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Journal articles on the topic 'Fuzzy Linear Programming Problem'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

ZANGIABADI, M., and H. R. MALEKI. "A METHOD FOR SOLVING LINEAR PROGRAMMING PROBLEMS WITH FUZZY PARAMETERS BASED ON MULTIOBJECTIVE LINEAR PROGRAMMING TECHNIQUE." Asia-Pacific Journal of Operational Research 24, no. 04 (2007): 557–73. http://dx.doi.org/10.1142/s0217595907001395.

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In the real-world optimization problems, coefficients of the objective function are not known precisely and can be interpreted as fuzzy numbers. In this paper we define the concepts of optimality for linear programming problems with fuzzy parameters based on those for multiobjective linear programming problems. Then by using the concept of comparison of fuzzy numbers, we transform a linear programming problem with fuzzy parameters to a multiobjective linear programming problem. To this end, we propose several theorems which are used to obtain optimal solutions of linear programming problems wi

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Jyoti, Arora, and Sharma Surbhi. "Solving Trapezoidal Fuzzy Linear Programming Problem using Modified Big-M." Journal of Applied Mathematics and Statistical Analysis 4, no. 3 (2023): 1–5. https://doi.org/10.5281/zenodo.10165868.

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<i>The fuzzy logic and fuzzy numbers have been applied in many areas of Mathematical Programming. Optimization under uncertainty is one of the most important problem in Mathematical Programming. This paper proposes a Modified Big M method to solve fully fuzzy Trapezoidal linear programming problem with fuzzy decision variables and fuzzy parameters. </i>

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Someshwar, Siddi* Dr. Y. Raghunatha Reddy. "SOLUTION OF INTEGER LINEAR PROGRAMMING PROBLEMS WITH TRIANGULAR FUZZY NUMBERS." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 6, no. 3 (2017): 325–28. https://doi.org/10.5281/zenodo.400958.

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Fuzzy Integer Linear Programming problem is an application of fuzzy set theory in linear decision problems and most of these problems are related to linear programming with fuzzy variables. In this paper, we proposed a method for Integer linear programming problems with fuzzy variables. Two numerical examples were illustrated with the help of the proposed method. This method is a simple tool for the best solution to a variety of Integer linear programming problems.

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Towfik, Zaki, and Sabiha Jawad. "Proposed Method for Optimizing Fuzzy linear programming Problems by using Two-Phase Technique." Iraqi Journal for Electrical and Electronic Engineering 6, no. 2 (2010): 89–96. http://dx.doi.org/10.37917/ijeee.6.2.2.

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Fuzzy linear programming (FLP ) is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming contains fuzzy constrains or crisp objectives function or contains crisp constrains with fuzzy objectives function, which called fuzzy linear programming (FLP) with triplet fuzzy numbers consist a hybrid fuzzy. The crisp constrains used in the problems of types (= or ≥) with a proposed optimization fuzzy objectives and fuzzy constrains. In this paper proposed method for solving fuzzy linear programming problem by using Two-phase t

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SN, Mohamed Assarudeen, and Devi M. "A Study on A Solution Approach to Fuzzy Linear Frctional Programming Problems." Journal of Computational Mathematica 7, no. 1 (2023): 110–19. http://dx.doi.org/10.26524/cm166.

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In this paper, we propose a method of solving the fully fuzzy linear fractional programming problems, Express all the parameters and variables are triangular fuzzy numbers. Convert all the triangular fuzzy numbers in their parametric form, we convert the fractional programming problem in to a single objective linear programming problem in parametric form. We put new fuzzy arithmetic and fuzzy ranking, we obtain the optimal solution the given fully fuzzy linear fractional programming problem without converting to its equivalent crisp linear programming problem. A numerical example is provided t

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Cheng, Haifang, Weilai Huang, and Jianhu Cai. "Solving a Fully Fuzzy Linear Programming Problem through Compromise Programming." Journal of Applied Mathematics 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/726296.

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In the current literatures, there are several models of fully fuzzy linear programming (FFLP) problems where all the parameters and variables were fuzzy numbers but the constraints were crisp equality or inequality. In this paper, an FFLP problem with fuzzy equality constraints is discussed, and a method for solving this FFLP problem is also proposed. We first transform the fuzzy equality constraints into the crisp inequality ones using the measure of the similarity, which is interpreted as the feasibility degree of constrains, and then transform the fuzzy objective into two crisp objectives b

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Das, Krishnapada. "On Fuzzy Linear Programming Problems." International Journal of Science and Social Science Research 2, no. 3 (2024): 27–31. https://doi.org/10.5281/zenodo.13917823.

