Nonlinear Fuzzy Research Articles

On Impulsive Nonlocal Nonlinear Fuzzy Integro-Differential Equations in Banach Space

The aim of this article is to investigate the existence, uniqueness and other qualitative properties of the solution of first-order nonlocal impulsive nonlinear fuzzy integro-differential equations in Banach space by using the concept of fuzzy numbers whose values are normal, upper semicontinuous, compact, and convex. The result is attained by utilizing a modified version of the Banach contraction principle. We offer an example as an application of the results.

Impulsive Formation Tracking of Nonlinear Fuzzy Multiagent Systems With Input Saturation Constraints

Impulsive Formation Tracking of Nonlinear Fuzzy Multiagent Systems With Input Saturation Constraints

Application of the Homotopy Analysis Method in Solving Fuzzy Nonlinear Integral Equations for Birthrate

Application of the Homotopy Analysis Method in Solving Fuzzy Nonlinear Integral Equations for Birthrate

Delivering Goods Sustainably: A Fuzzy Nonlinear Multi-Objective Programming Approach for E-Commerce Logistics in Taiwan

With the booming development of e-commerce, the importance of controlling carbon emissions has become increasingly prominent in Taiwan. This study explores the trade-offs among time, cost, quality, and carbon emissions (TCQCE) in e-commerce logistics. Will carbon emissions mitigation lead to decreased logistics efficiency and increased costs? This article differs from other studies that use precise numbers and linear model situations. This study adopts fuzzy theory, nonlinear methods, and multi-objective programming models closer to the actual situation to study the decision-making between delayed logistics delivery times and reduced carbon emissions. This article also uses Project D as a case to enhance readers’ understanding of decision-making methods in real-life e-commerce logistics cases. The results show that extended delivery times could significantly reduce carbon emissions, ranging from 5259.31 to 419,199.60 tons, and reduce delivery quality under the 90.00% threshold and even under 75.25%. Extending delivery times is a viable business strategy, particularly by extending delivery to push carbon reduction policies to minimize environmental impact. However, consumer acceptance is crucial, as consumers willing to embrace longer wait times can significantly contribute to emission mitigation and support businesses committed to sustainability. This research uses a fuzzy nonlinear multi-objective programming model (FNMOPM) to contribute novel time management to mitigate carbon emissions. Moreover, this study uses a fuzzy and nonlinear approach to fill in the gaps of previous research to balance the efficiency and carbon emission mitigation goals of ESG (environmental, social, and governance) principles. The framework presented in this article solves the complex trade-off situations in the TCQCE issues. This article provides practical, actionable guidance for decision-making regarding sustainable e-commerce logistics, instilling confidence in its implementation.

Multigranulation variable-scale fuzzy neighborhood measures and corresponding Choquet-like integrals for feature selection

Choquet-like integrals, a nonlinear fuzzy aggregation function, are diffusely applied in several real problems. However, the corresponding fuzzy measures in them are provided by human intervention and not by data-driven methods. As an effective knowledge representation tool, rough set models in different approximation spaces are established for data processing. Particularly, the multigranulation fuzzy β-covering approximation space has been concerned with only a single scale β∈(0,1]. However, different granulation structures should have different scales. Therefore, establishing a multigranulation approximation space with a variable scale by inducing fuzzy measures through data-driven methods and using corresponding Choquet-like integrals in practical problems is a significant challenge. To address this challenge, the notion of multigranulation variable-scale fuzzy Θ-covering group approximation space is presented here, as well as multigranulation variable-scale fuzzy neighborhood measures in it. Furthermore, Choquet-like integrals with the presented measures are constructed to solve the issue of feature selection (i.e., attribute reduction) under the new approximation spaces. Firstly, the concept of multigranulation variable-scale fuzzy Θ-covering group approximation space is presented, where different fuzzy β-coverings have different scales β∈Θ. Moreover, multigranulation variable-scale fuzzy neighborhood measures in it, as fuzzy measures, are presented. Subsequently, Choquet-like integrals with multigranulation variable-scale fuzzy neighborhood measures are constructed. A novel attribute reduction method under Choquet-like integrals with multigranulation variable-scale fuzzy neighborhood measures is proposed for any decision information table. Finally, the presented method is selected for solving problems of classification and diagnosis of rolling bearing faults. Several public data sets are used to demonstrate the effectiveness and feasibility of the presented methods mentioned above.

