Fuzzy Linear Programming Problems and Solutions Using Ranking Function and Simplex Method

Authors

  • Kumari Tanu Mittal  Research Scholar, University Department of Mathematics, B. R. A. Bihar University, Muzaffarpur, Bihar, India
  • Dr. Ashok Kumar Sah  Assistant Professor, Department of Mathematics, Dr. R. M. L. S. College, Muzaffarpur, B. R. A. Bihar University, Muzaffarpur, Bihar, India

Keywords:

Fully Fuzzy Linear Programming (FFLP), Linear Programming Problem (LPP), Triangular Fuzzy Number (TFN), LR-Flat Fuzzy Numbers (LRFFN), (Multi Objective Linear Programming Problem (MOLP).

Abstract

In this paper fuzzy linear programming problems and solutions using ranking function and simplex method with various techniques are discussed. The modeling and solving the optimization problems that come across our real life and business is one of the most important daily problems. Fuzzy linear programming problem is one of the most powerful tools to deal with the imprecise nature (not well-defined) of data. From studies it is noted that mathematical programming problem has a well-defined objective function and set of constraints, the systematic determination of optimal solutions leads to the development of large numbers of methods and algorithms.

References

  1. Control Mehdi Dehghan, Behnam Hashemi, Mehdi Ghate, Computational Methods for Solving Fully Fuzzy Linear Systems, Applied mathematics and Computational 179(2006)328-343.
  2. T. Allahviranlov, F. Hosseinzadeh Lotif, M. Kh-Kiasary, N. A. Kiani and L. Alizadeh, Solving Fully Fuzzy Linear Programming problem by Ranking Function, Applied Mathematical Sciences, vol.2, 2008(19-32).
  3. Amit Kumar, Jagdeep Kaur, A new method for solving fuzzy linear programming with trapezoidal fuzzy numbers, Journal of Fuzzy Set Valued Analysis, vol.2011, doi:10.5899/201/jfsva-00102.
  4. Amit Kumar, Jagdeep Kaur and Pushpinder Singh, New method for solving Fully fuzzy Linear Programming Problems, Applied Mathematical Modelling, 35(2011)817-823.
  5. M. Jayalakshmi and P. Pandian, A new method for finding an optimal fuzzy solution for fully fuzzy linear programming problems, vol. 2, issue-4, July-Aug 2012(247-254).
  6. Amit Kumar & Jagdeep Kaur, General form of LPP with fuzzy parameters, Journal of Applied Research and Technology, 629-635, vol. 11, ost-2013.
  7. Jagdeep Kaur, Amit Kumar, Mehar’s Method for solving Fully Fuzzy Linear Programming Problems, Applied Mathematical Modeling 37(2013)7142-7153.
  8. Neha Bhatia, Amit Kumar, Mehar’s Method for solving fuzzy sensitivity analysis problems with LR flat fuzzy Numbers, Applied Mathematical Modelling, 36(2012)4087-4095.
  9. Izaz Ullah Khan, Tahir Ahmed, Narmah Maan, A simplified novel technique for solving fully fuzzy linear programming problems, J option Theory Appl(2013)159:536-546.
  10. H. Saberi Najafi, S. A. Edalatpanah, A note on “A new method for solving fully fuzzy linear programming problems”, Applied Mathematical Modelling 37(2013)7865-7867.
  11. Abbas Hatami, Hamed Kazemipoor, Solving fully fuzzy linear programming with symmetric trapezoidal fuzzy numbers using Mehar’s Method, J. Math.Comput. Sci. 4(2014) No.2, 463-470, http://scik.org.
  12. Uday Shrama, A new method to solve fuzzy linear programming problem, International Journal of Science and Research (IJSR), vol. 4, Issue.7, July 2015.
  13. R. Ezzati, E. Kharram and R. Enayati, A new algorithm to solve fully fuzzy linear programming problems using MOLP problem, Applied Mathematical Modelling39(2015)3183-3193.
  14. A. Hosseinzadeh & S. A. Edalatpanah, A new approach for solving fully fuzzy linear programming problems by using the lexicography method, Advances in Fuzzy Systems, Vol.2016, http://dx.doi.org/10.1155/2016/153896

International Journal of Scientific Research in Science and Technology

Downloads

Published

2023-08-30

Issue

Volume 9, Issue 6, November-December-2022

Section

Research Articles

License

Copyright (c) IJSRST

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
Kumari Tanu Mittal, Dr. Ashok Kumar Sah, " Fuzzy Linear Programming Problems and Solutions Using Ranking Function and Simplex Method, International Journal of Scientific Research in Science and Technology(IJSRST), Online ISSN : 2395-602X, Print ISSN : 2395-6011, Volume 9, Issue 6, pp.738-743, November-December-2022.