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In this paper, we concentrate on solving Fuzzy Linear Programming Problems (FLPP) in which the costcoefficients, the right-hand side vector and the technological coefficients are fuzzy numbers by defining a kind offuzzy inequality between two fuzzy numbers and then compare the results obtained by solving fuzzy linearprogramming problems (FLPP) with the ranking function method of solving FLPP. In this paper we discuss thecase of triangular fuzzy numbers. 

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Archana, D. "Fuzzy Linear Fractional Programming Problem Using Trapezoidal Fuzzy Numbers." International Journal for Research in Applied Science and Engineering Technology 13, no. 3 (2025): 3483–88. https://doi.org/10.22214/ijraset.2025.67956.

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Abstract: In order to solve Fully Fuzzy Linear Fractional Programming Problems (FFLFPP) with trapezoidal fuzzy integers as the objective function and constraints, this study aims to develop a novel trapezoidal fuzzy number ranking function. The simplex method and crisp linear fractional programming serve as the foundation for the suggested approach. With the aid of a recently proposed ranking function, we first converted FFLFPP into a Crisp Linear Programming Problem. The resulting problem was then transformed into LPP. The suggested method is demonstrated using a numerical example.

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Princy Flora, M. "Solving Fuzzy Linear Programming as Multi Objective Linear Programming Problem." Asian Journal of Science and Applied Technology 5, no. 1 (2016): 28–32. http://dx.doi.org/10.51983/ajsat-2016.5.1.2545.

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The constraints and the objective function of the fuzzy linear programming problem are converted into the multi-objective optimization problem (i.e.,) into an equivalent crisp linear problem.Finally, the multi-objective linear programming problem is converted into the weighted linear programming problem to show that they are independent of weights and obtained the complete optimal solution.

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10

Das, Krishnapada. "On Fully Fuzzy Linear Programming Problems." International Journal of Science and Social Science Research 2, no. 3 (2024): 72–76. https://doi.org/10.5281/zenodo.14010593.

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The fuzzy linear programming problem has been used as an important tool in different disciplines such as engineering, business, economics, commerce, defence etc. Fully Fuzzy Linear Programming Problems (FFLP) are those in which all the parameters that is the cost coefficients, the technological coefficients, the right-hand side of the constraints, and the decision variable are fuzzy numbers. Ezzati et al. [1] suggested an algorithm to solve fully fuzzy linear programming problems. In this paper, we propose two methods to find the optimal solution of fully fuzzy linear programming pro

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Mervat, M. Elshafei. "Fully Fuzzy Quadratic programming with unrestricted Fully Fuzzy variables and Parameters." Journal of Progressive Research in Mathematics 15, no. 3 (2019): 2654–67. https://doi.org/10.5281/zenodo.3974031.

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There exist several methods for solving fuzzy linear or nonlinear programming problems under positivity fuzzy variables and restricted fuzzy coefficients. Due to the limitation of these methods, they can’t be applied for solving fully fuzzy linear or non- linear programming problems with unrestricted fuzzy coefficients and fuzzy variables. In this paper an efficient method to find the fuzzy optimal solution for fully fuzzy quadratic programming (FFQP) problem with unrestricted variables and parameters has been proposed. All the coefficients and decision variables of both objective functi

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Jenifer D H. "A Methodology for Solving Fuzzy Linear Programming Problem as a Fuzzy Linear Complementarity Problem." Communications on Applied Nonlinear Analysis 31, no. 2s (2024): 01–08. http://dx.doi.org/10.52783/cana.v31.587.

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In this paper, the linear complementarity problem with Fuzzy parameters is discussed. The Linear Programming Problem can be transformed into a Linear Complementarity Problem. The Maximum Index method is used to solve the converted Linear programming problem. The maximum index method has been introduced as a potential approach for identifying a complementarity feasible solution to the Linear Complementarity Problem. The fuzzy arithmetic operations are utilized for the triangular fuzzy numbers. A real-life example has been provided to demonstrate the suggested approach.

