Search Results (79)

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

We present a unified framework for fuzzy statistical convergence of Grünwald–Letnikov (GL) fractional differences in Bag–Samanta fuzzy normed linear spaces, addressing memory effects and nonlocality inherent to fractional-order models. Theoretically, we establish the uniqueness, linearity, and invariance of fuzzy statistical limits and prove a Cauchy characterization: fuzzy statistical convergence implies fuzzy statistical Cauchyness, while the converse holds in fuzzy-complete spaces (and in the completion, otherwise). We further develop an inclusion theory linking fuzzy strong Cesàro summability—including weighted means—to fuzzy statistical convergence. Via the discrete Q-operator, all statements transfer verbatim between nabla-left and delta-right GL forms, clarifying the binomial GL↔discrete Riemann–Liouville correspondence. Beyond structure, we propose density-based residual diagnostics for GL discretizations of fractional initial-value problems: when GL residuals are fuzzy statistically negligible, trajectories exhibit Ulam–Hyers-type robustness in the fuzzy topology. We also formulate a fuzzy Korovkin-type approximation principle under GL smoothing: Cesàro control on the test set $\{1,x,x^2\}$ propagates to arbitrary targets, yielding fuzzy statistical convergence for positive-operator sequences. Worked examples and an engineering-style case study (thermal balance with memory and bursty disturbances) illustrate how the diagnostics certify robustness of GL numerical schemes under sparse spikes and imprecise data. Full article

To effectively deal with the uncertainty of value assessments of industry-characteristic universities, this paper proposes a new fuzzy multi-attribute assessment method. Firstly, we define the complex cubic fractional orthotriple fuzzy set (CCFOFS) for expressing ambiguous information and present some basic operational rules and information measures. Then, we present the complex cubic fractional orthotriple fuzzy Dombi-weighted power-partitioned Muirhead mean (CCFOFDWPPMM) operator, which combines the superiority of the Dombi operations, power average (PA) operator, and partitioned Muirhead mean (PMM) operator. Further, a multi-attribute assessment method is constructed based on the CCFOFDWPPMM operator and the Integrated Determination of Objective Criteria Weights (IDOCRIW) method. Furthermore, we constructed a novel assessment index system for the construction of first-class disciplines. Finally, this paper verifies the validity and applicability of the method by applying the novel multi-attribute assessment method to a practical case of first-class discipline construction in industry-characteristic universities. 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 study, we present a novel mathematical framework for pricing financial derivates and modelling asset behaviour by bringing together fractional Brownian motion (fBm), fuzzy logic, and jump processes, all aligned with no-arbitrage principle. In particular, our mathematical developments include fBm defined through Mandelbrot-Van Ness kernels, and advanced mathematical tools such Molchan martingale and BDG inequalities ensuring rigorous theoretical validity. We bring together these different concepts to model uncertainties like sudden market shocks and investor sentiment, providing a fresh perspective in financial mathematics and derivatives pricing. By using fuzzy logic, we incorporate subject factors such as market optimism or pessimism, adjusting volatility dynamically according to the current market environment. Fractal mathematics with the Hurst exponent close to zero reflecting rough market conditions and fuzzy set theory are combined with jumps, representing sudden market changes to capture more realistic asset price movements. We also bridge the gap between complex stochastic equations and solvable differential equations using tools like Feynman-Kac approach and Girsanov transformation. We present simulations illustrating plausible scenarios ranging from pessimistic to optimistic to demonstrate how this model can behave in practice, highlighting potential advantages over classical models like the Merton jump diffusion and Black-Scholes. Overall, our proposed model represents an advancement in mathematical finance by integrating fractional stochastic processes with fuzzy set theory, thus revealing new perspectives on derivative pricing and risk-free valuation in uncertain environments. Full article

