An optimal solution to multi-goal fuzzy linear programming problems using elementary transformations

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Authors

  • Ramakant Bhardwaj Amity University Kolkata WB
  • Arti Shrivastava Department of Mathematics, Rabindranath Tagore University, Bhopal
  • Bharti Saxena Department of Mathematics, Rabindranath Tagore University, Bhopal
  • Vandana Rathore 2School of Engineering and Technology, Jagran Lakecity University, Bhopal

Keywords:

Linear Programming Problem (LPP), Multi-goal, Elementary Transformation Method, Triangular Number.

Abstract

This article explores how to solve multipurpose problems to obtain optimal solutions using fuzzy linear programming. Our goal is to minimize production and transportation costs by using the most basic transportation methods and comparing the results to conventional methods. We discuss the results of numerical examples and illustrate this method.

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References

Y. Tan and Y. Long, “Option-game approach to analyze technology innovation investment under fuzzy environment,” Journal of Applied Mathematics, vol. 2012, Article ID 830850, 9 pages, 2012.

L. Zhang, X. Xu, and L. Tao, “Some similarity measures for triangular fuzzy number and their applications in multiple criteria group decision-making,” Journal of Applied Mathematics, vol. 2013, Article ID 538261, 7 pages, 2013.

H. Tsai and T. Chen, “A fuzzy nonlinear programming approach for optimizing the performance of a four-objective fluctuation smoothing rule in a wafer fabrication factory,” Journal of Applied Mathematics, vol. 2013, Article ID 720607, 15 pages, 2013.

M. Delgado, J. L. Verdegay, and M. A. Vila, “A general model for fuzzy linear programming,” Fuzzy Sets and Systems, vol. 29, no. 1, pp. 21–29, 1989.

H. Rommelfanger, “Fuzzy linear programming and applications,” European Journal of Operational Research, vol. 92, no. 3, pp. 512–527, 1996.

N. van Hop, “Solving fuzzy (stochastic) linear programming problems using superiority and inferiority measures,” Information Sciences, vol. 177, no. 9, pp. 1977–1991, 2007.

M. Jiménez, M. Arenas, A. Bilbao, and M. V. Rodríguez, “Linear programming with fuzzy parameters: an interactive method resolution,” European Journal of Operational Research, vol. 177, no. 3, pp. 1599–1609, 2007.

H.-C. Wu, “Optimality conditions for linear programming problems with fuzzy coefficients,” Computers & Mathematics with Applications, vol. 55, no. 12, pp. 2807–2822, 2008.

X. Liu, “Measuring the satisfaction of constraints in fuzzy linear programming,” Fuzzy Sets and Systems, vol. 122, no. 2, pp. 263–275, 2001.

J. Chiang, “Fuzzy linear programming based on statistical confidence interval and interval-valued fuzzy set,” European Journal of Operational Research, vol. 129, no. 1, pp. 65–86, 2001.

K. D. Jamison and W. A. Lodwick, “Fuzzy linear programming using a penalty method,” Fuzzy Sets and Systems, vol. 119, no. 1, pp. 97–110, 2001.

T. León and E. Vercher, “Solving a class of fuzzy linear programs by using semi-infinite programming techniques,” Fuzzy Sets and Systems, vol. 146, no. 2, pp. 235–252, 2004.

N. Mahdavi-Amiri and S. H. Nasseri, “Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables,” Fuzzy Sets and Systems, vol. 158, no. 17, pp. 1961–1978, 2007.

K. Ganesan and P. Veeramani, “Fuzzy linear programs with trapezoidal fuzzy numbers,” Annals of Operations Research, vol. 143, no. 1, pp. 305–315, 2006.

H. R. Maleki, M. Tata, and M. Mashinchi, “Linear programming with fuzzy variables,” Fuzzy Sets and Systems, vol. 109, no. 1, pp. 21–33, 2000.

S. M. Hashemi, M. Modarres, E. Nasrabadi, and M. M. Nasrabadi, “Fully fuzzified linear programming, solution and duality,” Journal of Intelligent and Fuzzy Systems, vol. 17, no. 3, pp. 253–261, 2006.

T. Allahviranloo, F. H. Lotfi, M. K. Kiasary, N. A. Kiani, and L. Alizadeh, “Solving fully fuzzy linear programming problem by the ranking function,” Applied Mathematical Sciences, vol. 2, no. 1–4, pp. 19–32, 2008.

F. H. Lotfi, T. Allahviranloo, M. A. Jondabeh, and L. Alizadeh, “Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution,” Applied Mathematical Modelling, vol. 33, no. 7, pp. 3151–3156, 2009.

A. Kumar, J. Kaur, and P. Singh, “A new method for solving fully fuzzy linear programming problems,” Applied Mathematical Modelling, vol. 35, no. 2, pp. 817–823, 2011.

X. Guo and D. Shang, “Fuzzy approximate solution of positive fully fuzzy linear matrix equations,” Journal of Applied Mathematics, vol. 2013, Article ID 178209, 7 pages, 2013.

Published

24-04-2024

How to Cite

Bhardwaj, R., Shrivastava, A. ., Saxena, B., & Rathore , V. (2024). An optimal solution to multi-goal fuzzy linear programming problems using elementary transformations : -. Communications in Mathematics and Applications, 15(1). Retrieved from http://www.rgnpublications.com/journals/index.php/cma/article/view/2402

Issue

Vol. 15 No. 1 (2024)

Section

Research Article

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