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linear fractional programming problem with max-Hamacher FRI

IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE 2018年第A2期42卷 693-705页

作者： Aliannezhadi, Samaneh Molai, Ali Abbasi Damghan Univ Sch Math & Comp Sci POB 36715-364 Damghan Iran

In this paper, the linear fractional programming problem subject to a system of fuzzy relation inequalities (FRI) with the max-Hamacher composition operator is studied. First, the structure of its feasible domain is investigated, and its feasible solution set determined. Then, some sufficient conditions are given that under them, some of the optimal components of the problem are directly determined. The optimal solution of the linear fractional programming problem might not be any of the minimal solutions. However, in the process of obtaining the optimal solution, we need to compute the minimal solutions. Therefore, some reductions are presented that under them, we can compute the minimal solutions fast. The original problem can be transformed into some traditional linear fractional programming subproblems and eventually optimized in a small search space. Finally, an algorithm is designed to solve the problem based on the above reductions. An application and some numerical examples are provided to illustrate the procedure.

关键词： linear fractional programming problem Fuzzy relation inequality Max-Hamacher composition Fuzzy optimization

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Solving the linear fractional programming problem in a fuzzy environment: Numerical approach

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APPLIED MATHEMATICAL MODELLING 2016年第11-12期40卷 6148-6164页

作者： Chinnadurai, Veeramani Muthukumar, Sumathi PSG Coll Technol Dept Appl Math & Computat Sci Coimbatore Tamil Nadu India PSG Coll Technol Dept Math Coimbatore Tamil Nadu India

The fuzzy linear fractional programming problem is an important planning tool in different areas such as engineering, business, finance, and economics. In this study, we propose the use of the (alpha, r) acceptable optimal value for a linear fractional programming problem with fuzzy coefficients and fuzzy decision variables, as well as developing a method for computing them. To obtain acceptable (alpha, r) optimal values, we take an alpha-cut on the objective function and r-cut on the constraints. We then formulate an equivalent bi-objective linear fractional programming problem to calculate the upper and lower bounds of the fully fuzzy LFP problem. Using the upper and lower bounds obtained, we construct the membership functions of the optimal values numerically. We illustrate the proposed procedure using numerical and real life examples. (C) 2016 Elsevier Inc. All rights reserved.

关键词： Bi-objective linear fractional programming problem linear fractional programming problem linear programming problem Triangular fuzzy number

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Reducing the search space of a linear fractional programming problem under fuzzy relational equations with max-Archimedean t-norm composition

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FUZZY SETS AND SYSTEMS 2008年第24期159卷 3347-3359页

作者： Wu, Yan-Kuen Guu, Sy-Ming Liu, Julie Yu-Chih Vanung Univ Dept Ind Management Tao Yuan 320 Taiwan Yuan Ze Univ Dept Business Adm Tao Yuan 320 Taiwan Yuan Ze Univ Dept Informat Management Tao Yuan 320 Taiwan

Prior studies have demonstrated that one of the minimal solutions of a fuzzy relational equation with the max-Archimedean t-norm composition is an optimal solution of a linear objective function with positive coefficients. However, this property cannot be adopted to optimize the problem of a linear fractional objective function. This study presents an efficient method to optimize such a linear fractional programming problem. First, some theoretical results are developed based on the properties of max-Archimedean t-norm composition. The result is used to reduce the feasible domain. The problem can thus be simplified and converted into a traditional linear fractional programming problem, and eventually optimized in a small search space. A numerical example is provided to illustrate the procedure. (C) 2008 Elsevier B.V. All rights reserved.