Persistent atrial fibrillation (AF), a prevalent cardiac arrhythmia, is primarily sustained by rotor-type reentries, with their localization crucial for successful ablation treatment. Fractionated atrial electrogram (EGM) signals have been associated with the tips of the rotors and are thus considered as ablation targets. However, the typical noise problems of physiological signals affect the results of EGM processing tools, and consequently the ablation outcome. This study proposes a data fusion framework based on the Joint Directors of Laboratories model with six levels and information quality (IQ) assessment for locating rotor tips from EGMs simulated in a two-dimensional model of human atrial tissue under AF conditions. Validation tests were conducted using a set of 13 IQ criteria and their corresponding metrics. First, EGMs were contaminated with different types of noise and artifacts (power-line interference, spikes, loss of samples, and loss of resolution) to assess tolerance. The signals were then preprocessed, and five statistical features (sample entropy, approximate entropy, Shannon entropy, mean amplitude, and standard deviation) were extracted to generate rotor location maps using a wavelet fusion technique. Fuzzy inference was applied for situation and risk assessment, followed by IQ mapping using a support vector machine by level. Finally, the IQ criteria were optimized through a particle swarm optimization algorithm. The proposed framework outperformed existing EGM-based rotor detection methods, demonstrating superior functionality and performance compared to existing EGM-based rotor detection methods. It achieved an accuracy of approximately 90%, with improvements of up to 10% through tuning and adjustments based on IQ variables, aligned with higher-level system requirements. The novelty of this approach lies in evaluating the IQ across signal-processing stages and optimizing it through data fusion to enhance rotor tip position estimation. This advancement could help specialists make more informed decisions in EGM acquisition and treatment application. Full article

As a non-associative connective in fuzzy logic, the analysis and research of overlap functions have been extended to many generalized cases, such as interval-valued and intuitionistic fuzzy overlap functions (IFOFs). However, overlap functions face challenges in the Pythagorean fuzzy (PF) environment. This paper first extends overlap functions to the PF domain by proposing PF overlap functions (PFOFs), discussing their representable forms, and providing a general construction method. It then introduces a new PF similarity measure which addresses issues in existing measures (e.g., the inability to measure the similarity of certain PF numbers) and demonstrates its effectiveness through comparisons with other methods, using several examples in fractional form. Based on the proposed PFOFs and their induced residual implication, new generalized PF rough sets (PFRSs) are constructed, which extend the PFRS models. The relevant properties of their approximation operators are explored, and they are generalized to the dual-domain case. Due to the introduction of hesitation in IF and PF sets, the approximate accuracy of classical rough sets is no longer applicable. Therefore, a new PFRS approximate accuracy is developed which generalizes the approximate accuracy of classical rough sets and remains applicable to the classical case. Finally, three multi-criteria decision-making (MCDM) algorithms based on PF information are proposed, and their effectiveness and rationality are validated through examples, making them more flexible for solving MCDM problems in the PF environment. Full article

This work is devoted to the study and solution of the problems of modeling complex objects on the example of the atmospheric block of the primary oil refining unit, associated with the deficit and fuzziness of the necessary initial information. Since many real technological objects of oil refining and other industries are often characterized by a deficit and fuzziness of the necessary information for their study, modeling, and optimization, this work allows solving an urgent scientific and practical problem. An effective method has been proposed that allows, based on a system approach, expert assessment methods, theories of fuzzy sets, and available information of various natures to develop hybrid models of complex objects in conditions of deficiency and fuzzy initial information. Based on the proposed hybrid method and available statistical and fuzzy information, effective hybrid models of atmospheric block columns of the primary oil refining unit were developed. In this case, statistical models were developed based on experimental and statistical data. With crisp input, mode parameters, and fuzzy output parameters, atmospheric block fuzzy models based on the proposed method, determining the quality of the manufactured products, were developed. Moreover, with the fuzzy input, mode, and output parameters of the atmospheric block columns, linguistic models based on the methods of expert assessments, logical rules of conditional inference, and the proposed method, assessing the quality of the produced gasoline, were developed. The linguistic models developed in Fuzzy Logic Toolbox allow for the assessment of the quality of gasoline from the atmospheric block depending on the content of chloride salts and the mass fraction of sulfur in the raw material. The results obtained using the proposed modeling method show their advantages in comparison with known modeling methods. Full article

