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ABS Solution of Linear Programming Problems with Fuzzy Variables

Author Affiliations

  • 1Department of Mathematics, Government Engineering College, Ajmer, Rajasthan, India
  • 2Bhagwant University Ajmer, Rajasthan, India

Res. J. Mathematical & Statistical Sci., Volume 4, Issue (7), Pages 1-6, August,12 (2016)

Abstract

ABS method has been broadly used to solve linear and nonlinear system of equations containing a good number of variables and constraints. In this paper, ABS method is being applied to solve linear programming problems with fuzzy variables provided that degeneracy has been treated correctly. This can be verified by graphical method and simplex method of linear programming problems.

References

  1. Tanaka H., Okuda T. and Asai K. (1973)., On Fuzzy Mathematical Programming., Journal of Cybernetics and Systems, 3, 37-46.
  2. Zimmerman H.J. (1978)., Fuzzy Programming and Linear Programming with Several Objective Functions., Fuzzy Sets and Systems, 1, 45-55.
  3. Campos L. and Verdegay J.L. (1989)., Linear Programming Problems and Ranking of Fuzzy Numbers., Fuzzy Sets and Systems, 32, 1-11.
  4. Feng E., Wang X. and Wang X. L. (1997)., On the Application of the ABS algorithm to Linear Programming and Linear Complementarily., OMS, 8,133-142.
  5. Feng S.C., Hu C.F., Wang H.F. and Wu S.Y. (1999)., Linear Programming with Fuzzy Coefficients in Constraints., Computers and Mathematics with Applications, 37, 63-76.
  6. Liu X. (2001)., Measuring the Satisfaction of Constraints in Fuzzy Linear Programming., Fuzzy Sets and Systems, 122, 263-275.
  7. Zhang G., Wu Y.H., Remias M. and Lu. J. (2003)., Formulation of Fuzzy Linear Programming Problems as Four- Objective Constrained Optimization Problems., Applied Mathematics and Computation, 139, 383-399.
  8. Spedicato E., Li- Ping Pang, Xia Zun- Quan and Wang Wei (2004)., A Method for Solving Linear Inequality System., QDMSIA, 19.
  9. Esmaeili H., Mahdavi- Amiri, Nezam and Spedicato E. (2004)., Explicit ABS Solution of a Class of Linear Inequality System and LP Problems., Bulletin of the Iranian Mathematical Society, 30(2), 21-38.
  10. Ramik J. (2005)., Duality in Fuzzy Linear Programming: Some New Concepts and Results., Fuzzy Optimization and Decision Making, 4, 25-39.
  11. Nasseri S.H. (2008)., A New Method for Solving Fuzzy Linear Programming by Solving Linear Programming., Applied Mathematical Sciences, 2, 2473-2480.
  12. Ebrahimnejad A. and Nasseri S.H. (2009)., Using Complementary Slackness Property to Solve Linear Programming with Fuzzy Parameters., Fuzzy Information and Engineering, 1, 233-245.
  13. Ebrahimnejad A., Nasseri S.H., Lotfi F.H. and Soltanifar M. (2010)., A Primal-Dual Method for Linear Programming Problems with Fuzzy Variables., European Journal of Industrial Engineering, 4, 189-209.