Amid the global wave of globalization, innovation has become the core driving force for corporate development, with the strength of innovation capability serving as the decisive factor for enterprises to stand out. Based on uncertainty theory, financing constraint theory, and flexible portfolio theory, this paper employs empirical research methods to deeply analyze how financial flexibility impacts corporate performance, with a focus on the mediating role of R&D investment. The study selects A-share listed companies on the main board of the Shanghai and Shenzhen stock exchanges from 2019 to 2024, screening a total of 6,354 sample data. Through empirical research and analysis, the following conclusions are drawn: (1) Enterprises can enhance financial performance by improving financial flexibility; (2) Higher financial flexibility promotes corporate R&D investment activities; (3) R&D investment acts as a mediator between financial flexibility and corporate performance. Finally, the paper proposes relevant recommendations based on the experimental results.

ABSTRACTBackgroundNew graduate nurses entering intensive care units (ICUs) directly after graduation often face challenges in clinical decision‐making, contributing to a sense of uncertainty—the inability to predict the outcome of a patient situation. Although uncertainty has been studied in other healthcare contexts, it remains underexplored among new graduate nurses in the ICU.AimTo explore the experience of uncertainty among new graduate nurses working in ICUs.Study DesignThis qualitative interpretive descriptive study was guided by a theory of uncertainty, which examines its conditions, causes, manifestations, remediation strategies and consequences. Semi‐structured interviews were conducted with new graduate nurses with < 2 years of ICU experience, and data were analysed using a constant comparative method.FindingsParticipants' experiences of uncertainty formed part of an iterative, experiential learning process. Uncertainty arose primarily from unfamiliar or critical patient situations and was exacerbated by the nursing team's scrutiny. In response, new graduate nurses engaged in self‐questioning about both clinical situations and their own competence. To mitigate uncertainty, they relied on personal knowledge, team expertise and available resources.ConclusionsUncertainty among new graduate nurses in the ICU is shaped not only by clinical complexity but also by interpersonal dynamics. The nursing team plays a significant role in both supporting and intensifying feelings of uncertainty. New graduate nurses question the trajectory of patient care and their role and legitimacy within the ICU environment.Relevance to Clinical PracticeThis study highlights the multifaceted nature of uncertainty among new graduate nurses in intensive care. Targeted support strategies—such as mentorship, structured feedback and reflective learning opportunities—are essential to foster confidence, clinical competence and professional integration.

Support vector classification (SVC) and support vectors regression (SVR) are learning machines that have excellent generalization performance. The data which used by classical statistical learning theory is assumed precise. However, the data from real world sometimes low-quality or imprecise, the uncertainty theory and uncertain statistics are appropriate methods to process the imprecise observations. In this paper, the optimal hyperplane under the framework of uncertainty theory be put forward as the basis of SVR. Based on the definition of optimal hyperplane, the theorem of SVR with imprecise observation be proposed, this theorem obtains the basic ideology and dual problem, can solves the support vector problem under the uncertainty theory. Moreover, the cross-validation (CV) method and the average test error (ATE) be employed to evaluate the generalization performance of regression models. After evaluation of models, the forecast value can be computed and the root mean squared error (RMSE) be used to measure the effect of prediction. Finally, a numerical example be given to show the excellent performance of SVR, SVR has the minimum ATE and RMSE among some models, then the forecast value of the test set be calculated.

ABSTRACT Drawing upon uncertainty theory, this study investigates the effects of the (in)congruence between objective and perceived economic policy uncertainty on firms’ persistent innovation. Utilising a panel data from 2,773 listed Chinese firms between 2011 and 2020, we employ polynomial regression and response surface analysis to test our hypotheses. We find that incongruence between objective and perceived economic policy uncertainty positively impacts persistent innovation compared to congruence. Furthermore, low – low congruence between objective and perceived economic policy uncertainty realises superior persistent innovation compared to high – high congruence. Moreover, high – low incongruence between objective and perceived economic policy uncertainty improves persistent innovation more than low – high incongruence. Finally, technological intensity strengthens the positive effect of incongruence between objective and perceived uncertainty on persistent innovation. We discuss the study’s implications and call for future research to jointly consider both dimensions of economic policy uncertainty in exploring the drivers of innovation.

