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Journal articles on the topic 'Multi-objective fractional programming'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Sulaiman, Nejmaddin A., and Maher A. Nawkhass. "Using Standard Division to Solve Multi- Objective Quadratic Fractional Programming Problems." Journal of Zankoy Sulaimani - Part A 18, no. 3 (2016): 157–64. http://dx.doi.org/10.17656/jzs.10544.

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2

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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3

Acharya, Srikumar, Berhanu Belay, and Rajashree Mishra. "MULTI-OBJECTIVE PROBABILISTIC FRACTIONAL PROGRAMMING PROBLEM INVOLVING TWO PARAMETERS CAUCHY DISTRIBUTION." Mathematical Modelling and Analysis 24, no. 3 (2019): 385–403. http://dx.doi.org/10.3846/mma.2019.024.

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The paper presents the solution methodology of a multi-objective probabilistic fractional programming problem, where the parameters of the right hand side constraints follow Cauchy distribution. The proposed mathematical model can not be solved directly. The solution procedure is completed in three steps. In ﬁrst step, multi-objective probabilistic fractional programming problem is converted to deterministic multi-objective fractional mathematical programming problem. In the second step, it is converted to its equivalent multi-objective mathematical programming problem. Finally, ε -constraint

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4

Chakraborty, M., and Sandipan Gupta. "Fuzzy mathematical programming for multi objective linear fractional programming problem." Fuzzy Sets and Systems 125, no. 3 (2002): 335–42. http://dx.doi.org/10.1016/s0165-0114(01)00060-4.

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5

CHARLES, V., and D. DUTTA. "IDENTIFICATION OF REDUNDANT OBJECTIVE FUNCTIONS IN MULTI-OBJECTIVE STOCHASTIC FRACTIONAL PROGRAMMING PROBLEMS." Asia-Pacific Journal of Operational Research 23, no. 02 (2006): 155–70. http://dx.doi.org/10.1142/s0217595906000863.

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Redundancy in constraints and variables are usually studied in linear, integer and non-linear programming problems. However, main emphasis has so far been given only to linear programming problems. In this paper, an algorithm that identifies redundant objective functions in multi-objective stochastic fractional programming problems is provided. A solution procedure is also illustrated. This reduces the number of objective functions in cases where redundant objective functions exist.

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6

Youness, E. A., O. E. Emam, and M. S. Hafez. "Fuzzy Bi-Level Multi-Objective Fractional Integer Programming." Applied Mathematics & Information Sciences 8, no. 6 (2014): 2857–63. http://dx.doi.org/10.12785/amis/080622.

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7

Charles, V., and D. Dutta. "Extremization of multi-objective stochastic fractional programming problem." Annals of Operations Research 143, no. 1 (2006): 297–304. http://dx.doi.org/10.1007/s10479-006-7389-7.

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8

Baky, Ibrahim. "Fuzzy Goal Programming Procedures for Multi-Level Multi-Objective Linear Fractional Programming Problems." International Conference on Mathematics and Engineering Physics 6, no. 6 (2012): 1–20. http://dx.doi.org/10.21608/icmep.2012.29744.

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9

Ţigan, Ş., and I. M. Stancu-Minasian. "Efficiency and generalized concavity for multi-objective set-valued programming." Journal of Numerical Analysis and Approximation Theory 32, no. 2 (2003): 235–42. http://dx.doi.org/10.33993/jnaat322-752.

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The purpose of this paper is to give sufficient conditions of generalized concavity type for a local (weakly) efficient solution to be a global (weakly) efficient solution for a vector maximization set-valued programming problem. In the particular case of the vector maximization set-valued fractional programming problem, we derive some characterizations properties of efficient and properly efficient solutions based on a parametric procedure associated to the fractional problem.

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10

Nahar, Samsun, Md Asadujjaman, Khadiza Begum, Mahede-Ul-Hassan, and Md Abdul Alim. "Characteristics of Multi-Objective Linear Programming Problem and Multi-Objective Linear Fractional Programming Problem Taking Maximum Value of Multi-Objective Functions." Applied Mathematics 15, no. 01 (2024): 22–32. http://dx.doi.org/10.4236/am.2024.151003.

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11

Bhurjee, Ajay Kumar, and Geetanjali Panda. "Parametric multi-objective fractional programming problem with interval uncertainty." International Journal of Operational Research 35, no. 1 (2019): 132. http://dx.doi.org/10.1504/ijor.2019.099546.

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Bhurjee, Ajay Kumar, and Geetanjali Panda. "Parametric multi-objective fractional programming problem with interval uncertainty." International Journal of Operational Research 35, no. 1 (2019): 132. http://dx.doi.org/10.1504/ijor.2019.10021036.

