Search Results (145)

In this work, we develop a disturbance suppression-oriented fuzzy sliding mode secured sampled-data controller for third-order parabolic partial differential equations that ought to cope with nonlinearities, hybrid cyber attacks, and modeled disturbances. This endeavor is mainly driven by formulating an observer model with a T–S fuzzy mode of execution that retrieves the latent state variables of the perceived system. Progressing onward, the disturbance observers are formulated to estimate the modeled disturbances emerging from the exogenous systems. In due course, the information received from the system and disturbance estimators, coupled with the sliding surface, is compiled to fabricate the developed controller. Furthermore, in the realm of security, hybrid cyber attacks are scrutinized through the use of stochastic variables that abide by the Bernoulli distributed white sequence, which combat their unpredictability. Proceeding further in this framework, a set of linear matrix inequality conditions is established that relies on the Lyapunov stability theory. Precisely, the refined looped Lyapunov–Krasovskii functional paradigm, which reflects in the sampling period that is intricately split into non-uniform intervals by leveraging a fractional-order parameter, is deployed. In line with this pursuit, a strictly $({\Phi }_1,{\Phi }_2,{\Phi }_3)-\varrho$ dissipative framework is crafted with the intent to curb norm-bounded disturbances. A simulation-backed numerical example is unveiled in the closing segment to underscore the potency and efficacy of the developed control design technique. Full article

Environmental, social, and governance (ESG) initiatives have gained increasing attention in the hotel industry, yet the consumer-level psychological processes through which such activities relate to booking intentions remain incompletely understood. This study aims to examine how hotel ESG activities are associated with consumers’ booking intentions by focusing on the mediating roles of corporate image and consumer trust, as well as the moderating role of environmental awareness. Survey data were collected from consumers with recent hotel stay experiences in China and analyzed using a dual-method approach, combining partial least squares structural equation modeling (PLS-SEM) and fuzzy-set qualitative comparative analysis (fsQCA). The results show that social and governance activities are positively associated with corporate image, whereas environmental and social activities are positively associated with consumer trust. Corporate image and consumer trust are, in turn, associated with higher booking intentions, while environmental awareness strengthens only the relationship between environmental activities and corporate image. In addition, the fsQCA results reveal multiple configurational pathways through which different combinations of ESG activities and consumer psychological responses are associated with high booking intention. Overall, the findings suggest that hotel ESG initiatives relate to booking intentions through differentiated psychological mechanisms and multiple pathways. Full article

In this research article, we propose a fuzzy fractional-order SEI$R_i{U}_i$HR model to describe the transmission dynamics of COVID-19, comprising susceptible, exposed, infected, reported, unreported, hospitalized, and recovered compartments. The uncertainty in initial conditions is represented using fuzzy numbers, and the fuzzy Laplace transform combined with the Adomian decomposition method is employed to solve nonlinear differential equations and also to derive approximate analytical series of solutions. In addition to fuzzy lower and upper bound solutions, a model is introduced to provide a representative trajectory under uncertainty. A key feature of the proposed model is its inherent symmetry in compartmental transitions and structural formulation, which show the difference in reported and unreported cases. Numerical experiments are conducted to compare fuzzy and normal (non-fuzzy) solutions, supported by 3D visualizations. The results reveal the influence of fractional-order and fuzzy parameters on epidemic progression, demonstrating the model’s capability to capture realistic variability and to provide a flexible framework for analyzing infectious disease dynamics. Full article

This research examines the approximate solutions to the system of atmospheric internal-wave (AIW) fuzzy fractional partial differential equations with the gH-Caputo derivative. Atmospheric internal waves are a type of wave that occurs within the Earth’s atmosphere, typically in the lower atmosphere or boundary layer. Vertical displacements of air parcels cause them to occur due to various factors such as wind shear, buoyancy, and topographic effects. These waves can propagate horizontally and vertically and play an important role in atmospheric dynamics, including energy transport, momentum, and pollutants. Using the residual power series method (RPSM), we obtained new effective numerical solutions to the AIW equation system with gH-Caputo derivatives and fuzzy initial conditions. The RPSM solutions are compared with other numerical methods to examine the suggested method’s accuracy and efficiency. Illustrative examples and a comparative analysis of our approach with present methods are given. Full article

In this paper, we introduce the notion of fuzzy exponential contractions within the framework of fuzzy metric spaces. These mappings, which involve point-dependent exponential terms, are studied under the assumptions of either fuzzy continuity or the weaker condition of fuzzy Picard continuity. We establish corresponding existence and uniqueness theorems, and we further demonstrate the scope of the theory through illustrative examples and by applying it to prove an existence and uniqueness result for a class of nonlinear fractional differential equations. Full article