In the field of assembly lines, human-robot collaborative assembly lines have become a production mode for many manufacturing enterprises. However, robots consume energy and generate carbon emissions during the production process. With the intensification of global warming, low-carbon and energy-saving development has emerged as the mainstream trend. This study aims to address the human-robot collaborative assembly line balancing problem with the number of stations and carbon emissions as the primary and secondary objective, respectively. In addition to the traditional ALBP constraints, this study also considers the uncertainty of task production time. A chance-constrained model is formulated based on the uncertainty theory. An improved reinforcement learning algorithm — the two-stage Q-learning algorithm is proposed. Furthermore, five crossover and three mutation actions are put forward. Finally, numerical experiments were conducted to validate the effectiveness of the algorithm. The managerial insights from the results as well as the limitations of the study are also highlighted.

While large language models (LLMs) such as ChatGPT, Claude, and DeepSeek are evaluated based on their accuracy and truthfulness, “hallucinations” betray underlying structural limitations. These results are not simply incorrect answers, but statistical resonances; they are instances where models stabilize into statistically significant (though semantically unfounded) response patterns. Current frameworks fail to accommodate contextual semantics, experiential time, and intentionality as key dimensions for effective experience-based decision-making in complex digital spaces. This article presents an integration paradigm offered by the theory of uncertainty and incompleteness of information, extended by the Sophimatics approach with 2D complex time (t = t + i·t0) and Super Time Cognitive Neural Network (STCNN) that provides both memory management, imagination enhancement, and creativity generation as computational primitives. By integrating probability with plausibility, credibility, and possibility, our model reconsiders the issue of evaluating the reliability of LLM results as a problem that goes beyond traditional probabilistic approaches. Accepting that hallucinations are an emerging phenomenon of resonance between statistical distributions, we suggest an extended probability method in which these resonances can be mitigated and directed towards a coherent cognitive understanding. The paper places this approach in the broader perspective of digital transformation at the information systems level and its implications for AI reliability, explainability, and adaptive decision-making in post-generative AI. Intuitive scenarios are described, based on the inclusion of complex time and Sophimatics in theoretical modelling, illustrating how prediction, historical-contextual adoption, and resistance to paradoxical or contradictory information are strengthened. The results point to this paradigm as a springboard for reliable, human-aligned AI capable of enabling digital transformation in sectors such as healthcare, finance, and governance.

The financial market is a dynamic and unpblackictable system, requiring portfolio managers to continuously adjust investment strategies in response to market fluctuations. This study addresses the portfolio adjustment problem by incorporating newly added stocks into an existing portfolio while considering transaction costs. We propose a novel mean-semi absolute deviation-skewness model for portfolio optimization in an uncertain framework, effectively capturing both risk and asymmetry in returns. Unlike traditional models, our approach explicitly treats the returns of newly added stocks as uncertain variables, estimated based on expert judgment. The proposed model is formulated as a constrained nonlinear optimization problem and solved using the “fmincon” function in MATLAB R2018a. A numerical example demonstrates the practical applicability of our model, and a comparative analysis highlights its advantages over existing portfolio optimization methods. The results show that our approach provides a more flexible and realistic framework for portfolio adjustments, particularly in uncertain financial environments.

ABSTRACT In response to the potential failure of traditional models when faced with issues of nonwhite noise residuals and imprecise data, this study extends the mixed data sampling (MIDAS) model to the field of uncertainty theory to tackle these challenges. Under the framework of uncertainty theory, this research addresses the frequency inconsistency in economic data collection by constructing two types of uncertain MIDAS models, aiming to fill the gap in uncertainty theory's handling of predictive analysis for variables with different frequencies. Furthermore, this study integrates the dual perspectives of energy consumption and energy‐related carbon dioxide emissions. By building uncertain MIDAS models with uncertain disturbance terms and traditional MIDAS models, the research systematically establishes and comparatively analyzes univariate and multivariate energy consumption, departmental carbon dioxide emissions, and multivariate models that combine these two perspectives. The study's results not only confirm the nonwhite noise characteristics of residuals and validate the rationality of treating residuals as uncertain disturbance terms but also demonstrate through comparative analysis that the uncertain MIDAS model outperforms the traditional MIDAS model in terms of forecasting effectiveness. Moreover, the multivariate forecasting method that considers both perspectives can more comprehensively describe and predict the US quarterly gross domestic product (GDP), showing its superior predictive capability. Furthermore, by altering the evaluation criterion, substituting GDP with nominal GDP and introducing the control variables for robustness analysis, we have further verified the robustness of the model and its results.

