposed to deal with interval uncertainties. The principal advantages of the proposed method are: (1) It characterizes random variables using aPC, requiring only statistical moments from sample data and eliminating the reliance on pre-assumed precise probability distributions. (2) It seamlessly integrates this with a Chebyshev-based treatment of interval variables, providing a robust and efficient analysis tool. The validity and advantages of the proposed method are demonstrated through numerical examples and representative engineering case studies.

The challenges presented by market fluctuations and environmental events such as lightning are addressed in this paper by integrating fuzzy logic with Markov models. The challenges presented by market fluctuations and environmental events such as lightning are addressed in this paper by integrating fuzzy logic with Markov models. This integration is critically needed because market uncertainties (e.g., prices) often follow probabilistic patterns, while lightning impacts involve imprecise, linguistic assessments. A unified Fuzzy-Markov framework is therefore essential to holistically manage these hybrid uncertainties and enhance decision-making in smart grid self-scheduling. The objective of this research is to create a dependable framework for improving the predictability and stability of smart grid systems under unforeseen circumstances. The proposed Fuzzy-Markov approach facilitates the proactive decision-making process and the effective forecasting of future market conditions by categorizing complex numerical data into fuzzy states and analyzing the transition probabilities between these states. One of the most significant contributions is the successful classification of financial metrics, including price, revenue, and sales, into qualitative fuzzy states. The Markov transition matrix's construction and analysis provide critical insights into state transitions, with the model attaining an accuracy of 56.13%. Although this accuracy is moderate, it illustrates the model's effectiveness in predicting future conditions, superseding random conjecture and establishing a strong foundation for strategic planning. The research also emphasizes significant findings through rolling statistics, which are crucial for risk management. The novelty of this work is its distinctive integration of fuzzy logic and Markov models to address both market and environmental uncertainties in smart grids.

AL-ViT: Label-efficient Robusta coffee-bean defect detection in Thailand using active learning vision transformers

This paper addresses the multi-source uncertainties faced by horizontal pumped storage-wind-solar (HWS) hybrid systems in the day-ahead market by proposing a hybrid stochastic-robust optimization model for bidding and scheduling. The model employs a scenario-based method to capture the randomness of wind and solar power output, utilizes Information Gap Decision Theory (IGDT) to handle the epistemic uncertainty in runoff inflow forecasting, and constructs a price-acceptance probability function based on historical statistics to characterize the market mechanism. By maximizing the system’s tolerable uncertainty immunity gap, the model co-optimizes generation schedules, pumped-storage operation, and market bids while ensuring that revenue under the worst-case inflow scenario does not fall below a predefined threshold. Simulation results based on an actual project in Hubei Province demonstrate that the proposed method effectively balances revenue and risk, showing significant advantages in both revenue stability and robustness compared to the system before retrofitting. This study provides practical decision-making support for hybrid systems with horizontal pumped storage participating in electricity markets.

Abstract As a core part of large rotating machinery (e.g., aero-engines, gas turbines), rotor systems’ operational reliability directly impacts equipment safety and service life. Traditional reliability methods, mostly probabilistic, hardly handle hybrid uncertainties from cognitive factors (e.g., fuzziness, info gaps). This paper proposes a constantentropy- based unified framework to transform triangular fuzzy variables into equivalent normal random variables for consistent uncertainty quantification. With an improved Jeffcott rotor rubbing model, linear/nonlinear performance functions are built. FOSM is used for reliability calculation, verified by CMC. Results show it ensures efficiency with <1% reliability error and good engineering applicability, providing a full theoretical/practical method for rotor reliability under hybrid uncertainties.

