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A fuzzy approach for the intuitionistic multi-objective linear fractional programming problem using a bisection method

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2025年第2期49卷 1-24页

作者： Kara, Nurdan Kocken, Hale Gonce Akdemir, Hande Gunay Natl Def Univ TR-34334 Istanbul Turkiye Yildiz Tech Univ Dept Math Engn TR-34220 Istanbul Turkiye Giresun Univ Dept Math TR-28200 Giresun Turkiye

In this paper, intuitionistic fuzzy multi-objective linear fractional programming problems (IFMOLFPs) with several fractional criteria, including profit/cost, profit/time, or profitability ratio maximization, are considered. Moreover, all parameters, with the exception of the decision variables, are characterized as triangular intuitionistic fuzzy numbers. The component-wise optimization method is employed to transform IFMOLFP into an equivalent crisp multi-objective linear fractional problem. Then, we use an iterative fuzzy methodology that integrates linear programming with a bisection approach. The proposed approach addresses single-objective and real-life multi-objective organizational planning problems, which are approached using various methods in the literature. It is used for non-linear membership functions in solving these problems. Furthermore, the values obtained using the ranking function are compared. Ultimately, the decision-maker selects the most appropriate solution technique based on the weights of the objective functions.

关键词： Multi-objective linear programming Fractional programming Fuzzy programming Intuitionistic fuzzy number bisection method Membership function

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bisection method for accurate modeling and simulation of fouling in hollow fiber membrane system

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ENVIRONMENTAL SCIENCE AND POLLUTION RESEARCH 2017年第16期24卷 14346-14354页

作者： Liang, Shuang Zhao, Yubo Zhang, Jian Song, Lianfa Shandong Univ Sch Environm Sci & Engn Shandong Prov Key Lab ofWater Pollut Control & Re Jinan 250100 Shandong Peoples R China Texas Tech Univ Dept Civil Environm & Construct Engn Lubbock TX 79409 USA

Accurate description and modeling of fouling on hollow fibers imposes a serious challenge to more effective fouling mitigation and performance optimization of the membrane system. Although the governing equations for membrane fouling can be constructed based on the known theories from membrane filtration and fluid dynamics, they are unsolvable analytically due to the complex spatially and temporally varying nature of fouling on hollow fibers. The current available numerical solutions for the governing equations are either unreliable or inconvenient to use because of the uses of unfounded assumptions or cumbersome calculation methods. This work presented for the first time a rigorous numerical procedure to solve the governing equations for fouling development on hollow fibers. A critical step to achieve the goal is the use of bisection method to determine the transmembrane pressure at the dead end of the fibers. With this procedure, fouling behavior in the hollow fiber membrane system under a given condition can be simulated within a second. The model simulations were well calibrated and verified with the published experimental data from literature. Also presented in the paper were simulations for performances of the hollow fiber membrane system under various operation conditions.

关键词： Hollow fiber membrane Mathematical modeling Numerical solution bisection method Membrane fouling Transmembrane pressure

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A threshold varying bisection method for cost sensitive learning in neural networks

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EXPERT SYSTEMS WITH APPLICATIONS 2008年第2期34卷 1456-1464页

作者： Pendharkar, Parag C. Penn State Univ Sch Business Adm Middletown PA 17057 USA

We propose a bisection method for varying classification threshold value for cost sensitive neural network learning. Using simulated data and different misclassification cost asymmetries, we test the proposed threshold varying bisection method and compare it with the traditional fixed-threshold method based neural network and a probabilistic neural network. The results of our experiments illustrate that the proposed threshold varying bisection method performs better than the traditional fixed-threshold method based neural network. However, when compared to probabilistic neural network, the proposed method works well only when the misclassification cost asymmetries are low. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： neural networks classification bisection method misclassification costs

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Prediction of loading path for tube hydroforming with radial crushing by combining genetic algorithm and bisection method

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART B-JOURNAL OF ENGINEERING MANUFACTURE 2015年第1期229卷 110-121页

作者： Yang, Lianfa Tao, Zhihua He, Yulin Guilin Univ Elect Technol Fac Mech & Elect Engn Guilin Peoples R China