Uncertain singular non-causal systems are a class of singular systems that satisfy the regularity constraint and inherently involve uncertainty. This paper presents zero-sum games within the framework of the Hurwicz criterion, which balances both optimistic and pessimistic perspectives under uncertainty. By applying the principles of uncertainty theory and dynamic programming, recursive equations are derived to solve Hurwicz-type zero-sum games for such systems. This study explores two specific cases of zero-sum games for linear and nonlinear uncertain singular non-causal systems under the Hurwicz criterion. For each case, the explicit analytical expression for the equilibrium solution is derived from the recursive equations. Additionally, three numerical examples are provided to validate the effectiveness of the main results.

Performance prediction of floating photovoltaic frames based on uncertainty theory

A fundamental transformation of the industrial safety management paradigm from a deterministic to a probabilistic and scholastic approach requires a reevaluation of the methodological basics of project management within the framework of risk and uncertainty theory. This study develops the conceptual apparatus of the integration of F. Knight’s classic risk theory, D. Bernoulli’s expected utility theory, R. Coase and O. Williamson's transaction cost theory, and the modern Project Management Body of Knowledge (PMBoK) methodology developed and supported by the US Institute of Project Management in order to form a comprehensive system for managing the modernization of occupational safety systems at hazardous production facilities. Based on the synthesis of neoclassical and institutional economic theories, a modified function for optimizing a safety project portfolio that considers not only direct economic effects but also the reduction of transactional costs resulting from inter-organizational coordination in the industrial safety system has been developed. The empirical verification of the model using data from the Federal State Statistics Service and the Federal Service for Labor and Employment for the period 2017–2024 has confirmed the statistical significance of institutional environment factors in determining the efficiency of modernization projects. The economic and mathematical model proposed is based on modifying H. Markowitz's portfolio theory, incorporating occupational safety risk components as a specific organizational asset that generates a negative correlation with traditional production risks. Calculations considering current macroeconomic conditions of September 2025 (Central Bank key rate 18 %, medium-term OFZ yield 14.5 %) demonstrate the potential achieving a Pareto-optimal state with safety investments at the level of 2.8–3.2 % of the enterprise's gross revenue, which corresponds to best practices in developed economies and ensures a 37–42 % reduction in integral risk while maintaining the profitability of core activities.

Catalytic resonance theory for parametric uncertainty of programmable catalysis

Although previous qualitative work has identified the role of intolerance of uncertainty in the development of anxiety in autism, there has been little research on what uncertainty means exactly for autistic people and/or what types of uncertainties may be particularly anxiety provoking. Fifteen autistic adults (five women) took part in this qualitative interview study in which we probed their understanding and experiences of uncertainty and its links to feelings of anxiety. We applied a grounded theory approach to transcripts of the interviews, broadly following Charmaz's constructivist epistemology, to derive a theory of uncertainty as it is experienced by the autistic people we interviewed. From the interviews, we derived a model of uncertainty, which identified three different levels of uncertainty, ranging from the certainty of the "known," through to the relatively manageable uncertainty of the "known unknown," to the anxiety-provoking "unknown unknown" or that which cannot be made known. We propose in this model that anxiety can be understood as resulting from difficulties with avoiding or controlling the latter types of uncertainty through planning or information gathering. Previous researchers had treated uncertainty as a unified construct. However, they may not have explored what uncertainty might mean for autistic people. We have shown in this study that not all uncertainties are experienced equally. We hope that this research will help develop a more nuanced understanding and that it constitutes the first step in disentangling anxiety from intolerance of uncertainty in autism.