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Taleshian, Fatemeh, and Jafar Fathali. "A Mathematical Model for Fuzzyp-Median Problem with Fuzzy Weights and Variables." Advances in Operations Research 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/7590492.

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We investigate thep-median problem with fuzzy variables and weights of vertices. The fuzzy equalities and inequalities transform to crisp cases by using some technique used in fuzzy linear programming. We show that the fuzzy objective function also can be replaced by crisp functions. Therefore an auxiliary linear programming model is obtained for the fuzzyp-median problem. The results are compared with two previously proposed methods.

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Dewi Lestari, Siska, and Subanar Subanar. "PENDEKATAN ALGORITMA GENETIKA DALAM MENYELESAIKAN PERMASALAHAN FUZZY LINEAR PROGRAMMING." IJCCS (Indonesian Journal of Computing and Cybernetics Systems) 5, no. 3 (2011): 36. http://dx.doi.org/10.22146/ijccs.5211.

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Fuzzy linear programming is one of the linear programming developments which able to accommodate uncertainty in the real world. Genetic algorithm approach in solving linear programming problems with fuzzy constraints has been introduced by Lin (2008) by providing a case which consists of two decision variables and three constraint functions. Other linear programming problem arise with the presence of some coefficients which are fuzzy in linear programming problems, such as the coefficient of the objective function, the coefficient of constraint functions, and right-hand side coefficients const

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Usenik, Janez. "FUZZY DYNAMIC LINEAR PROGRAMMING IN ENERGY SUPPLY PLANNING." Journal of Energy Technology 4, no. 4 (2024): 45–62. https://doi.org/10.18690/jet.4.4.45-62.2011.

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Linear programming is an important field of optimisation. Many practical problems can be expressed as linear programming problems and be solved with a simplex method. When all data in a linear program are determined and quantities are known in advance, the simplex algorithm, i.e. the simplex method, is explicit. However, in special cases the coefficients in the linear programming problem can be a) fuzzy numbers or b) functions of time with specific requests. In this manner, we have either fuzzy linear programming in the first situation or continuous dynamic linear programming in the second. Th

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Maher A. Nawkhass. "Revised Harmonious Fuzzy Technique for Solving Fully Fuzzy Multi-Objective Linear Fractional Programming Problems." Zanco Journal of Pure and Applied Sciences 37, no. 2 (2025): 53–65. https://doi.org/10.21271/zjpas.37.2.6.

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The revised harmonious fuzzy technique (RHFT) is a method used to solve fuzzy optimization problems. It was capitalized as an extension of the classical linear programming technique to handle constraints and objectives that are fuzzy. The harmonious fuzzy technique HFT aims to find a solution that satisfies the uncertain restraints and optimizes the uncertain objectives while taking into account the uncertainty or fuzziness of the problem parameters. This work demonstrates how the RHFT can be utilized to dexterously solve “fully fuzzy multi-goal linear fractional programming (FFMOLFP) problems

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Kabiraj, Arpita, Prasun Kumar Nayak, and Swapan Raha. "Solving Intuitionistic Fuzzy Linear Programming Problem." International Journal of Intelligence Science 09, no. 01 (2019): 44–58. http://dx.doi.org/10.4236/ijis.2019.91003.

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Kané, L., M. Konaté, L. Diabaté, M. Diakité, and H. Bado. "NEW IMPROVED METHOD FOR SOLVING THE FUZZY LINEAR PROGRAMMING PROBLEMS WITH VARIABLES GIVEN AS FUZZY NUMBERS." Advances in Mathematics: Scientific Journal 10, no. 12 (2021): 3699–723. http://dx.doi.org/10.37418/amsj.10.12.11.

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The present paper aims to propose an alternative solution approach in obtaining the fuzzy optimal solution to a fuzzy linear programming problem with variables given as fuzzy numbers with minimum uncertainty. In this paper, the fuzzy linear programming problems with variables given as fuzzy numbers is transformed into equivalent interval linear programming problems with variables given as interval numbers. The solutions to these interval linear programming problems with variables given as interval numbers are then obtained with the help of linear programming technique. A set of six random nume

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Mitlif, Rasha Jalal. "An Application Model for Linear Programming with an Evolutionary Ranking Function." Ibn AL-Haitham Journal For Pure and Applied Sciences 35, no. 3 (2022): 146–54. http://dx.doi.org/10.30526/35.3.2817.