Tube hydroforming with radial crushing is a new tube hydroforming process to manufacture very long components with complex cross sections. A loading path is generally considered a major factor that greatly affects the formability of a component by tube hydroforming. In this study, the tube hydroforming with radial crushing process of a square cross-sectional component was investigated by using the finite element method, and a method to predict the optimal loading path for the tube hydroforming with radial crushing process was developed from the finite element simulation. A multi-object function was first built in terms of the die-filling ability, cross-sectional symmetry, and wall thickness uniformity. Subsequently, a multi-strategy approach, characterized by a genetic algorithm and the bisection method, was developed to predict the optimal loading path. The effectiveness of the prediction method was verified by comparing the formability of components deformed under the optimal and conventional loading paths. Furthermore, the developed multi-strategy approach was demonstrated to have high efficiency when the total calculation times for the multi-strategy approach and for genetic algorithm alone were compared.

关键词： Tube hydroforming loading path genetic algorithm bisection method finite element method

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Improved Muller method and bisection method with,global and asymptotic superlinear convergence of both point and interval for solving nonlinear equations

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APPLIED MATHEMATICS AND COMPUTATION 2005年第2期166卷 299-311页

作者： Wu, XY Nanjing Univ Dept Math State Key Lab Novel Software Technol Nanjing 210093 Peoples R China

A new and improved version of Muller method and bisection method with global and asymptotic superlinear convergence for finding a simple root x* of a nonlinear equation f(x) = 0 in the interval [a, b] is proposed in this paper. The new iteration procedure combines Muller method with bisection method to generate simultaneously two sequences {x(n)} which goes to x* and {[a(n), b(n)]} which encloses x*. The global and superlinear convergence for the both sequences {x(r)} and {b(n) - a(n)} are analyzed. The asymptotic efficiency index of the improved Muller method and bisection method for the both sequences {x(n)} and {b(n) - a(n)} proves to be 1.84 approximately on certain conditions, in the sense of Ostrowski. As a result, the new and improved version of Muller method and bisection method preserve their respective nice property and remove their respective defect. The new version has been tested on a series of elementary functions. The numerical results show that the new version of Muller method and bisection method proposed in this paper is more effective compared with the traditional version for solving nonlinear equations. For the computation of multiple zeros a effective strategy is discussed. (c) 2004 Published by Elsevier Inc.

关键词： Muller's method bisection method nonlinear equations root findings global convergence superlinear convergence convergence of internal diameter iteration method

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An Enhancement of the bisection method Average Performance Preserving Minmax Optimality

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ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE 2021年第1期47卷 1–24页

作者： Oliveira, I. F. D. Takahashi, R. H. C. Fed Univ Valleys Jequitinhonha & Mucuri Inst Sci Engn & Technol R Cruzeiro 1 BR-39803371 Teofilo Otoni MG Brazil Univ Fed Minas Gerais Dept Math Av Pres Antonio Carlos 6627 BR-31270901 Belo Horizonte MG Brazil

We identify a class of root-searching methods that surprisingly outperform the bisection method on the average performance while retaining minmax optimality. The improvement on the average applies for any continuous distributional hypothesis. We also pinpoint one specific method within the class and show that under mild initial conditions it can attain an order of convergence of up to 1.618, i.e., the same as the secant method. Hence, we attain both an improved average performance and an improved order of convergence with no cost on the minmax optimality of the bisection method. Numerical experiments show that, on regular functions, the proposed method requires a number of function evaluations similar to current state-of-the-art methods, about 24% to 37% of the evaluations required by the bisection procedure. In problems with non-regular functions, the proposed method performs significantly better than the state-of-the-art, requiring on average 82% of the total evaluations required for the bisection method, while the other methods were outperformed by bisection. In the worst case, while current state-of-the-art commercial solvers required two to three times the number of function evaluations of bisection, our proposed method remained within the minmax bounds of the bisection method.