Purpose This study investigates how corporate entrepreneurs utilize artificial intelligence (AI) to make decisions under different types of uncertainty, examining AI’s role in facilitating transparency and supporting decision-making under complex conditions. Design/methodology/approach Data were gathered from 39 semi-structured interviews with corporate entrepreneurs across industries to understand how AI assists them in coping with different types of uncertainty. A flexible pattern matching approach (FPMA) was used to analyze the data, integrating both theoretical perspectives and novel empirical insights. Findings The findings reveal a critical insight: while AI can enhance transparency and improve decision-making under high uncertainty, it may paradoxically increase uncertainty in tasks of lower complexity due to AI’s remaining error susceptibility for such tasks. This suggests that while AI is a powerful tool for addressing complex challenges, it may introduce new uncertainties in more predictable contexts. Research limitations/implications Besides advancing conventional entrepreneurial uncertainty theory, this research extends the theories of entrepreneurial effectuation and causation by examining AI’s distinct role in helping (corporate) entrepreneurs make decisions under uncertainty. Our findings suggest that entrepreneurs need a balanced approach, adopting both causal and effectual strategies when utilizing AI. Practically, these insights can guide corporate managers and policymakers in developing strategies for effective AI integration that address varying uncertainties. Originality/value By focusing on how AI supports entrepreneurial decision-making under uncertainty, this study provides a novel perspective on AI’s impact across different uncertainty types, offering a framework to optimize AI’s potential while mitigating its limitations to entrepreneurial decision-making.

To explore the applicability of uncertainty theory in practice and improve the effectiveness of online rumor debunking, this paper constructs a multi-dimensional IPA (Information-Level, Platform-Level, Audience-Level) index system and establishes an uncertain comprehensive evaluation model. Key debunking factors are weighted via expert estimation based on historical data, while subjective uncertainty during evaluation process is characterized by uncertain variables. Next, the grades of core influence factors and debunking effectiveness are determined through the maximum membership principle. Finally, empirical analysis of the “Shuanghuanglian inhibits novel coronavirus” rumor case during COVID-19 validates the rationality and feasibility of the evaluation index system and evaluation model. Results demonstrate that the information-level (e.g., credibility, release timeliness) is the most critical dimension, followed by audience-level and platform-level. The model scientifically identifies core influencing factors and provides actionable decision support for optimizing debunking strategies, contributing novel research ideas and methods to online rumor governance.

Music data exhibits numerous distinct symmetric and asymmetric patterns—ranging from symmetric pitch sequences and rhythmic cycles to asymmetric phrase structures and dynamic shifts. These varied and often subjective patterns present notable challenges for data analysis, such as distinguishing meaningful structural features from noise and adapting analytical methods to accommodate both regularity and irregularity. To tackle this challenge, we present a novel uncertain hypothesis test, referred to as the conservative hypothesis test, which is designed to assess the validity of statistical hypotheses associated with the symmetric and asymmetric patterns exhibited by two multivariate normal uncertain populations. Specifically, we extend the uncertain hypothesis test for the mean difference between two single-characteristic normal uncertain populations to the multivariate case, filling a research gap in uncertainty theory. Building on this two-population multivariate hypothesis test, we propose the conservative hypothesis test—a feasible uncertain hypothesis testing method for multivariable scenarios, developed based on multiple comparison procedures. To demonstrate the practical utility of these methods, we apply them to music-related statistical data, assessing whether two groups of evaluators use consistent criteria to score music. In essence, the hypothesis tests proposed in this paper hold significant value for social sciences, particularly music statistics, where data inherently contains ambiguity and uncertainty.

Multivariate time series analysis is a crucial tool for examining the interdependence of multiple variables over time. Traditional probabilistic models require precise observational data. However, in practical applications, some variables are subject to inherent uncertainties that cannot be accurately quantified. To address this limitation, this paper introduces an uncertain vector autoregressive model with exogenous variables (UVARX) to incorporate uncertainty into multivariate time series analysis. The proposed model distinguishes between endogenous and exogenous variables, leveraging uncertainty theory to accommodate imprecise observations. A rigorous statistical framework — encompassing parameter estimation, residual analysis, uncertain hypothesis test, cross-validation, and predictive evaluation — is employed to validate the model. Empirical analysis on the joint forecasting of [Formula: see text] emissions and GDP, with electricity consumption as an exogenous factor, demonstrates the model’s capability to handle imprecise data effectively. Results indicate that the UVARX model outperforms conventional approaches in forecasting accuracy, providing a robust analytical tool for uncertain multivariate time series. Since the transportation sector, particularly the automotive industry, is a major contributor to global [Formula: see text] emissions, the proposed methodology demonstrates strong potential for applications in intelligent vehicle systems and AI-driven energy management.