Due to low passenger retention rates, autonomous Ride-hailing Vehicles (ARVs) face a critical bottleneck in commercialization, especially in the Chinese market. Based on 312 survey responses from Wuhan, this study systematically explored the mechanisms influencing customers’ continuance usage intention toward autonomous Ride-hailing Vehicles (ARVs), by integration of Structural Equation Modeling (SEM) and fuzzy-set Qualitative Comparative Analysis (fsQCA). The empirical findings revealed that perceived usefulness, trust in technology, perceived value, perceived price fairness, and psychological ownership exert significant positive effects on sustainable usage intention, with trust in technology demonstrating the strongest direct effect. In contrast, concerns about safety equality demonstrate a significant negative impact. Trust in technology serves as an indirect mediator and emerges as a necessary condition in high-intention fsQCA configurations. Building on all insights, the study proposed a four-dimensional “Technology-Psychology-Safety-Economy” (TPSE) driving model, established a novel theoretical framework for user behavior research in intelligent transportation, and offered empirical guidance for differentiated corporate strategies and technology adoption. Full article

The Laplace equation is an important partial differential equation, typically used to describe the properties of steady-state distributions or passive fields in physical phenomena. Its Cauchy problem is one of the classic, serious, ill-posed problems, characterized by the fact that minor disturbances in the data can lead to significant errors in the solution and lack stability. Secondly, the determination of the parameters of the classical Laplace equation is difficult to adapt to the requirements of complex applications. For this purpose, in this paper, the Laplace equation with uncertain parameters is defined, and the uncertainty is represented by fuzzy numbers. In the case of granular differentiability, it is transformed into a granular differential equation, proving its serious ill-posedness. To overcome the ill-posedness, the Fourier regularization method is used to stabilize the numerical solution, and the stability estimation and error analysis between the regularization solution and the exact solution are given. Finally, numerical examples are given to illustrate the effectiveness and practicability of this method. Full article

The purpose of this paper is to investigate a class of novel symmetric coupled fuzzy fractional partial differential equation system involving the Caputo–Katugampola (C-K) generalized Hukuhara (gH) derivative. Within the framework of C-K gH differentiability, two types of gH weak solutions are defined, and their existence is rigorously established through explicit constructions via employing Schauder fixed point theorem, overcoming the limitations of traditional Lipschitz conditions and thereby extending applicability to non-smooth and nonlinear systems commonly encountered in practice. A typical numerical example with potential applications is proposed to verify the existence results of the solutions for the symmetric coupled system. Furthermore, we introduce Ulam–Hyers stability (U-HS) theory into the analysis of such symmetric coupled systems and establish explicit stability criteria. U-HS ensures the existence of approximate solutions close to the exact solution under small perturbations, and thereby guarantees the reliability and robustness of the systems, while it prevents significant deviations in system dynamics caused by minor disturbances. We not only enrich the theoretical framework of fuzzy fractional calculus by extending the class of solvable systems and supplementing stability analysis, but also provide a practical mathematical tool for investigating complex interconnected systems characterized by uncertainty, memory effects, and spatial dynamics. Full article

This study introduces a novel Fuzzy Piecewise Fractional Derivative (FPFD) framework to enhance epidemiological modeling, specifically for the multi-phasic co-infection dynamics of Omicron and malaria. We address the limitations of traditional models by incorporating two key realities. First, we use fuzzy set theory to manage the inherent uncertainty in biological parameters. Second, we employ piecewise fractional operators to capture the dynamic, phase-dependent nature of epidemics. The framework utilizes a fuzzy classical derivative for initial memoryless spread and transitions to a fuzzy Atangana–Baleanu–Caputo (ABC) fractional derivative to capture post-intervention memory effects. We establish the mathematical rigor of the FPFD model through proofs of positivity, boundedness, and stability of equilibrium points, including the basic reproductive number (R0). A hybrid numerical scheme, combining Fuzzy Runge–Kutta and Fuzzy Fractional Adams–Bashforth–Moulton algorithms, is developed for solving the system. Simulations show that the framework successfully models dynamic shifts while propagating uncertainty. This provides forecasts that are more robust and practical, directly informing public health interventions. Full article

This study combines Structural Equation Modeling (SEM) and Fuzzy-Set Qualitative Comparative Analysis (fsQCA) methods to systematically analyze the key factors affecting the digital transformation of construction enterprises, and to propose differentiated implementation paths and strategies based on these factors. The results of the fsQCA analysis show that the four combination configurations affecting the effectiveness/success of digital transformation of construction enterprises from a group perspective are identified as/can be categorized as “technology-organization dual-driven” and “environment-capability leverage”. The study proposes countermeasures based on the results of the model and the current challenges, in order to offer insights for/serve as a reference for the successful implementation of digital transformation in construction enterprises. Full article

