Article
Operations Research & Management Science
Manuel Arana-Jimenez
Summary: This paper proposes a new method for obtaining fuzzy Pareto solutions of a fully fuzzy multiobjective linear programming problem. By combining triangular fuzzy numbers and variables with fuzzy partial orders and fuzzy arithmetic, algorithms are provided to generate fuzzy Pareto solutions, including compromise fuzzy Pareto solutions, which is a novelty in this field.
RAIRO-OPERATIONS RESEARCH
(2022)
Article
Management
Maria Joao Alves, Carlos Henggeler Antunes
Summary: In this paper, we study linear bilevel programming problems with multiple objective functions at the lower level. We propose an exact method and a heuristic procedure to compute the optimistic optimal solution. While the heuristic procedure can only find a local optimum and does not guarantee the global optimal solution, it has been shown to be effective in problems where obtaining the global optimum within a reasonable timeframe is difficult. A computational study is conducted to evaluate the performance of the exact method and the heuristic procedure, comparing them with other methods proposed by different authors. Our approach reveals interesting results in problems with few upper-level variables.
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
(2022)
Article
Operations Research & Management Science
Fatima Bellahcene, Philippe Marthon
Summary: The proposed approach is applicable to multiobjective stochastic linear programming problems with continuous random variables. The minimum-risk criterion and the Chebyshev problem are utilized to find the optimal or epsilon optimal solution through an algorithm combining the bisection method and goal achievement probabilities. An illustrative example is provided to clarify the developed theory.
OPERATIONAL RESEARCH
(2021)
Article
Operations Research & Management Science
Ramzi Kasri, Fatima Bellahcene
Summary: This paper presents an approach for solving multiobjective stochastic linear programming problems using a combination of multiobjective methods and nonconvex techniques. The problem is first transformed into a deterministic multiobjective problem and reduced to a mono-objective quadratic problem through a weighting method. The final problem is then solved using DC programming and algorithm.
RAIRO-OPERATIONS RESEARCH
(2021)
Article
Engineering, Multidisciplinary
E. Fathy, A. E. Hassanien
Summary: This paper demonstrates the effectiveness of the fuzzy harmonic mean technique in solving fully fuzzy multilevel multiobjective linear programming problems by converting the problem into crisp multiobjective linear programming subproblems and aggregating the objectives using the harmonic mean technique to obtain a fuzzy compromise solution.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Mathematics
Qing Wang, Yi Huang, Shiming Kong, Xinqiang Ma, Youyuan Liu, S. K. Das, S. A. Edalatpanah
Summary: Linear programming is commonly used in operational research, but may face challenges in obtaining optimal solutions. To address this, neutrosophic set theory is introduced to handle real-world scenarios, specifically proposing a method for solving multiobjective LP problems with triangular neutrosophic numbers.
JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Md. Musa Miah, Ali AlArjani, Abdur Rashid, Aminur Rahman Khan, Md. Sharif Uddin, El-Awad Attia
Summary: Considering the uncertainty in transporting goods, the paper proposes mathematical models using fuzzy non-linear membership functions to optimize multi-objective transportation problems. The models consider the DM's selection of confidence level and provide a compromise solution along with the satisfaction level. Based on experimental results, the hyperbolic membership function shows stability and 100% satisfaction in many instances compared to exponential and linear functions.
Article
Engineering, Multidisciplinary
E. Fathy
Summary: Uncertainty linear programming (ULP) has been a significant subject of study and interest in recent decades. This paper focuses on the ULP problem where all parameters and/or decision variables are expressed as interval-valued intuitionistic fuzzy (IVIF) numbers. Two methods, IVIFLP and FIVIFLP, are proposed to solve the LP problem with IVIF parameters and variables. The methods involve reducing the problems into smaller crisp linear problems (CLPs) and applying reduction techniques based on linear combinations between variables. The proposed methods are illustrated numerically and demonstrate improvements over existing methods for solving transportation problems in an IVIF environment.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Mathematics, Applied
Muhammad Akraml, Inayat Ullah, Tofigh Allahviranloo
Summary: In this study, we identified the inadequacy of existing arithmetic operations for trapezoidal fuzzy numbers and proposed new operations. We also found drawbacks in the existing Simplex method for solving fully fuzzy linear programming problems and developed a new strategy. Our results were compared with existing methods.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Computer Science, Artificial Intelligence
Xue Deng, Chuangjie Chen
Summary: In this paper, a new approach is proposed to assist investors in making rational portfolio selections without time series data. The problem is formulated as a multi-criteria decision making problem using intuitionistic fuzzy sets, and the TOPSIS method is modified to better balance returns and risks. Several novel linear programming models are introduced to allocate investment ratios according to investors' demands. Compared to traditional methods, the new approach demonstrates greater effectiveness and flexibility in providing appropriate investment strategies based on investors' preferences and demands.
EGYPTIAN INFORMATICS JOURNAL
(2022)
Article
Computer Science, Artificial Intelligence
Sapan Kumar Das
Summary: This article addresses a fully fuzzy triangular linear fractional programming problem with parameters and decision variables characterized by triangular fuzzy numbers. A new concept is proposed to reduce computational complexity without sacrificing effectiveness. Mathematical models are used to evaluate the legitimacy, usefulness, and applicability of the method, showing that the novel strategies are superior to current techniques.