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One of the most important methodologies in operations research (OR) is the linear programming problem (LPP). Many real-world problems can be turned into linear programming models (LPM), making this model an essential tool for today's financial, hotel, and industrial applications, among others. Fuzzy linear programming (FLP) issues are important in fuzzy modeling because they can express uncertainty in the real world. There are several ways to tackle fuzzy linear programming problems now available. An efficient method for FLP has been proposed in this research to find the best answer. This meth

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BUCKLEY, JAMES J., THOMAS FEURING, and YOICHI HAYASHI. "MULTI-OBJECTIVE FULLY FUZZIFIED LINEAR PROGAMMING." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 09, no. 05 (2001): 605–21. http://dx.doi.org/10.1142/s0218488501001083.

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In this paper we wish to solve multi-objective fully fuzzified linear programming problems which are multi-objective linear programming problems where all the parameters and variables are fuzzy numbers. We change this problem into a single objective fuzzy linear programming problem and then show that our solution procedure can be used to explore the whole undominated set. An evolutionary algorithm is then designed to generate undominated solutions. An example is presented showing our evolutionary algorithm solution.

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Stanojevic, B., and I. M. Stancu-Minasian. "Evaluating fuzzy inequalities and solving fully fuzzified linear fractional programs." Yugoslav Journal of Operations Research 22, no. 1 (2012): 41–50. http://dx.doi.org/10.2298/yjor110522001s.

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In our earlier articles, we proposed two methods for solving the fully fuzzified linear fractional programming (FFLFP) problems. In this paper, we introduce a different approach of evaluating fuzzy inequalities between two triangular fuzzy numbers and solving FFLFP problems. First, using the Charnes-Cooper method, we transform the linear fractional programming problem into a linear one. Second, the problem of maximizing a function with triangular fuzzy value is transformed into a problem of deterministic multiple objective linear programming. Illustrative numerical examples are given to clarif

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Jenifer D H. "An Interval approach to solve Fuzzy Fractional Programming Problem as a Fuzzy Linear Complementarity Problem." Communications on Applied Nonlinear Analysis 32, no. 5s (2024): 353–60. https://doi.org/10.52783/cana.v32.3106.

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An optimization problem where the goal function is a proportion between two functions is known as fractional programming, and the goal is to maximize or minimize the ratio. This paper discusses a methodology to resolve Fuzzy Fractional Programming Problem as a Fuzzy Linear Complementarity Problem. The study seeks to emphasize the key characteristics, make some new observation and motivate further application in linear complementarity problem. The constraints of the Fractional Programming problem is taken as a Fuzzy Linear Programming problem and further it transformed in to Fuzzy Linear Comple

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Jyoti, Arora, and Sharma Surbhi. "Solving Triangular Fuzzy Linear Fractional Programming Problem." Journal of Applied Mathematics and Statistical Analysis 4, no. 1 (2023): 8–14. https://doi.org/10.5281/zenodo.7808513.

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<em>In this paper we propose to solve linear fractional programming problem, where all the decision parameters are trapezoidal fuzzy numbers. Our approach and computational procedures may be efficient and simple to implement for calculation in a trapezoidal fuzzy environment for all fields of engineering and science where impreciseness occur. Here we are formulating the given objective function into three objective bounds with constraints which can be solved further by Simplex method. A numerical example is presented to illustrate the proposed approach.</em>

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Ren, Aihong. "A Novel Method for Solving the Fully Fuzzy Bilevel Linear Programming Problem." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/280380.

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We address a fully fuzzy bilevel linear programming problem in which all the coefficients and variables of both objective functions and constraints are expressed as fuzzy numbers. This paper is to develop a new method to deal with the fully fuzzy bilevel linear programming problem by applying interval programming method. To this end, we first discretize membership grade of fuzzy coefficients and fuzzy decision variables of the problem into a finite number ofα-level sets. By usingα-level sets of fuzzy numbers, the fully fuzzy bilevel linear programming problem is transformed into an interval bi

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Veeramani, Chinnadurai, and Muthukumar Sumathi. "Fuzzy Mathematical Programming approach for Solving Fuzzy Linear Fractional Programming Problem." RAIRO - Operations Research 48, no. 1 (2014): 109–22. http://dx.doi.org/10.1051/ro/2013056.