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13

Nayak, Suvasis, Sujit Maharana, and RASHMI OTA. "Multi-level multi-objective linear fractional programming problem: A solution approach." International Journal of Mathematical Modelling and Numerical Optimisation 1, no. 1 (2023): 1. http://dx.doi.org/10.1504/ijmmno.2023.10049623.

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14

Nayak, Suvasis, Sujit Maharana, and Rashmi Ranjan Ota. "Multi-level multi-objective linear fractional programming problem: a solution approach." International Journal of Mathematical Modelling and Numerical Optimisation 13, no. 1 (2023): 84. http://dx.doi.org/10.1504/ijmmno.2023.127840.

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15

Prakash, Jay, Sangeeta Singh, and Dr Umesh Sharma. "Investigation of Markovian Process in Server Break-down." INTERANTIONAL JOURNAL OF SCIENTIFIC RESEARCH IN ENGINEERING AND MANAGEMENT 08, no. 008 (2024): 1–7. http://dx.doi.org/10.55041/ijsrem37372.

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In day to day life goods produced at a number of places are consumed at different locations and then the problem faced by producer or dealer is to transfer goods from numerous places of origin to various places of consumption such that cost of transportation, time required, damages to the product etc. are optimum. This is called classical transportation problem. In this study we have studied transportation problem solve by Markov Decision Process. Introduction to the operations research is made along with over view of optimization techniques of single objective transportation problem. For lite

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16

Stanojević, Bogdana, and Milan Stanojević. "Comment on “Fuzzy mathematical programming for multi objective linear fractional programming problem”." Fuzzy Sets and Systems 246 (July 2014): 156–59. http://dx.doi.org/10.1016/j.fss.2014.02.007.

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17

Nayak, Suvasis, and Akshay Ojha. "On multi-level multi-objective linear fractional programming problem with interval parameters." RAIRO - Operations Research 53, no. 5 (2019): 1601–16. http://dx.doi.org/10.1051/ro/2018063.

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This paper develops a method to solve multi-level multi-objective linear fractional programming problem (ML-MOLFPP) with interval parameters as the coefficients of decision variables and the constants involved in both the objectives and constraints. The objectives at each level are transformed into interval-valued fractional functions and approximated by intervals of linear functions using variable transformation and Taylor series expansion. Interval analysis and weighting sum method with analytic hierarchy process (AHP), are used to determine the non-dominated solutions at each level from whi

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18

Anukokila, Paraman, Bheeman Radhakrishnan, and Antony Anju. "Goal programming approach for solving multi-objective fractional transportation problem with fuzzy parameters." RAIRO - Operations Research 53, no. 1 (2019): 157–78. http://dx.doi.org/10.1051/ro/2019005.

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In this paper, authors studied a goal programming approach for solving multi-objective fractional transportation problem by representing the parameters (γ, δ) in terms of interval valued fuzzy numbers. Fuzzy goal programming problem with multiple objectives is difficult for the decision makers to determine the goal valued of each objective precisely. The proposed model presents a special type of non-linear (hyperbolic) membership functions to solve multi-objective fractional transportation problem with fuzzy parameters. To illustrate the proposed method numerical examples are solved.

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19

Pramy, Farhana Akond. "An Approach for Solving Fuzzy Multi-Objective Linear Fractional Programming Problems." International Journal of Mathematical, Engineering and Management Sciences 3, no. 3 (2018): 280–93. http://dx.doi.org/10.33889/ijmems.2018.3.3-020.

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In this paper, an attempt has been taken to develop a method for solving fuzzy multi-objective linear fractional programming (FMOLFP) problem. Here, at first the FMOLFP problem is converted into (crisp) multi-objective linear fractional programming (MOLFP) problem using the graded mean integration representation (GMIR) method proposed by Chen and Hsieh. That is, all the fuzzy parameters of FMOLFP problem are converted into crisp values. Then the MOLFP problem is transformed into a single objective linear programming (LP) problem using a proposal given by Nuran Guzel. Finally the single objecti

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20

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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21

Kumar, N. Suresh, and S. N. Md Assarudeen. "Solving neutrosophic multi-objective linear fractional programming problem using central measures." Scientific Temper 14, no. 04 (2023): 1212–16. http://dx.doi.org/10.58414/scientifictemper.2023.14.4.23.