关键词： bisection method regula-falsi method root searching zero finding minmax worst-case performance average performance order of convergence

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An Image Encryption Algorithm Based on bisection method and One-Dimensional Piecewise Chaotic Map

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IEEE ACCESS 2021年 9卷 43411-43421页

作者： Elghandour, Aesha N. Salah, Ahmed M. Elmasry, Yasser A. Karawia, Abdelrahman A. Mansoura Univ Fac Sci Dept Math Mansoura 35516 Egypt King Khalid Univ Fac Sci Dept Math Abha 61413 Saudi Arabia

In this article, an image encryption algorithm via bisection method and one-dimensional piecewise chaotic map is proposed. It depends on the permutation-substitution model. Firstly, the pseudo-random sequence is defined using polynomial values at selected points by repeat interval of the bisection method. The plain image is shuffled using this sequence. Bit-wise XOR operation with a mask generated from the Tent chaotic map is applied on shuffled image to increase the protection of the proposed algorithm. Various types of images are tested using the proposed algorithm. The effectiveness of this algorithm is measured using several statistical tests and compared to a set of other algorithms to verify the security and performance of the algorithm. Furthermore, experimental results and Numerical simulations are performed to verify their ability to resist various attacks.

关键词： Encryption Manganese Indexes Ciphers Licenses Image coding Heuristic algorithms bisection method chaos confusion-diffusion model image encryption tent map

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A bisection method for solving distance-based clustering problems globally

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TOP 2024年 1-33页

作者： Kirst, Peter Bajbar, Tomas Merkel, Mario Wageningen Univ & Res Wageningen Netherlands Karlsruhe Inst Technol KIT Karlsruhe Germany

In this article, we consider distance-based clustering problems. In contrast to many approaches, we use the maximum norm instead of the more commonly used Euclidean norm to measure distances. This problem is nonsmooth and non-convex and, thus, difficult to solve to global optimality using standard approaches, which is common in cluster analysis. Therefore, we reformulate this continuous problem in light of graph-theoretical instances which enables us to construct a bisection algorithm converging to the globally minimal value of the original clustering problem by establishing valid upper and lower bounding procedures. Our numerical results indicate that our method performs well on data sets exhibiting clear cluster-pattern structure even for bigger data instances while still guaranteeing the global optimality of the computed solution. We compare our approach with the classical k-means algorithm and also discuss the limits and challenges of the proposed procedure.

关键词： Clustering problem Global optimization Maximal clique bisection method k-means problem

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Generalization of the bisection method and its applications in nonlinear equations

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ADVANCES IN CONTINUOUS AND DISCRETE MODELS 2023年第1期2023卷 1-12页

作者： Gulshan, Ghazala Budak, Huseyin Hussain, Rashida Sadiq, Asad Mirpur Univ Sci & Technol MUST Fac Sci Dept Math Mirpur 10250 AJK Pakistan Duzce Univ Fac Sci & Arts Dept Math Duzce Turkiye

The aim of the current work is to generalize the well-known bisection method using quantum calculus approach. The results for different values of quantum parameter q are analyzed, and the rate of convergence for each q ? (0,1) is also determined. Some physical problems in engineering are resolved using the QBM technique for various values of the quantum parameter q up to three iterations to examine the validity of the method. Furthermore, it is proven that QBM is always convergent and that for each interval there exists q ? (0,1) for which the first approximation of root coincides with the precise solution of the problem.

关键词： Nonlinear equations bisection method

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Complexity of the bisection method

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THEORETICAL COMPUTER SCIENCE 2007年第2期382卷 131-138页

作者： Gutierrez, Claudio Gutierrez, Flavio Rivara, Maria-Cecilia Univ Chile Dept Comp Sci Santiago Chile Univ Valparaiso Valparaiso Chile

The bisection method is the consecutive bisection of a triangle by the median of the longest side. In this paper we prove a subexponential asymptotic upper bound for the number of similarity classes of triangles generated on a mesh obtained by iterative bisection. which previously was known only to be finite. The relevant parameter is gamma/sigma, where gamma is the biggest and a is the smallest angle of the triangle. We get this result by introducing a taxonomy of triangles that precisely captures the behaviour of the bisection method. We also prove that the number of directions on the plane given by the sides of the triangles generated is finite. Additionally, we give purely geometrical and intuitive proofs of classical results for the bisection method. (c) 2007 Elsevier B.V. All rights reserved.

关键词： bisection method longest edge bisection triangulation

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