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Singh, Sujeet Kumar, and Shiv Prasad Yadav. "Fuzzy Programming Approach for Solving Intuitionistic Fuzzy Linear Fractional Programming Problem." International Journal of Fuzzy Systems 18, no. 2 (2015): 263–69. http://dx.doi.org/10.1007/s40815-015-0108-2.

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M.Jayalakshmi, M. Jayalakshmi, and P. Pandian P.Pandian. "Solving Fully Fuzzy Multi-Objective Linear Programming Problems." International Journal of Scientific Research 3, no. 4 (2012): 1–6. http://dx.doi.org/10.15373/22778179/apr2014/174.

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Bharati, S. K., and S. R. Singh. "Interval-Valued Intuitionistic Fuzzy Linear Programming Problem." New Mathematics and Natural Computation 16, no. 01 (2020): 53–71. http://dx.doi.org/10.1142/s1793005720500040.

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In many existing methods of linear programming problem (LPP), precise values of parameters have been used but parameters of LPP are imprecise and ambiguous due to incomplete information. Several approaches and theories have been developed for dealing LPP based on fuzzy set (FS), intuitionistic fuzzy set (IFS) which are characterized by membership degree, membership and non-membership degrees, respectively. It’s interesting to note that single membership and non-membership degrees do not deal properly the state of uncertainty and hesitation. Further, we face a kind of uncertainty occurs a kind

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Vaishali, K. "Non-Linear Programming Problem using Pentagonal Fuzzy Numbers." International Journal for Research in Applied Science and Engineering Technology 13, no. 3 (2025): 3489–92. https://doi.org/10.22214/ijraset.2025.67958.

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Abstract: In this study, pentagonal fuzzy numbers are used as the decision parameters. To solve these fuzzy nonlinear programming problems, we first convert all of the pentagonal fuzzy numbers into crisp values using robust ranking method. Next, we obtain a crisp nonlinear programming problem. Finally, we apply the Kuhn-Tucker conditions to obtain the best solution.

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Sivakumar, Karthick, Saraswathi Appasamy, and Ahmad Seyyed. "Fuzzy linear fractional programming problem using the lexicography method." Vojnotehnicki glasnik 72, no. 3 (2024): 965–79. http://dx.doi.org/10.5937/vojtehg72-50429.

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Introduction/purpose: In solving real-life fractional programming problems, uncertainty and hesitation are often encountered due to various uncontrollable factors. To overcome these limitations, the fuzzy logic approach is applied to these problems. Methods: The discussion focused on solving the fuzzy linear fractional programming problem (FLFPP). First, the FLFP problem was converted into a lexicographic optimization problem, which was then solved to obtain the solution. Results: A numerical example was presented to simplify the explanation of the algorithm. While most researchers solve FLFPP

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Hasuike, Takashi, Hideki Katagiri, and Hiroaki Ishii. "Multiobjective Random Fuzzy Linear Programming Problems Based on the Possibility Maximization Model." Journal of Advanced Computational Intelligence and Intelligent Informatics 13, no. 4 (2009): 373–79. http://dx.doi.org/10.20965/jaciii.2009.p0373.

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Two multiobjective random fuzzy programming problems considered based on the possibility maximization model using possibilistic and stochastic programming are not initially well defined due to the random variables and fuzzy numbers included. To solve them analytically, probability criteria are set for objective functions and chance constraints are introduced. Taking into account the decision maker’s subjectivity and the original plan’s flexibility, a fuzzy goal is introduced for each objective function. The original problems are then changed into deterministic equivalent problems to make the p

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Stanojevic, Bogdana, and Milan Stanojevic. "Penalty method for fuzzy linear programming with trapezoidal numbers." Yugoslav Journal of Operations Research 19, no. 1 (2009): 149–56. http://dx.doi.org/10.2298/yjor0901149s.

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In this paper we shall propose an algorithm for solving fuzzy linear programming problems with trapezoidal numbers using a penalty method. We will transform the problem of maximizing a function having trapezoidal fuzzy number values under some constraints into a deterministic multi-objective programming problem by penalizing the objective function for possible constraint violation. Furthermore, the obtained deterministic problem will have only unavoidable inequalities between trapezoidal fuzzy numbers parameters as constraints.

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Leung, Y. "Interregional Equilibrium and Fuzzy Linear Programming: 2." Environment and Planning A: Economy and Space 20, no. 2 (1988): 219–30. http://dx.doi.org/10.1068/a200219.