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In this article, we present different kind of mean technique to solve Multi-Objective Linear Fractional Programming Problem (MOLFPP) in Neutrosophic Environment. Here in these mean techniques the MOLFPP is converted into Single Objective Linear Programming problem(SOLPP) and then we obtained the optimal solution by simplex method in Neutrosophic Environment. The proposed method is illustrated with the help of a numerical example.

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22

El Sayed, Mohamed A., Mohamed A. El-Shorbagy, Farahat A. Farahat, Aisha F. Fareed, and Mohamed A. Elsisy. "Stability of Parametric Intuitionistic Fuzzy Multi-Objective Fractional Transportation Problem." Fractal and Fractional 5, no. 4 (2021): 233. http://dx.doi.org/10.3390/fractalfract5040233.

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In this study, a parametric intuitionistic fuzzy multi-objective fractional transportation problem (PIF-MOFTP) is proposed. The current PIF-MOFTP has a single-scalar parameter in the objective functions and an intuitionistic fuzzy supply and demand. Based on the (α,β)-cut concept a parametric (α,β)-MOFTP is established. Then, a fuzzy goal programming (FGP) approach is utilized to obtain (α,β)-Pareto optimal solution. We investigated the stability set of the first kind (SSFK) corresponding to the solution by extending the Kuhn-Tucker optimality conditions of multi-objective programming problems

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23

Goyal, Vandana, Namrata Rani, and Deepak Gupta. "Parametric approach to quadratically constrained multi-level multi-objective quadratic fractional programming." OPSEARCH 58, no. 3 (2021): 557–74. http://dx.doi.org/10.1007/s12597-020-00497-y.

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24

Osman, M. S., O. E. Emam, and M. A. El Sayed. "Stochastic Fuzzy Multi-level Multi-objective Fractional Programming Problem: A FGP Approach." OPSEARCH 54, no. 4 (2017): 816–40. http://dx.doi.org/10.1007/s12597-017-0307-8.

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25

Lachhwani, Kailash. "Modified FGP approach for multi-level multi objective linear fractional programming problems." Applied Mathematics and Computation 266 (September 2015): 1038–49. http://dx.doi.org/10.1016/j.amc.2015.06.027.

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26

Osman, Mohamed, Kamal Raslan, Osama Emam, and Farahat Farahat. "Solving Multi-level Multi-objective Fractional Programming Problem with Rough Intervals in the Objective Functions." British Journal of Mathematics & Computer Science 21, no. 2 (2017): 1–17. http://dx.doi.org/10.9734/bjmcs/2017/30626.

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27

Borza, Mojtaba, and Azmin Sham Rambely. "A Linearization based on Taylor Expansion to Multi-Objective Linear Fractional Program with Fuzzy Coefficients and Fuzzy Decision Variables." Sains Malaysiana 53, no. 11 (2024): 3803–15. http://dx.doi.org/10.17576/jsm-2024-5311-22.

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Reaching an efficient solution for multi-objective programming problem (MOPP) is not easy and may encompass some hardships due to existing more than one objective. The aim of this research was to introduce a new efficient method to tackle fully fuzzy multi-objective linear fractional programming problem (FFMOLFPP) i.e., a multi-objective linear fractional programming problem (MOLFPP) with fuzzy coefficients and fuzzy decision variables. To construct the approach, the of the fuzzy numbers, variable transformations, the first-order Taylor series, the membership functions, and the weighted sum me

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28

Solomon, Mohamed, Hegazy Mohamed Zaher, and Naglaa Ragaa Saied. "Intuitionistic fuzzy optimization method for solving multi-objective linear fractional programming problems." International Journal of ADVANCED AND APPLIED SCIENCES 10, no. 4 (2023): 44–52. http://dx.doi.org/10.21833/ijaas.2023.04.006.

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An iterative technique based on the use of parametric functions is proposed in this paper to obtain the best preferred optimal solution of a multi-objective linear fractional programming problem (MOLFPP). Each fractional objective is transformed into a non-fractional parametric function using certain initial values of parameters. The parametric values are iteratively calculated and the intuitionistic fuzzy optimization method is used to solve a multi-objective linear programming problem. Also, some basic properties and operations of an intuitionistic fuzzy set are considered. The development o

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29

Banerjee, Durga, and Surapati Pramanik. "GOAL PROGRAMMING APPROACH TO CHANCE CONSTRAINED MULTI-OBJECTIVE LINEAR FRACTIONAL PROGRAMMING PROBLEM BASED ON TAYLORâ€™S SERIES APPROXIMATION." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 2, no. 2 (2012): 77–80. http://dx.doi.org/10.24297/ijct.v2i2a.6784.