This research paper delves into the application of optimality results in orthogonal fuzzy metric spaces to demonstrate the existence and uniqueness of solutions of nonlinear differential equations with boundary conditions and nonlinear integral equations, emphasizing the importance of orthogonal fuzzy metric spaces in extending fixed-point theory. Through introducing this innovative concept, the study provides a theoretical framework for analyzing mappings in diverse scenarios. In this study, we introduce the concept of best proximity point (BPP) within the framework of orthogonal fuzzy metric spaces by employing orthogonal fuzzy proximal contractive mappings. Moreover, this research explores the implications of the established results, considering both self-mappings and non-self mappings that share the same parameter set. Additionally, some examples are provided to illustrate the practical relevance of the proven results and consequences in various mathematical contexts. The findings of this study can open up avenues for further exploration and application in solving real-world problems. Full article

This paper investigates a novel class of weighted fuzzy fractional Volterra–Fredholm integro-differential equations (FWFVFIDEs) subject to integral boundary conditions. The analysis is conducted within the framework of Caputo-weighted fractional calculus. Employing Banach’s and Krasnoselskii’s fixed-point theorems, we establish the existence and uniqueness of solutions. Stability is analyzed in the Ulam–Hyers (UHS), generalized Ulam–Hyers (GUHS), and Ulam–Hyers–Rassias (UHRS) senses. A modified Adomian decomposition method (MADM) is introduced to derive explicit solutions without linearization, preserving the problem’s original structure. The first numerical example validates the theoretical findings on existence, uniqueness, and stability, supplemented by graphical results obtained via the MADM. Further examples illustrate fuzzy solutions by varying the uncertainty level (r), the variable (x), and both parameters simultaneously. The numerical results align with the theoretical analysis, demonstrating the efficacy and applicability of the proposed method. Full article

In this paper, we present the notion of fuzzy $\mathcal{R}-F-$contractive mappings and provide some fuzzy fixed point results in the setting of fuzzy metric spaces, which are endowed with binary relations. Furthermore, we apply our newly established fuzzy fixed point results to solve certain boundary value problems for nonlinear fractional differential equations involving the Caputo fractional derivatives. Also, we provide some examples to show the utility of our new results. Full article

In this paper, we propose a fuzzy formulation of the classic Frankot–Chellappa algorithm by which surfaces can be reconstructed using normal vectors. In the fuzzy formulation, the surface normal vectors may be uncertain or ambiguous, yielding a fuzzy Poisson partial differential equation that requires appropriate definitions of fuzzy derivatives. The solution of the resulting fuzzy model is approached by adopting a fuzzy variant of the discrete sine transform, which results in a fast and robust algorithm for surface reconstruction. An adaptive defuzzification strategy is also introduced to improve noise handling in highly uncertain regions. In experiments, we demonstrate that our fuzzy Frankot–Chellappa algorithm achieves accuracy on par with the classic approach for smooth surfaces and offers improved robustness in the presence of noisy normal data. We also show that it can naturally handle missing data (such as gaps) in the normal field by filling them using neighboring information. Full article

Individual willingness to pay (WTP) for green energy plays a vital role in mitigating climate change. Based on social cognitive theory (SCT), which emphasizes the dynamic interaction among individual cognition, behavior and the environment, this study develops a theoretical model to identify factors influencing green energy WTP. The study is based on 585 valid questionnaire responses from urban areas in China and uses Structural Equation Modeling (SEM) to reveal the linear causal path. Meanwhile, fuzzy-set Qualitative Comparative Analysis (fsQCA) is utilized to identify the combined paths of multiple conditions leading to a high WTP, making up for the limitations of SEM in explaining complex mechanisms. The SEM analysis shows that social trust, social networks, and social norms have a significant positive impact on individual green energy WTP. And this influence is further transmitted through the mediating role of environmental self-efficacy and expectations of environmental outcomes. The FsQCA results identified three combined paths of social capital and environmental cognitive conditions, including the Network–Norm path, the Network–efficacy path and the Network–Outcome path, all of which can achieve a high level of green energy WTP. Among them, the social networks are a core condition in every path and a key element for enhancing the high green energy WTP. This study promotes the expansion of SCT, from emphasizing the linear role of individual cognition to focusing on the configuration interaction between social structure and psychological cognition, provides empirical evidence for formulating differentiated social intervention strategies and environmental education policies, and contributes to sustainable development and the green energy transition. Full article