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Extended on the approach in the first part of this two-part series of papers, multiobjective interregional equilibrium is analyzed within a multiobjective fuzzy linear programming framework. Interregional problems with precise objectives and precise constraints, with fuzzy objectives and precise constraints, and with fuzzy objectives and fuzzy constraints are individually examined. Properties of the equilibrium solution and of the associated dual optimal problem are investigated. The present framework comprises ordinary multiobjective interregional equilibrium problems as a special case. A var

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Surapati, Pramanik*. "NEUTROSOPHIC MULTI-OBJECTIVE LINEAR PROGRAMMING." Global Journal of Engineering Science and Research Management 3, no. 8 (2016): 36–46. https://doi.org/10.5281/zenodo.59949.

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For modeling imprecise and indeterminate data for multi-objective decision making, two different methods: neutrosophic multi-objective linear/non-linear programming  neutrosophic goal programming, which have been very recently proposed in the literatuire. In many economic problems, the well-known probabilities or fuzzy solutions procedures are not suitable because they cannot deal the situation when indeterminacy inherently involves in the problem. In this case we propose a new concept in optimization problem under uncertainty and indeterminacy. It is an extension of fuzzy and intuitionis

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Lone, MA, MS Puktha, and SA Mir. "Fuzzy linear mathematical programming in agriculture." BIBECHANA 13 (December 3, 2015): 72–76. http://dx.doi.org/10.3126/bibechana.v13i0.13363.

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In this paper we present a Fuzzy linear Mathematical programming approach for optimal allocation of land under cultivation. Fuzzy Mathematical programming approach is more realistic and flexible optimal solution for the agricultural land cultivation problem. In this study we have discussed how to deal with decision making problems that are described by Fuzzy linear programming (Flp) models and formulated with the elements of uncertainty. This form of approximation can be convenient and sufficient for making good decisions. BIBECHANA 13 (2016) 72-76

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Ren, Aihong. "Solving the Fully Fuzzy Bilevel Linear Programming Problem through Deviation Degree Measures and a Ranking Function Method." Mathematical Problems in Engineering 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/7069804.

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This paper is concerned with a class of fully fuzzy bilevel linear programming problems where all the coefficients and decision variables of both objective functions and the constraints are fuzzy numbers. A new approach based on deviation degree measures and a ranking function method is proposed to solve these problems. We first introduce concepts of the feasible region and the fuzzy optimal solution of a fully fuzzy bilevel linear programming problem. In order to obtain a fuzzy optimal solution of the problem, we apply deviation degree measures to deal with the fuzzy constraints and use a ran

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Ebrahimnejad, Ali, Seyed Hadi Nasseri, and Sayyed Mehdi Mansourzadeh. "Bounded Primal Simplex Algorithm for Bounded Linear Programming with Fuzzy Cost Coefficients." International Journal of Operations Research and Information Systems 2, no. 1 (2011): 96–120. http://dx.doi.org/10.4018/joris.2011010105.

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In most practical problems of linear programming problems with fuzzy cost coefficients, some or all variables are restricted to lie within lower and upper bounds. In this paper, the authors propose a new method for solving such problems called the bounded fuzzy primal simplex algorithm. Some researchers used the linear programming problem with fuzzy cost coefficients as an auxiliary problem for solving linear programming with fuzzy variables, but their method is not efficient when the decision variables are bounded variables in the auxiliary problem. In this paper the authors introduce an effi

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Mehmood, Muhammad Athar, Muhammad Akram, Majed G. Alharbi, and Shahida Bashir. "Solution of Fully Bipolar Fuzzy Linear Programming Models." Mathematical Problems in Engineering 2021 (April 22, 2021): 1–31. http://dx.doi.org/10.1155/2021/9961891.

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The Yin-Yang bipolar fuzzy set is a powerful mathematical tool for depicting fuzziness and vagueness. We first extend the concept of crisp linear programming problem in a bipolar fuzzy environment based on bipolar fuzzy numbers. We first define arithmetic operations of unrestricted bipolar fuzzy numbers and multiplication of an unrestricted trapezoidal bipolar fuzzy number (TrBFN) with non-negative TrBFN. We then propose a method for solving fully bipolar fuzzy linear programming problems (FBFLPPs) with equality constraints in which the coefficients are unrestricted triangular bipolar fuzzy nu

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Iqbal, Salma, Naveed Yaqoob, and Muhammad Gulistan. "An Investigation of Linear Diophantine Fuzzy Nonlinear Fractional Programming Problems." Mathematics 11, no. 15 (2023): 3383. http://dx.doi.org/10.3390/math11153383.