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This paper deals with goal programming approach to chance constrained multi-objective linear fractional programming problem based on Taylorâ€™s series approximation. We consider the constraints with right hand parameters as the random variables of known mean and variance. The random variables are transformed into standard normal variables with zero mean and unit variance. We convert the chance constraints with known confidence level into equivalent deterministic constraints. The goals of linear fractional objective functions are determined by optimizing it subject to the equivalent determinist

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30

Banerjee, Durga, and Surapati Pramanik. "GOAL PROGRAMMING APPROACH TO CHANCE CONSTRAINED MULTI-OBJECTIVE LINEAR FRACTIONAL PROGRAMMING PROBLEM BASED ON TAYLORâ€™S SERIES APPROXIMATION." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 2, no. 2 (2012): 77–80. http://dx.doi.org/10.24297/ijct.v2i2b.2635.

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This paper deals with goal programming approach to chance constrained multi-objective linear fractional programming problem based on Taylorâ€™s series approximation. We consider the constraints with right hand parameters as the random variables of known mean and variance. The random variables are transformed into standard normal variables with zero mean and unit variance. We convert the chance constraints with known confidence level into equivalent deterministic constraints. The goals of linear fractional objective functions are determined by optimizing it subject to the equivalent determinist

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31

Alburaikan, Alhanouf, S. A. Edalatpanah, Rabab Alharbi, and Hamiden Abd El-Wahed Khalifa. "Towards neutrosophic Circumstances goal programming approach for solving multi-objective linear fractional programming problems." International Journal of Neutrosophic Science 23, no. 1 (2024): 350–65. http://dx.doi.org/10.54216/ijns.230130.

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Indeterminacy is common in practical decision-making circumstances. So the mathematical models of decision making represent the situations in a better way if the parameters are considered as neutrosophic. This article studies a general framework of multi-objective neutrosophic linear fractional programming problem (MONLFPP) and proposes unique approach. The issue's parameters are thought of as triangular neutrosophic numbers. The problem is converted into an equal crisp multi-objective linear programming problem (MOLPP) with the help of variable transformation technique and a ranking function.

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32

Osman, M. S., O. E. Emam, and M. A. El sayed. "Interactive Approach for Multi-level Multi-objective Fractional Programming Problem under hybrid uncertainty." Journal of Statistics Applications & Probability 6, no. 3 (2017): 549–66. http://dx.doi.org/10.18576/jsap/060311.

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33

Osman, M. S., O. E. Emam, and M. A. Elsayed. "Interactive Approach for Multi-Level Multi-Objective Fractional Programming Problems with Fuzzy Parameters." Beni-Suef University Journal of Basic and Applied Sciences 7, no. 1 (2018): 139–49. http://dx.doi.org/10.1016/j.bjbas.2017.08.005.

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34

Lotfi, Farhad Hosseinzadeh, Abbas Ali Noora, Gholam Reza Jahanshahloo, Mohammad Khodabakhshi, and Ali Payan. "A linear programming approach to test efficiency in multi-objective linear fractional programming problems." Applied Mathematical Modelling 34, no. 12 (2010): 4179–83. http://dx.doi.org/10.1016/j.apm.2010.04.015.

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35

Rani, Namrata, Vandana Goyal, and Deepak Gupta. "On Solving Bi-level Multi-Objective Fully Quadratic Fractional Optimization Model with Fuzzy Demands." International Journal of Mathematical, Engineering and Management Sciences 6, no. 6 (2021): 1612–28. http://dx.doi.org/10.33889/ijmems.2021.6.6.096.

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This paper has been designed to introduce the method for solving the Bi-level Multi-objective (BL-MO) Fully Quadratic Fractional Optimization Model through Fuzzy Goal Programming (FGP) approach by utilising non-linear programming. In Fully Quadratic Fractional Optimization Model, the objective functions are in fractional form, having quadratic functions in both numerator and denominator subject to quadratic constraints set. The motive behind this paper is to provide a solution to solve the BL-MO optimization model in which number of decision-makers (DM) exists at two levels in the hierarchy. F

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36

Li, Henan, Zhe Hong, and Do Sang Kim. "A Minimax-Program-Based Approach for Robust Fractional Multi-Objective Optimization." Mathematics 12, no. 16 (2024): 2475. http://dx.doi.org/10.3390/math12162475.