关键词： linear fractional programming problem Fuzzy relational equations Max-Archimedean t-norm composition

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A proposed model for solving fuzzy linear fractional programming problem: Numerical Point of View

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JOURNAL OF COMPUTATIONAL SCIENCE 2018年 25卷 367-375页

作者： Das, Sapan Kumar Edalatpanah, S. A. Mandal, T. Natl Inst Technol Jamshedpur Dept Math Jamshedpur Jharkhand India Ayandegan Inst Higher Educ Dept Appl Math Tonekabon Iran

In solving real life fractional programming problem we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To overcome these limitations, the fuzzy logic approach is applied to this problem. In this paper, we propose the concepts of simple ranking approach between two triangular fuzzy numbers. We also formulate an equivalent tri-objective linear fractional programming problem to calculate the upper, middle and lower bounds of the Fuzzy linear fractional programming (FLFP) problem. Furthermore, from the obtained upper, middle and lower bounds, we construct the optimal values numerically. Finally, the effectiveness of the proposed procedure is illustrated through numerical and real life examples. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Triangular fuzzy number linear fractional programming problem Multi objective programming Ranking function

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An Application of Fully Intuitionistic Fuzzy Multi-objective linear fractional programming problem in E-education System

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INTERNATIONAL JOURNAL OF FUZZY SYSTEMS 2022年第8期24卷 3544-3563页

作者： Malik, Manisha Gupta, S. K. Indian Inst Technol Roorkee Dept Math Roorkee 247667 Uttar Pradesh India

This article addresses a special class of non-linear programming problems, viz., linear fractional programming problems having multiple objectives. In solving the real-life linear fractional optimization problems, the ambiguity and hesitation in the decision are inherent and ever-present, therefore, it is perfectly viable to formulate and solve these optimization models using the intuitionistic fuzzy environment. The purpose of this study is to propose a simple and computationally efficient approach to obtain the solution of multiple objective linear fractional programming problems having all the decision variables and parameters expressed in terms of triangular intuitionistic fuzzy numbers. The proposed solution algorithm is primarily based on the goal programming approach, fuzzy-based linearization technique, and a membership function strategy. The original linear fractional programming problem is first converted to its equivalent deterministic/crisp multi-objective linear fractional optimization problem using the weighted goal programming methodology along with the linear membership technique to resolve the intuitionistic fuzzy constraints into the crisp one. Finally, the variable transformation technique for the under- and over-deviational variables of the goal programming model is employed to linearize all the fractions involved in the problem so as to convert the original problem to an equivalent linear optimization problem. Further, this linear programming problem can be solved using any available commercial packages. Moreover, a numerical illustration is provided to demonstrate the steps of the proposed technique followed by the analysis and solution of an E-education set-up problem. The discussion and comparisons of the practical case establish the relevancy and usefulness of the proposed model.

关键词： Multi-objective programming Triangular intuitionistic fuzzy number Goal programming linear fractional programming problem Fuzzy mathematical programming

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OPTIMIZING A linear fractional programming problem WITH MAX-PRODUCT FUZZY RELATIONAL EQUATION CONSTRAINTS

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JOURNAL OF INDUSTRIAL AND PRODUCTION ENGINEERING 2008年第4期25卷 314-325页

作者： Wu, Yan-Kuen Vanung Univ Dept Ind Management 1 Van Nung Rd Taoyuan 320 Taiwan

This study investigates a new framework that a linear fractional programming problem is subject to fuzzy relational equations with max-product composition. Three folds are presented. First, some theoretical results are developed to optimize such a linear fractional programming problem based on the properties of max-product composition. Second, the results are adopted to reduce the feasible domain. The problem can thus be simplified and converted into a traditional linear fractional programming problem. Third, a procedure is presented to solve this optimization problem without looking for all potential minimal solutions. Numerical examples are provided to illustrate the procedure.

关键词： linear fractional programming problem fuzzy relational equations max-product composition

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The Optimal Conditions of the linear fractional programming problem with Constraint

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Chinese Quarterly Journal of Mathematics 2006年第4期21卷 553-556页

作者： SUN Jian-she YE Liu-qing Department of Mathematics Jiaozuo Teacher＇s College Jiaozuo 454150 China Department of Math-ematics Zhengzhou University Zhengzhou 450052 China

In this article,the authors discuss the optimal conditions of the linear fractionalprogramming problem and prove that a locally optional solution is a globally optional solution and the locally optimal solution can be... 详细信息

关键词： linear fractional programming problem pseudo-convex function optimal solution constraint

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A solution programming approaches on the multi-objective capacitated fractional transportation problem