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The linear Diophantine fuzzy set notion is the main foundation of the interactive method of tackling nonlinear fractional programming problems that is presented in this research. When the decision maker (DM) defines the degree α of α level sets, the max-min problem is solved in this interactive technique using Zimmermann’s min operator method. By using the updating technique of degree α, we can solve DM from the set of α-cut optimal solutions based on the membership function and non-membership function. Fuzzy numbers based on α-cut analysis bestowing the degree α given by DM can first be used

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M., S. Osman, E. Emam O., and A. El Sayed M. "Multi-level Multi-objective Quadratic Fractional Programming Problem with Fuzzy Parameters: A FGP Approach." Asian Research Journal of Mathematics 5, no. 3 (2017): 1–19. https://doi.org/10.9734/ARJOM/2017/34864.

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The motivation behind this paper is to present multi-level multi-objective quadratic fractional programming (ML-MOQFP) problem with fuzzy parameters in the constraints. ML-MOQFP problem is an important class of non-linear fractional programming problem. These type of problems arise in many fields such as production planning, financial and corporative planning, health care and hospital planning. Firstly, the concept of the -cut and fuzzy partial order relation are applied to transform the set of fuzzy constraints into a common crisp set. Then, the quadratic fractional objective functions in eac

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Kané, Ladji, Lassina Diabaté, Daouda Diawara, Moussa Konaté, and Souleymane Kané. "A Simplified Novel Technique for Solving Linear Programming Problems with Triangular Fuzzy Variables via Interval Linear Programming Problems." Academic Journal of Applied Mathematical Sciences, no. 72 (February 17, 2021): 82–93. http://dx.doi.org/10.32861/ajams.72.82.93.

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This study proposes a novel technique for solving Linear Programming Problems with triangular fuzzy variables. A modified version of the well-known simplex method and the Existing Method for Solving Interval Linear Programming problems are used for solving linear programming problems with triangular fuzzy variables. Furthermore, for illustration, some numerical examples and one real problem are used to demonstrate the correctness and usefulness of the proposed method. The proposed algorithm is flexible, easy, and reasonable.

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Iqbal, Salma, Naveed Yaqoob, and Muhammad Gulistan. "Multi-Objective Non-Linear Programming Problems in Linear Diophantine Fuzzy Environment." Axioms 12, no. 11 (2023): 1048. http://dx.doi.org/10.3390/axioms12111048.

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Due to various unpredictable factors, a decision maker frequently experiences uncertainty and hesitation when dealing with real-world practical optimization problems. At times, it’s necessary to simultaneously optimize a number of non-linear and competing objectives. Linear Diophantine fuzzy numbers are used to address the uncertain parameters that arise in these circumstances. The objective of this manuscript is to present a method for solving a linear Diophantine fuzzy multi-objective nonlinear programming problem (LDFMONLPP). All the coefficients of the nonlinear multi-objective functions a

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Alrefaei, Mahmoud H., and Marwa Z. Tuffaha. "Fuzzy linear programming with the intuitionistic polygonal fuzzy numbers." International Journal of Electrical and Computer Engineering (IJECE) 14, no. 2 (2024): 2242–53. https://doi.org/10.11591/ijece.v14i2.pp2242-2253.

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In real world applications, data are subject to ambiguity due to several factors; fuzzy sets and fuzzy numbers propose a great tool to model such ambiguity. In case of hesitation, the complement of a membership value in fuzzy numbers can be different from the non-membership value, in which case we can model using intuitionistic fuzzy numbers as they provide flexibility by defining both a membership and a non-membership functions. In this article, we consider the intuitionistic fuzzy linear programming problem with intuitionistic polygonal fuzzy numbers, which is a generalization of the previou

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Yang, Xiao-Peng, Xue-Gang Zhou, Bing-Yuan Cao, and S. H. Nasseri. "A MOLP Method for Solving Fully Fuzzy Linear Programming withLRFuzzy Parameters." Mathematical Problems in Engineering 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/782376.