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In this paper, by making use of some advanced tools from variational analysis and generalized differentiation, we establish necessary optimality conditions for a class of robust fractional minimax programming problems. Sufficient optimality conditions for the considered problem are also obtained by means of generalized convex functions. Additionally, we formulate a dual problem to the primal one and examine duality relations between them. In our results, by using the obtained results, we obtain necessary and sufficient optimality conditions for a class of robust fractional multi-objective opti

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37

Mishra, Rajashree, Srikumar Acharya, and Berhanu Belay. "Application of Multi-Objective Probabilistic Fractional Programming Problem in Production Planning." International Journal of Operational Research 1, no. 1 (2020): 1. http://dx.doi.org/10.1504/ijor.2020.10034935.

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38

Belay, Berhanu, Srikumar Acharya, and Rajashree Mishra. "Application of multi-objective probabilistic fractional programming problem in production planning." International Journal of Operational Research 43, no. 1/2 (2022): 150. http://dx.doi.org/10.1504/ijor.2022.121491.

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39

Abdalla, Snoor, Ayad Ramadan, and Ronak Abdullah. "Transforming and Solving Multi-Objective Linear Plus Linear Fractional Programming Problem." Diyala Journal For Pure Science 16, no. 4 (2020): 40–58. http://dx.doi.org/10.24237/djps.16.04.531c.

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40

Arya, Rubi, and Pitam Singh. "Fuzzy efficient iterative method for multi-objective linear fractional programming problems." Mathematics and Computers in Simulation 160 (June 2019): 39–54. http://dx.doi.org/10.1016/j.matcom.2018.11.013.

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41

Kharbanda, Pallavi, and Divya Agarwal. "Non-smooth multi-objective fractional programming problem involving higher order functions." International Journal of Computing Science and Mathematics 10, no. 4 (2019): 351. http://dx.doi.org/10.1504/ijcsm.2019.10024352.

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Kharbanda, Pallavi, and Divya Agarwal. "Non-smooth multi-objective fractional programming problem involving higher order functions." International Journal of Computing Science and Mathematics 10, no. 4 (2019): 351. http://dx.doi.org/10.1504/ijcsm.2019.102688.

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43

Hassan, Mansur, Adam Baharum, and Majid Khan Majahar Ali. "Logarithmic penalty function method for invex multi-objective fractional programming problems." Journal of Taibah University for Science 14, no. 1 (2020): 211–16. http://dx.doi.org/10.1080/16583655.2020.1715051.

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44

Khalid Jaber, Waleed, and Zeanab k. jabar. "The method of Weighted Multi objective Fractional Linear Programming Problem (MOFLPP)." Journal of University of Anbar for Pure Science 7, no. 2 (2013): 1–6. http://dx.doi.org/10.37652/juaps.2013.85017.

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45

Lalitha, C. S., Pankaj K. Garg, and Seema Khurana. "Duality for Multi Objective Fractional Programming via Linearization and Scalarization Approaches." OPSEARCH 42, no. 1 (2005): 37–54. http://dx.doi.org/10.1007/bf03398712.

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46

Emam, O. E. "Interactive approach to bi-level integer multi-objective fractional programming problem." Applied Mathematics and Computation 223 (October 2013): 17–24. http://dx.doi.org/10.1016/j.amc.2013.07.085.

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47

Chauhan Priyank Hasmukhbhai and Ritu Khanna. "Multi-objective optimization of lithography alignment using fractional dynamics and fuzzy meta-goal programming." World Journal of Advanced Engineering Technology and Sciences 15, no. 3 (2025): 2179–208. https://doi.org/10.30574/wjaets.2025.15.3.1150.

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Lithography alignment in semiconductor manufacturing demands nanometer-scale precision amidst inherent challenges such as mechanical vibrations, thermal drift, and actuator nonlinearities. Traditional integer-order control strategies often fail to optimally balance competing objectives like positional accuracy, settling time, and energy efficiency. This paper introduces a Fuzzy Meta Goal Programming (FMGP) framework integrated with fractional calculus to address these limitations. The alignment process is modeled using a fractional-order differential equation (FDE) governed by the Caputo deriv

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48

Osman, Mohamed S., Osama E. Emam, Kamal R. Raslan, and Farahat A. Farahat. "Solving Fully Rough Interval Multi-level Multi-objective linear Fractional Programming Problems via FGP." Journal of Statistics Applications & Probability 7, no. 1 (2018): 115–26. http://dx.doi.org/10.18576/jsap/070111.

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Osman, M., O. Emam, and M. Sayed. "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. http://dx.doi.org/10.9734/arjom/2017/34864.

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50

Osman, M., O. Emam, and M. Sayed. "On Parametric Multi-level Multi-objective Fractional Programming Problems with Fuzziness in the Constraints." British Journal of Mathematics & Computer Science 18, no. 5 (2016): 1–19. http://dx.doi.org/10.9734/bjmcs/2016/28531.

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