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INTERNATIONAL JOURNAL OF SYSTEM ASSURANCE ENGINEERING AND MANAGEMENT 2025年 1-22页

作者： Ali, Wajahat Sadia, Sheema Ahmad, Firoz Javaid, Shakeel Abidi, Naseem Aligarh Muslim Univ Dept Stat & Operat Res Aligarh 202002 India Indian Inst Sci Bangalore Karnataka India Skyline Univ Coll Sharjah U Arab Emirates

In this study, we developed a mathematical model of a multi-objective capacitated fractional transportation problem (MOCFTP) with mixed constraints formulated as a multi-objective linear fractional programming problem (MOLFPP). Two advanced methodologies were applied to solve this mathematical model: the proposed weighted goal programming method (PWGPM) and the proposed neutrosophic goal programming approach (PNGPA). The PWGPM model minimizes deviations from predefined goals for each objective while adhering to linear constraints. In contrast, the PNGPA leverages neutrosophic optimization, integrating truth, falsity, and indeterminacy to address uncertainty in decision-making. The mathematical model of MOCFTP aims to optimize transportation schedules by minimizing total cost, total time, and damage cost while satisfying supply and demand constraints. A numerical example is provided to demonstrate the practicality and effectiveness of the mathematical model of MOCFTP. The compromise optimal solution for the proposed problem is obtained using the Pulp optimization library in Python. The findings indicate that the PNGPA outperforms others regarding solutions, and it offers a robust framework for complex, real-world transportation scenarios potentially beneficial for various logistics applications.

关键词： linear fractional programming problem fractional transportation problem Weighted goal programming approach Mixed constraints Multi-objective programming problems

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A Survey on Generalized Fuzzy Parameter-Based fractional programming problem

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NEW MATHEMATICS AND NATURAL COMPUTATION 2025年第1期21卷 281-321页

作者： Verma, Vaishaly Singh, Pitam Motilal Nehru Natl Inst Technol Allahabad Dept Math Paryagraj 211004 UP India

In fuzzy sets, the elements of a universal set may belong to that set completely, may not belong to that set, or may belong partially. Therefore, fuzzy sets are called generalizations of crisp sets. Due to the diverse nature of problems in real-world situations, fuzzy set theory is found to be unable to address some of the other features of ambiguity. Therefore, researchers extended fuzzy sets to picture fuzzy sets, orthopair, intuitionistic, Pythagorean, Fermatean, neutrosophic, spherical fuzzy sets, etc. Real-world problems can be solved using the method of fractional programming. Decision-makers are trying to get good results using generalized fuzzy numbers in fractional programming problems;hence, this review paper provides a specific framework for generalized fuzzy sets and generalized fuzzy fractional programming problems. Furthermore, it is a platform for researchers who want to work on generalized fuzzy parameter-based fractional programming problems. This research paper summarizes all the basic concepts and prior research on fractional programming and generalized fuzzy linear fractional programming problems.

关键词： Fuzzy set basic concepts of fuzzy sets linear fractional programming problem fuzzy numbers generalized fuzzy sets

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A branch and bound algorithm for solving low rank linear multiplicative and fractional programming problems

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JOURNAL OF GLOBAL OPTIMIZATION 2000年第3期18卷 283-299页

作者： Konno, H Fukaishi, K Tokyo Inst Technol Dept Ind Engn & Management Meguro Ku Tokyo 152 Japan NTT Data Corp Tokyo Japan

This paper is concerned with a practical algorithm for solving low rank linear multiplicative programming problems and low rank linear fractional programming problems. The former is the minimization of the sum of the product of two linear functions while the latter is the minimization of the sum of linear fractional functions over a polytope. Both of these problems are nonconvex minimization problems with a lot of practical applications. We will show that these problems can be solved in an efficient manner by adapting a branch and bound algorithm proposed by Androulakis-Maranas-Floudas for nonconvex problems containing products of two variables. Computational experiments show that this algorithm performs much better than other reported algorithms for these class of problems.

关键词： linear multiplicative programming problem linear fractional programming problem global minimization branch and bound method linear underestimating function

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