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Kaur and Kumar, 2013, use Mehar’s method to solve a kind of fully fuzzy linear programming (FFLP) problems withLRfuzzy parameters. In this paper, a new kind of FFLP problems is introduced with a solution method proposed. The FFLP is converted into a multiobjective linear programming (MOLP) according to the order relation for comparing theLRflat fuzzy numbers. Besides, the classical fuzzy programming method is modified and then used to solve the MOLP problem. Based on the compromised optimal solution to the MOLP problem, the compromised optimal solution to the FFLP problem is obtained. At last,

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VASANT, PANDIAN. "INDUSTRIAL PRODUCTION PLANNING USING INTERACTIVE FUZZY LINEAR PROGRAMMING." International Journal of Computational Intelligence and Applications 04, no. 01 (2004): 13–26. http://dx.doi.org/10.1142/s1469026804001173.

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Any modern industrial manufacturing unit inevitably faces problems of vagueness in various aspects such as raw material availability, human resource availability, processing capability and constraints and limitations imposed by marketing department. Such a complex problem of vagueness and uncertainty can be handled by the theory of fuzzy linear programming. In this paper, a new fuzzy linear programming based methodology using a modified S-curve membership function is used to solve fuzzy mix product selection problem in Industrial Engineering. Profits and satisfactory level have been computed u

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Mohanaselvi, S., K. Prabakaran, and K. Suja. "FUZZY LINEAR PROGRAMMING PROBLEM WITH GENERALIZED TRAPEZOIDAL FUZZY NUMBERS." Advances in Mathematics: Scientific Journal 9, no. 12 (2020): 10437–45. http://dx.doi.org/10.37418/amsj.9.12.33.

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Liu, Qiumei, and Xin Gao. "Fully Fuzzy Linear Programming Problem with Triangular Fuzzy Numbers." Journal of Computational and Theoretical Nanoscience 13, no. 7 (2016): 4036–41. http://dx.doi.org/10.1166/jctn.2016.5246.

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Pérez-Cañedo, Boris, José Luis Verdegay, Eduardo René Concepción-Morales, and Alejandro Rosete. "Lexicographic Methods for Fuzzy Linear Programming." Mathematics 8, no. 9 (2020): 1540. http://dx.doi.org/10.3390/math8091540.

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Fuzzy Linear Programming (FLP) has addressed the increasing complexity of real-world decision-making problems that arise in uncertain and ever-changing environments since its introduction in the 1970s. Built upon the Fuzzy Sets theory and classical Linear Programming (LP) theory, FLP encompasses an extensive area of theoretical research and algorithmic development. Unlike classical LP, there is not a unique model for the FLP problem, since fuzziness can appear in the model components in different ways. Hence, despite fifty years of research, new formulations of FLP problems and solution method

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Gholamtabar, Sh. "AN IMPROVING APPROACH FOR INTERVAL AND FUZZY NUMBER LINEAR PROGRAMMING PROBLEMS." Advanced Mathematical Models & Applications 9, no. 3 (2024): 370–86. https://doi.org/10.62476/amma93370.

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In this study, Interval number and Fuzzy number Linear Programming problems are addressed. We deal with some convenient methods to solve the addressed problems. We focus on preparing an improving approach based on Tang Shaocheng method to solve linear programming problems with interval or fuzzy numbers. Also, some applications of our proposed approach in fractional programming are presented. Particularly, we propose an algorithm using our improved approach to solve a fuzzy multi-objective linear fractional programming problem. Finally, we illustrate the proposed approach using numerical and so

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Abo-Sinna, Mahmoud A., and Ibrahim A. Baky. "Fuzzy Goal Programming Procedure to Bilevel Multiobjective Linear Fractional Programming Problems." International Journal of Mathematics and Mathematical Sciences 2010 (2010): 1–15. http://dx.doi.org/10.1155/2010/148975.

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This paper presents a fuzzy goal programming (FGP) procedure for solving bilevel multiobjective linear fractional programming (BL-MOLFP) problems. It makes an extension work of Moitra and Pal (2002) and Pal et al. (2003). In the proposed procedure, the membership functions for the defined fuzzy goals of the decision makers (DMs) objective functions at both levels as well as the membership functions for vector of fuzzy goals of the decision variables controlled by first-level decision maker are developed first in the model formulation of the problem. Then a fuzzy goal programming model to minim

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