Study of the Fuzzy Optimal Solution of Fully Fuzzy Linear Programming Problems

Authors

  • Prof. Mushtaque Khan Professor of Mathematics, K. R. College, Gopalganj, J. P. University, Chapra Author
  • Md. Raza Ansari Research Scholar, University Department of Mathematics, J. P. University, Chapra Author

Keywords:

Fuzzy Integer Linear Programming, Linear Programming Problem, Fuzzy Number

Abstract

In this paper, a new method is proposed to find the fuzzy optimal solution of fully fuzzy linear programming problems with triangular fuzzy numbers. The proposed method is very easy to understand and to apply for fully fuzzy linear programming problems occurring in real life situations as compared to the existing methods.

Downloads

Download data is not yet available.

References

T. Allahviranloo, F. Hosseinzadeh, M.Kh Kiassary, N.A Kiani and L.Alizadeh, “Solving fully fuzzy linear programming problem by the ranking function”, Applied mathematical sciences, vol.8, pp. 19-32, 2008.

Amit kumar, Jagdeep kaur and pushpinder sign, “Fuzzy optimal solution of fully fuzzy linear programming problems with inequality constraints”, International Journal of mathematical and computer science, pp. 37-40, 2010.

Km T. Mittal and A. K. Sah, “Fuzzy linear programming problems and solutions using Ranking function and simplex method”, IJSRST, vol.9, Issue 6, pp. 738-743, 2022.

R.E Bellman and L.A Zadeh ,“Decision making in a fuzzy environment”, Management sciences, vol.17, pp. 141-164, 1970.

J.M. Cadenas and J.L. Verdegay, “Using Fuzzy Numbers in linear programming”, IEEE Transactions on Systems, vol. 27, pp. 1016-1022, 1997.

S.Chanas, “The use of parametric programming in fuzzy linear programming”, Fuzzy Sets and Systems, vol. 11, pp. 229-241, 1983.

S.C.Fang, C.F.Hu, H.F.Wang and S.Y. Wu, “Linear programming with fuzzy coefficients in constraints”, Computers and Mathematics with Applications, vol.37, pp.63-76, 1999.

M.Jimenez, M.Arenas, A.Bilbao and M.V. Rodrguez, “Linear programming with fuzzy parameters: An Interactive Method Resolution”, European Journal of Operation Research, vol. 177, pp. 1599-1609, 2007.

Km T. Mittal and A. K. Sah, “Fuzzy linear programming problems and solutions using Ranking function and simplex method”, IJSRST, vol.9, Issue 6, pp. 738-743, 2022.

Kolman and Hill, “Fuzzy variable linear programming by use of a certain linear ranking function”, Applied Mathematics, vol.18, 1984.

F.H.Lotfi, T. Allahviranloo, M.A. Jondabeha and L.Alizadeh, “Solving a fully fuzzy linear programming using Lexicography method and fuzzy Approximate solution”, Applied Mathematical Modeling, vol.33, pp. 3151-3156, 2009.

H.R. Maleki, M.Tata and M. Mashinchi, “Linear programming with fuzzy variable”, Fuzzy sets and systems, pp. 21-33, 2000.

A.Nagoor Gani and S.N. Mohamed Assarudeen, “A new operation on triangular fuzzy number for solving fully fuzzy linear programming problem”, Applied Mathematical sciences, vol.6, No.11, pp. 525-632, 2012.

S.H. Nasseri and Z.Alizade, “Solving linear programming problem fuzzy with right hand sides”,Mathematics and computer science, vol.3, No.3, pp. 318-328, 2011.

H.M.Nehi, H.R. Maleki and M.Mashinichi, “Solving Fuzzy number linear programming problem by Lexicographic Ranking function”, Italian Journal of pure and applied Mathematics, vol .15, pp. 9-20, 2004.

J.Ramik, “Duality in fuzzy linear programming: Some New concepts and Results”, Fuzzy Optimization and decision Making, vol. 4, pp. 25-39, 2005.

B.Werners, “An interactive fuzzy programming system, Fuzzy sets and systems”, vol.23, pp. 131-147, 1987.

G.Zhang, Y.H.Wu, M.Remias and J.Lu, “Formulation of Fuzzy linear programming problems as Four-Objective Constrained Optimization problems”, Applied Mathematics and Computation, vol. 139, pp. 383-399, 2003.

H.J. Zimmermann, “Fuzzy programming and linear programming with objective functions”, Fuzzy sets and systems, vol.1, pp. 37-46, 1978.

Downloads

Published

13-03-2024

Issue

Section

Research Articles

How to Cite

Study of the Fuzzy Optimal Solution of Fully Fuzzy Linear Programming Problems . (2024). International Journal of Scientific Research in Science and Technology, 11(2), 984-987. https://ijsrst.com/index.php/home/article/view/IJSRST24113254

Similar Articles

1-10 of 59

You may also start an advanced similarity search for this article.