Computational Solution and Analysis of Fuzzy Nonlinear HIV Infection Model via New Multistage Fuzzy Variational Iteration Method

Computational Solution and Analysis of Fuzzy Nonlinear HIV Infection Model via New Multistage Fuzzy Variational Iteration Method

SOLVING FUZZY NONLINEAR PROGRAMMING PROBLEMS WITH EXTERIOR PENALTY FUZZY VALUED FUNCTIONS

In this article, we explore the exterior penalty fuzzy valued function method for Fuzzy Nonlinear Programming Problems (FNLPP). We present methods of penalty fuzzy valued function for solving constrained optimization problems by converting to unconstrained optimization problems. Triangular fuzzy numbers are used to represent the problem’s decision variables and coefficients. Using a new fuzzy arithmetic and fuzzy ranking method on the parametric form of triangular fuzzy numbers, the optimal solution of the FNLPP is found by applying the exterior penalty fuzzy valued function method without changing to its equivalent crisp form. We present a numerical example of the suggested method and compare the results to those produced by existing methods

A Pivotal Operation on Triangular Fuzzy Number for Solving Fuzzy Nonlinear Programming Problems

A Pivotal Operation on Triangular Fuzzy Number for Solving Fuzzy Nonlinear Programming Problems

Method of directly defining the inverse mapping for nonlinear fuzzy heat-like partial differential equations

Natural phenomena or physical systems can be described using Partial Differential Equations (PDEs), such as wave equations, heat equations, Poisson’s equation, and so on. Consequently, investigations of PDEs have become one of the key areas of modern mathematical analyses, attracting a lot of attention. Many authors have recently expressed an interest in researching the theoretical framework of fuzzy Initial Value Problems (IVPs). The Method of Directly Defining the inverse Mapping (MDDiM) was effectively employed in this research to obtain the second-order approximate fuzzy solution of heatlike equations in one and two dimensions, and the results were compared with exact solutions. In each illustrated example, all the results achieved using Maple 16 were graphically depicted. This is the first time MDDiM was utilized to solve nonlinear Fuzzy Partial Differential Equations (FPDEs).

Robust H2 nonlinear fuzzy decentralized control design for a VSC‐HVDC link

SummaryA Robust Nonlinear Fuzzy Decentralized Controller ( RNFDC) is proposed to improve the overall robustness and tracking ability of a VSC‐HVDC link. The studied system is considered as composed by two overlapping nonlinear subsystems. The nonlinear interaction between the two subsystems is treated as a disturbance rejection problem by fuzzy control techniques. First, the Takagi Sugeno (TS) fuzzy model is adopted for fuzzy modeling of the uncertain nonlinear system. Next, new stability conditions for a generalized class of uncertain HVDC systems are derived from robust control techniques based on Linear Matrix Inequalities (LMIs). The design method employs the so‐called Parallel Distributed Compensation (PDC) to obtain RNFDC gains based on LMIs.The efficiency and robustness of the proposed controllers are analytically proven and tested through validation simulations. The main contributions of this paper are: (i) resilience: in case of failure of one converter or loss of measures or controls, the control of the other converter is not affected; (ii) robustness is improved in order to provide good responses in case of network variations and HVDC line parameters changes; (iii) fuzzy techniques are adopted to handle nonlinearities and changes of operating conditions. The proposed RNFDC is compared with Fuzzy H Decentralized State Feedback Control ( NFDC) and Linear Decentralized Control ( LDC) in simulation to illustrate the control synthesis and its effectiveness.

On the Initial Value Problem for Fuzzy Nonlinear Fractional Differential Equations

In this paper, we study the existence result of solutions for fuzzy nonlinear fractional differential equations involving Caputo differentiability of an arbitrary order 0 < q < 1. As application, an example is included to show the applicability of our result.

Solving Fuzzy Nonlinear Optimization Problems Using Null Set Concept

Solving Fuzzy Nonlinear Optimization Problems Using Null Set Concept

Retracted: Robust Adaptive Control for a Class of T-S Fuzzy Nonlinear Systems with Discontinuous Multiple Uncertainties and Abruptly Changing Actuator Faults

Retracted: Robust Adaptive Control for a Class of T-S Fuzzy Nonlinear Systems with Discontinuous Multiple Uncertainties and Abruptly Changing Actuator Faults

The Road to Sustainable Logistics: Using the Fuzzy Nonlinear Multi-Objective Optimization Model to Build Photovoltaic Stations in Taiwan’s Logistics Centers

In Taiwan, numerous company logistics centers have embraced installing solar photovoltaic power stations (SPPSs) on their rooftops. The primary objective of this study is to expedite the generation of green electricity for sale, bolstering the logistics center’s income and enhancing its environmental, social, and governance (ESG) profile. How can we secure solar photovoltaic power station (SPPS) projects with expedited construction timelines, reduced investment costs, and heightened quality aligned with the long-term ESG objectives? The study applies the critical path method (CPM) to determine the item’s path. Next, the mothed leverages Zimmermann’s mathematical models for nonlinear multi-objectives and Yager’s fuzzy sets to enhance project efficiency, minimizing completion time and cost while maximizing the quality ratio. Subsequently, the project uses Liou and Wang’s defuzzification values and incorporates Dong’s fuzzy to accelerate calculations. In this case, Project HP’s item J, the construction time is reduced from 24.3 to 3.2 days, ensuring that construction quality meets an 85% standard. Item J necessitates expanding the fuzzy cost interval (4549.90, 15,416.65, 26,283.41) (it refers to a scope of possible costs). It becomes evident that construction time plays a pivotal role in controlling costs. For Project HP’s item H, the unit time quality decision ranges from TWD 238,000 to 240,000, to turn into a cost interval of TWD 215,100, 239,000, and 262,900. Consequently, cost transformation transitions from an active to a more passive role, with quality and construction time becoming the driving components. This study uses a fuzzy nonlinear multi-objective model to guide the decision analysis of SPPSs within logistics centers. This strategy enables decision-makers to streamline logistics center operations, ensuring time, cost, and quality (TCQ) alignment during SPPS installation, thereby advancing ESG sustainability goals.