Evaluation-based multi-objective optimization for responsive-resilient supply chain network under hybrid uncertainty

A novel approach to seismic reliability analysis for subway stations considering quantifiable hybrid uncertainties from both soil-subway station interaction effect and ground motion

Accurate prognosis of the remaining useful life (RUL) for lithium-ion batteries is critical for mitigating range anxiety and ensuring the operational safety of electric vehicles. However, existing data-driven methods often struggle to maintain robustness when transferring from controlled laboratory conditions to complex, sensor-limited, real-world environments. To bridge this gap, this study presents U-H-Mamba, a novel uncertainty-aware hierarchical framework trained on a massive hybrid repository comprising over 146,000 charge–discharge cycles from both laboratory benchmarks and operational electric vehicle datasets. The proposed architecture employs a two-level design to decouple degradation dynamics, where a Multi-scale Temporal Convolutional Network functions as the base encoder to extract fine-grained electrochemical fingerprints, including derived virtual impedance proxies, from high-frequency intra-cycle measurements. Subsequently, an enhanced Pressure-Aware Multi-Head Mamba decoder models the long-range inter-cycle degradation trajectories with linear computational complexity. To guarantee reliability in safety-critical applications, a hybrid uncertainty quantification mechanism integrating Monte Carlo Dropout with Inductive Conformal Prediction is implemented to generate calibrated confidence intervals. Extensive empirical evaluations demonstrate the framework’s superior performance, achieving a RMSE of 3.2 cycles on the NASA dataset and 5.4 cycles on the highly variable NDANEV dataset, thereby outperforming state-of-the-art baselines by 20–40%. Furthermore, SHAP-based interpretability analysis confirms that the model correctly identifies physics-informed pressure dynamics as critical degradation drivers, validating its zero-shot generalization capabilities. With high accuracy and linear scalability, the U-H-Mamba model offers a viable and physically interpretable solution for cloud-based prognostics in large-scale electric vehicle fleets.

Mobility-as-a-Service (MaaS) has emerged as a sustainable solution that integrates multiple transport services through digital platforms. Across different cities, MaaS development exhibits variation in terms of economic support, infrastructure capacity, service integration level, and long-term sustainability orientation. The complexity of multistakeholder interactions and functional components in MaaS ecosystems calls for a more comprehensive performance evaluation framework. To address this, this study proposes a holistic four-dimensional indicator system covering economic, infrastructure, integration and sustainability aspects. To address the hybrid uncertainties arising from the heterogeneous information aggregated by the proposed framework, encompassing both quantitative statistics and qualitative expert judgements, a novel rough–fuzzy best–worst method (BWM) and rough–fuzzy data envelopment analysis (DEA) approach is developed. The empirical application to six representative core cities in China reveals that high performance in “Integration” and “Economic” dimensions plays a pivotal role in determining overall MaaS performance, and coordinated enhancement across dimensions is also important. Comparative and sensitivity analyses validate the framework’s robustness, offering policymakers a reliable tool for benchmarking MaaS maturity.

Purpose In the contemporary landscape, medical tourism has emerged as a pivotal industry driving sustainable development. Investors in this sector face significant challenges, such as the optimal location of medical facilities, the range of medical services offered and the capacity of these centers. This study aims to introduce an innovative model to address these complexities. Design/methodology/approach A mixed-integer mathematical model is proposed that integrates a scenario-based robust optimization (SRO) framework with possibilistic chance-constrained programming (PCCP). It accounts for the stochastic nature of construction costs while treating the availability of human resources and their salaries as fuzzy parameters. The SRO method is used to deal with stochastic data, and its goal is to reduce the deviation of the objective function in different scenarios from the expected optimal value. The PCCP method is used to deal with fuzzy data, and the necessity criterion is used. Findings To demonstrate the practical applicability of the proposed model, a case study in Iran was conducted. Using mixed-integer linear programming, the model effectively identified suitable cities, specialties and the capacity for each specialty in each center. The outcomes of this research provide a standardized framework for researchers and organizations aiming to establish medical tourism centers in diverse countries while accommodating uncertainty. Originality/value Given the dual presence of random and epistemic uncertainties, this research is pioneering in its application of hybrid uncertainty to the medical tourism sector, offering valuable insights for future studies.

Robust green supply chain for flare waste gas recycling under hybrid uncertainty: A data-driven approach

Dempster–Shafer-informed levelized cost of energy: A robust approach for energy portfolio optimization under deep uncertainty

Self-adaptive hybrid uncertainty integration method via deterministic analytic formula

Regularization method for load reconstruction with hybrid uncertainties based on interval theory and convex model theory