COMPLEX & INTELLIGENT SYSTEMS
(2022)
Article
Mathematics, Applied
Abdullah Ali H. Ahmadini, Firoz Ahmad
Summary: This paper explores intuitionistic fuzzy multiobjective linear programming problems under neutrosophic uncertainty, focusing on neutral optimization techniques and different membership functions for marginal evaluation. The developed technique is implemented on numerical problems, showcasing its validity and applicability, with a comparative study presented alongside conclusions and future research directions.
Article
Engineering, Aerospace
Yufei Rong, Qin Sun, Kun Ma, Yazhou Yang, Ke Liang
Summary: In this paper, a novel method is proposed to transfer aerodynamic loads using distance-based weight functions. The method achieves optimal load transfer by adjusting the distance factor and weight functions. It shows great potential in the numerical analysis of aeroelastic behaviors for air-vehicle.
AEROSPACE SCIENCE AND TECHNOLOGY
(2022)
Article
Computer Science, Artificial Intelligence
Sumati Mahajan, S. K. Gupta
Summary: This study delves into the relationship between intuitionistic fuzzy set theory and multiobjective nonlinear programming problems, obtaining optimal solutions under different membership/non-membership functions through comparative research using optimistic, pessimistic and mixed approaches. The article also redefines the pessimistic and mixed perspectives, establishing the spirit of intuitionistic fuzzy numbers.
EXPERT SYSTEMS WITH APPLICATIONS
(2021)
Article
Computer Science, Artificial Intelligence
Hassan Ali, Jingwen Zhang
Summary: The selection of potential suppliers in the manufacturing industries has become a major challenge due to the spread of covid-19 and natural calamities. This study proposes a holistic model that combines economic, environmental, and transportation risk factors for global green supplier selection and order allocation in the textile industry. The proposed methodology effectively manages data uncertainties and can assist in overcoming current shortcomings and developing long-term relationships with buyers.
EXPERT SYSTEMS WITH APPLICATIONS
(2023)
Article
Mathematics, Applied
Junfeng Cao, Ke Chen, Huan Han
Summary: This paper proposes a two-stage image segmentation model based on structure tensor and fractional-order regularization. In the first stage, fractional-order regularization is used to approximate the Hausdorff measure of the MS model. The solution is found using the ADI scheme. In the second stage, thresholding is used for target segmentation. The proposed model demonstrates superior performance compared to state-of-the-art methods.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Dylan J. Oliver, Ian W. Turner, Elliot J. Carr
Summary: This paper discusses a projection-based framework for numerical computation of advection-diffusion-reaction (ADR) equations in heterogeneous media with multiple layers or complex geometric structures. By obtaining approximate solutions on a coarse grid and reconstructing solutions on a fine grid, the computational cost is significantly reduced while accurately approximating complex solutions.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Nathan V. Roberts, Sean T. Miller, Stephen D. Bond, Eric C. Cyr
Summary: In this study, the time-marching discontinuous Petrov-Galerkin (DPG) method is applied to the Vlasov equation for the first time, using backward Euler for a Vlasov-Poisson discretization. Adaptive mesh refinement is demonstrated on two problems: the two-stream instability problem and a cold diode problem.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Yizhi Sun, Zhilin Sun
Summary: This work investigates the convexity of a specific class of positive definite probability measures and demonstrates the preservation of convexity under multiplication and intertwining product. The study reveals that any integrable function on an interval with a polynomial expansion of fast absolute convergence can be decomposed into a pair of positive convex interval probabilities, simplifying the study of interval distributions and discontinuous probabilistic Galerkin schemes.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Bhagwan Singh, Komal Jangid, Santwana Mukhopadhyay
Summary: This paper examines the prediction of bending characteristics of nanoscale materials using the Moore-Gibson-Thompson thermoelasticity theory in conjunction with the nonlocal strain gradient theory. The study finds that the stiffness of the materials can be affected by nonlocal and length-scale parameters, and the aspect ratios of the beam structure play a significant role in bending simulations.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Guoliang Wang, Bo Zheng, Yueqiang Shang
Summary: This paper presents and analyzes a parallel finite element post-processing algorithm for the simulation of Stokes equations with a nonlinear damping term, which integrates the algorithmic advantages of the two-level approach, the partition of unity method, and the post-processing technique. The algorithm generates a global continuous approximate solution using the partition of unity method and improves the smoothness of the solution by adding an extra coarse grid correction step. It has good parallel performance and is validated through theoretical error estimates and numerical test examples.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Hao Xu, Zeng-Qi Wang
Summary: Fluid flow control problems are crucial in industrial applications, and solving the optimal control of Navier-Stokes equations is challenging. By using Oseen's approximation and matrix splitting preconditioners, we can efficiently solve the linear systems and improve convergence.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Zhengya Yang, Xuejuan Chen, Yanping Chen, Jing Wang
Summary: This paper focuses on the high-order stable numerical solutions of the time-space fractional diffusion equation. The Fourier spectral method is used for spatial discretization and the Spectral Deferred Correction (SDC) method is used for numerical solutions in time. As a result, a high-precision numerical discretization scheme for solving the fractional diffusion equation is obtained, and the convergence and stability of the scheme are proved. Several numerical examples are presented to demonstrate the effectiveness and feasibility of the proposed numerical scheme.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)