Observer-Based Finite-Time Event-Triggered Control for Stochastic T-S Fuzzy Nonlinear Systems with Time-Varying Delay

Observer-Based Finite-Time Event-Triggered Control for Stochastic T-S Fuzzy Nonlinear Systems with Time-Varying Delay

Developing the Third Order Linear and Nonlinear Fuzzy Ordinary Differential Equations in Hilbert Space by the Extension Principle.

In this study, a third nonlinear fuzzy ordinary differential equation is defined and established in Hilbert space using extension principle. The results obtained gives clear distinction between this work and the existing ones in the literature an example is formulated which shows that a closed subset of a Hilbert space is a Hilbert Space. It is recommended that future study should consider the development of system of third order linear and nonlinear fuzzy ordinary differential equations in Hilbert space by the extension principle.

Probabilistic and Fuzzy Nonlinear Discontinuous Aeroelastic Analysis of In-plane FG Panels in Supersonic Flow with Mechanical and Thermal In-plane Loadings

This paper is concerned with the uncertain discontinuous nonlinear aeroelastic behavior of in-plane bi-directional functionally graded (FG) metal nanocomposite panels. The panels are subjected to supersonic flow and in-plane mechanical and thermal loadings. This type of FG structures is manufactured using additive manufacturing technologies which might lead to uncertain properties of the manufactured parts due to manufacturing uncertainties, modeling uncertainties in the mathematical and physical formulations used to predict their properties, or uncertainties in the constituent materials properties themselves. These sources of uncertainties might be known with defined probability density functions or defined with uncertain intervals only (fuzzy). Therefore, the mechanical and thermal properties of the nanocomposite material are modeled as uncertain random variables or random fields with known probability distribution function (pdf) or uncertain fuzzy variables or fields with given intervals. The random fields are modeled using the Karhunen–Loève expansion (KLE), and the uncertain output variables are modeled using the Hermite polynomial chaos expansion method (HPCE). The effects of the material properties uncertainties type (fuzzy vs. probabilistic), the cross-correlation between the thermal and mechanical properties, the random fields properties (correlation length, stationary vs. non-stationary, etc.) on the dynamic stability thresholds and the nonlinear limit cycle oscillation are studied.

Application of a Modified Gauss Elimination Technique for Separable Fuzzy Nonlinear Programming Problems

Application of a Modified Gauss Elimination Technique for Separable Fuzzy Nonlinear Programming Problems

Autonomous Trajectory Tracking and Collision Avoidance Design for Unmanned Surface Vessels: A Nonlinear Fuzzy Approach

An intelligent fuzzy-based control system that consists of several subsystems—a fuzzy collision evaluator, a fuzzy collision avoidance acting timing indicator, a collision-free trajectory generator, and a nonlinear adaptive fuzzy robust control law—is proposed for the collision-free condition and trajectory tracking of unmanned surface vessels (USVs). For the purpose of ensuring that controlled USVs are capable of executing tasks in an actual ocean environment that is full of randomly encountered ships under collision-free conditions, the real-time decision making and the desired trajectory arrangements of this proposed control system were developed by following the “Convention on the International Regulations for Preventing Collisions at Sea” (COLREGs). From the simulation results, several promising properties were demonstrated: (1) robustness with respect to modeling uncertainties and ocean environmental disturbances, (2) a precise trajectory tracking ability, and (3) sailing collision avoidance was shown by this proposed system for controlled USVs.

Solving First-Order Nonlinear Fuzzy Initial Value Problems Using Two-Step Block Method with Presence of Higher Derivatives

Fuzzy differential equation models are suitable where uncertainty exists for real-world phenomena. Numerical techniques are used to provide an approximate solution to these models in the absence of an exact solution. However, existing studies that have developed numerical techniques for solving FIVPs possess an absolute error accuracy that could be improved. This is as a result of the low order and non-self-starting properties of the developed numerical techniques by previous studies. For this reason, this study, develops an Obrechkoff-type two-step implicit block method with the presence of second and third derivative for the numerical solution of first-order nonlinear fuzzy initial value problems. The convergence properties for the proposed block method are described in detail. Then the proposed method is adopted to solve first-order nonlinear fuzzy initial value problems with triangular and trapezoidal fuzzy numbers. The obtained results indicates that the proposed method effectively solves first-order nonlinear fuzzy initial value problems with better accuracy.