Support vector machine (SVM) models apply the Karush–Kuhn–Tucker (KKT-OC) optimality conditions in the ordinary derivative to the primal optimisation problem, which has a major influence on the weights associated with the dissimilarity between the selected support vectors and subsequently on the quality of the model’s predictions. Recognising the capacity of fractional derivatives to provide machine learning models with more memory through more microscopic differentiations, in this paper we generalise KKT-OC based on ordinary derivatives to KKT-OC using fractional derivatives (Frac-KKT-OC). To mitigate the impact of noise and identify support vectors from noise, we apply the Frac-KKT-OC method to the fuzzy intuitionistic version of SVM (IFSVM). The fractional fuzzy intuitionistic SVM model (Frac-IFSVM) is then evaluated on six sets of data from the UCI and used to predict the sentiments embedded in tweets posted by people with diabetes. Taking into account four performance measures (sensitivity, specificity, F-measure, and G-mean), the Frac-IFSVM version outperforms SVM, FSVM, IFSVM, Frac-SVM, and Frac-FSVM. Full article

This paper introduces a robust system designed to effectively manage and enhance the electrical output of a Wind Energy Conversion System (WECS) using a Cascaded Doubly Fed Induction Generator (CDFIG) connected to a power grid. The solution that was investigated is the use of a CDFIG that is based on a variable-speed wind power conversion chain. It comprises the electrical and mechanical connection of two DFIGs through their rotors. The originality of this paper lies in the innovative application of a fuzzy logic controller (FLC) in combination with a CDFIG for a WECS. To demonstrate that this novel configuration enhances control precision and performance in WECSs, we conducted a comparison of three different controllers: a proportional–integral (PI) controller, a fractional PID (FPID) controller, and a fuzzy logic controller (FLC). The results highlight the potential of the proposed system in optimizing power generation and improving overall system stability. It turns out that, according to the first results, the FLC performed optimally in terms of tracking and rejecting disturbances. In terms of peak overshoot for power and torque, the findings indicate that the proposed FLC-based technique (3.8639% and 6.9401%) outperforms that of the FOPID (11.2458% and 10.9654%) and PI controllers (11.4219% and 11.0712%), respectively. These results demonstrate the superior performance of the FLC in reducing overshoot, providing better control stability for both power and torque. In terms of rise time, the findings show that all controllers perform similarly for both power and torque. However, the FLC demonstrates superior performance with a rise time of 0.0016 s for both power and torque, compared to the FOPID (1.9999 s and 1.9999 s) and PI (0.0250 s and 0.0247 s) controllers. This highlights the FLC’s enhanced responsiveness in controlling power and torque. In terms of settling time, all three controllers have almost the same performance of 1.9999. An examination of total harmonic distortion (THD) was also employed to validate the superiority of the FLC. In terms of power quality, the findings prove that a WECS based on an FLC (0.93%) has a smaller total harmonic distortion (THD) compared to that of the FOPID (1.21%) and PI (1.51%) controllers. This system solves the problem by removing the requirement for sliding ring–brush contact. Through the utilization of the MATLAB/Simulink environment, the effectiveness of this control and energy management approach was evaluated, thereby demonstrating its capacity to fulfill the objectives that were set. Full article

Aiming at the problem of system controller performance failure caused by improperly setting the value of each weighting coefficient of the model predictive control (MPC), a fractional-order MPC strategy with Takagi–Sugeno fuzzy optimization (T–SFO MPC) is proposed for a vehicle active suspension system. Firstly, the fractional-order model predictive control framework for active suspension systems is designed based on a 1/4 vehicle model. Then, we analyze the influence of different weighting coefficients on the suspension performance and introduce the Takagi–Sugeno fuzzy optimization theory to adaptively adjust the weighting coefficients of the fractional-order MPC controller. Finally, the system responses of the T–SFO MPC, traditional MPC, linear quadratic regulator (LQR), and passive suspension control are numerically analyzed under various road conditions. Simulation results show that suspension response with the T–SFO MPC is significantly improved compared with passive suspension control, traditional MPC control, and LQR control, and the weight coefficients of the T–SFO MPC can be adaptively adjusted according to the dynamic changes of suspension response. Compared with passive suspension, the root mean square (RMS) value of the vertical acceleration of the T–SFO MPC under various roads decreased by a maximum of 37.97%, and the RMS value of suspension dynamic deflection and tire dynamic load decreased by a maximum of 32.94% and 37.8%, respectively. These results validate that the proposed control method can achieve coordinated optimization of vehicle comfort and handling stability. Full article