Objective: This randomized controlled trial aimed to determine the effect of the "Empowerment Program for Infertile Women," developed based on the Theory of Uncertainty in Illness, on the levels of coping with uncertainty and stress in women diagnosed with infertility. Methods: The study was conducted as a double-blind, pretest-posttest, control group experimental design. It was carried out between January and June 2022 with 35 infertile women in the intervention group and 35 in the control group, all diagnosed with infertility and meeting the inclusion criteria, who applied to the gynecology outpatient clinic of Ondokuz Mayıs University Faculty of Medicine Hospital. Data were collected using the Personal Information Form developed by the researcher based on the literature, the Mishel Uncertainty in Illness Scale–Community Form (MUIS-C), and the Coping with Infertility Stress Scale (CISS). After the pretest was administered to both groups, the intervention group received a four-week face-to-face education program. Three months after the completion of the Empowerment Program for Infertile Women, posttests were administered to both groups. Results: The mean age of women in the intervention group was 29.6 ± 5.0, and 28.9 ± 4.0 in the control group. According to the pretest-posttest results of the control group, the changes in scores related to coping with infertility stress and uncertainty due to infertility were not statistically significant. After the intervention, the mean total score on the Coping with Infertility Stress Scale in the intervention group was 50.3 ± 7.4, min-max = (34–71), indicating an increase compared to the pre-intervention score. The mean total score on the Mishel Uncertainty in Illness Scale–Community Form was 51.5 ± 20.4, min-max = (27–100), indicating a decrease compared to the pre-intervention score. Statistically significant differences were found in both within-group and between-group comparisons of the total scores for both scales in the intervention group (p &lt; 0.001). Conclusion: The results of the study indicated that the Empowerment Program for Infertile Women, developed based on the Theory of Uncertainty in Illness, positively affected the levels of coping with uncertainty and stress in women with infertility.

We develop a novel framework for modeling temperature dynamics and pricing weather derivatives within the setting of Uncertainty Theory. The temperature process is described by a mean-reverting uncertain differential equation with jumps, where continuous uncertainty is modeled via a canonical Liu process and abrupt changes are captured using an uncertain renewal process. This structure yields uncertainty distributions for temperature indices such as Heating Degree Days (HDD) and Cooling Degree Days (CDD), enabling derivative pricing without relying on traditional probability measures or risk-neutral assumptions. By replacing stochastic processes with uncertain ones, the model accommodates belief-driven dynamics and subjective economic impacts, making it especially useful in environments with limited historical data or ambiguous risk. The approach offers a robust and flexible alternative for derivative valuation in both theoretical and applied contexts.

This work delves into implementing two models of uncertainty theory, namely the Expected Value Model (EVM) and the Optimistic Value Model (OVM), to address the complexities of the Multi-Objective Travelling Salesman Problem (MOTSP) and the Multi-Objective Solid Travelling Salesman Problem (MOSTSP). The study con- siders the impact of carbon emissions in these models. It employs a newly developed Aspiration Level-based Multi-Objective Quasi Oppositional Jaya (AL-based MOQO Jaya) algorithm for solving problems based on real-world data from the city of Surat for 10 and 50 nodes. The significant advantage of using the AL-based MOQO Jaya algorithm is it does not require any algorithm-specific parameters. Hence, it can solve different optimization problems irrespective of parameter setting. The average run time of AL-based MOQO Jaya for the EVM model is 1.1952 sec, and for the OVM model is 1.0554 sec with ten nodes. For 50 nodes, the average run time for the EVM model is 1.5595 sec, and for OVM, it is 1.4764 sec, which is relatively lesser compared to CPLEX, FPT, HGA, and Rao algorithms for both MOTSP and MOSTSP. Further, the AL-based MOQO Jaya algorithm dominates the solutions obtained by other established techniques. The study concludes solutions obtained through the AL-based MOQO Jaya algorithm are more efficient and provide a viable alternative for decision-makers.