The fractional orthotriple fuzzy set (FOFS) model is a recently created extension of fuzzy sets (FS) for coping with ambiguity in DM. The purpose of this study is to define new exponential and Einstein exponential operational (EO) laws for fractional orthotriple fuzzy sets and the aggregation procedures that accompany them. We present the operational laws for exponential and Einstein exponential FOFSs which have crisp numbers as base values and fractional orthotriple fuzzy numbers as exponents (weights). The proposed operations’ qualities and characteristics are then explored. Based on the defined operation laws regulations, various new FOFS aggregation operators, named as fractional orthotriple fuzzy weighted exponential averaging (FOFWEA), fractional orthotriple fuzzy ordered weighted exponential averaging (FOFOWEA), fractional orthotriple fuzzy hybrid weighted averaging (FOFHWEA), fractional orthotriple fuzzy Einstein weighted exponential averaging (FOFEWEA), fractional orthotriple fuzzy Einstein ordered weighted exponential averaging (FOFEOWEA), and fractional orthotriple fuzzy Einstein hybrid weighted exponential averaging (FOFEHWEA) operators are presented. A decision-making algorithm based on the newly defined aggregation operators is proposed and applied to a multicriteria group decision-making (MCGDM) problem related to bank security. Finally, we compare our proposed method with other existing methods. Full article

This study addresses the problem of fractional-order nonlinear containment control of heterogeneous multi-agent systems within a leader–follower framework, focusing on the impact of False Data Injection (FDI) attacks. By employing adaptive mechanisms and fuzzy logic, the suggested method enhances system resilience, ensuring reliable coordination and stability even in the presence of deceptive disturbances. To deal with these uncertainties, our controller makes use of interval type-II (IT2) fuzzy sets, and we create matrix equalities and inequalities to account for the asymmetry of Laplace matrices. Also, we use the Lyapunov functions for the stability analysis of our system. Lastly, we explain the numerical simulations for the effectiveness of our theoretical results, and these simulated examples are used to verify the effectiveness of our approach and designed model. Full article

This paper investigates the existence, uniqueness, and symmetry of solutions for $\Phi$–Atangana–Baleanu fractional differential equations of order $\mu \in (1,2]$ under mixed nonlocal boundary conditions. This is achieved through the use of covariant and contravariant $JS$-contractions within a generalized framework of a sequential extended bipolar parametric metric space. As a consequence, we obtain the results on covariant and contravariant Ćirić, Chatterjea, Kannan, and Reich contractions as corollaries. Additionally, we substantiate our fixed-point findings with specific examples and derive similar results in the setting of sequential extended fuzzy bipolar metric space. Full article

An investigation is conducted in this paper into a performance analysis of fully intuitionistic fuzzy multi-objective multi-item solid fractional transport model (FIF-MMSFTM). It is to be anticipated that the parameters of the conveyance model will be imprecise by virtue of numerous uncontrollable factors. The model under consideration incorporates intuitionistic fuzzy (IF) quantities of shipments, costs and profit coefficients, supplies, demands, and transport. The FIF-MMSFTM that has been devised is transformed into a linear form through a series of operations. The accuracy function and ordering relations of IF sets are then used to reduce the linearized model to a concise multi-objective multi-item solid transportation model (MMSTM). Furthermore, an examination is conducted on several theorems that illustrate the correlation between the FIF-MMSFTM and its corresponding crisp model, which is founded upon linear, hyperbolic, and parabolic membership functions. A numerical example was furnished to showcase the efficacy and feasibility of the suggested methodology. The numerical data acquired indicates that the linear, hyperbolic, and parabolic models require fewer computational resources to achieve the optimal solution. The parabolic model has the greatest number of iterations, in contrast to the hyperbolic model which has the fewest. Additionally, the elapsed run time for the three models is a negligible amount of time: 0.2, 0.15, and 1.37 s, respectively. In conclusion, suggestions for future research are provided. Full article