International Journal of Applied Science and Engineering
Published by Chaoyang University of Technology

Amit Kumar and Neha Bhatia1

School of Mathematics and Computer Applications, Thapar University, Patiala India

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The fuzzy set theory is being applied massively in many fields these days. One of these is linear programming problems. Kheirfam and Hasani (Sensitivity analysis for fuzzy linear programming problems with fuzzy variables, Advanced Modeling and Optimization, 12 (2010) 257-272), proposed a method for the sensitivity analysis for fuzzy linear programming (FLP) problems with fuzzy variables. There are some important cases that are not considered by Kheirfam and Hasani. In this paper, those cases are considered and numerical examples are solved.

Keywords: fuzzy linear programming problem; trapezoidal fuzzy numbers; ranking function; sensitivity analysis.

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  1. [1] Bortolan, G. and Degani, R. 1985. A Review of Some Methods for Ranking Fuzzy Subsets, Fuzzy Sets and Systems, 15: 1-19.

  2. [2] Campos, L. and Verdegay, J. L. 1989. Linear Programming Problems and Ranking of Fuzzy Numbers, Fuzzy Sets and Systems, 32: 1-11.

  3. [3] Dutta, D., Rao, J. R., and Tiwari, R. N. 1992. Sensitivity Analysis in Fuzzy Linear Fractional Programming Problem, Fuzzy Sets and Systems, 48: 211-216.

  4. [4] Fuller, R. 1989. On Stability in Fuzzy Linear Programming Problems, Fuzzy Sets and Systems, 30: 339-344.

  5. [5] Gupta, P. and Bhatia, D. 2001. Sensitivity Analysis in Fuzzy Multi-Objective Linear Fractional Programming Problem, Fuzzy Sets and Systems, 122: 229-236.

  6. [6] Hamacher, H., Leberling, H. and Zimmermann, H. J. 1978. Sensitivity Analysis in Fuzzy Linear Programming, Fuzzy Sets and Systems, 1: 269-281.

  7. [7] Kaufmann, A. and Gupta, M. M. 1991. “Introduction to fuzzy arithmetics: Theory and   applications”, Newyork: Van Nostrand Reinhold.

  8. [8] Kheirfam, B. and Hasani, F. 2010. Sensitivity Analysis for Fuzzy Linear programming Problems with Fuzzy Variables, Advanced Modeling and Optimization, 12: 257-272.

  9. [9] Kim, K. and Park, K. S. 1990. Ranking Fuzzy Number with Index of Optimism, Fuzzy Sets and Systems, 35: 143-150.

  10. [10] Liou, T. S. and Wang, M. J. 1992. Ranking Fuzzy Numbers with Integral Value, Fuzzy Sets and Systems, 50: 247-255.

  11. [11] Lotfi, F. H., Jondabeh, M. A., and Faiz rahnemoon, M. 2010. Sensitivity Analysis in Fuzzy Environment, Applied Mathematical Sciences, 4: 1635-1646.

  12. [12] Mahdavi-Amiri, N. and Nasseri, S. H. 2007. Duality Results and a Dual Simplex Method for Linear Programming Problems with Trapezoidal Fuzzy Variables, Fuzzy Sets and Systems, 158: 1961-1978.

  13. [13] Nasseri, S. H., Ardil, E., Yazdani, A., and Zaefarian, R. 2005. Simplex Method for Fuzzy Variable Linear Programming Problems, World Academy of Science, Engineering and Technology, 10: 1307-6884.

  14. [14] Precup, R. E. and Preitl, S. 2006. Stability and Sensitivity Analysis of Fuzzy Control Systems, Mechatronics Applications, 3: 61-76.

  15. [15] Sakawa, M. and Yano, H. 1988. An Interactive Fuzzy Satisfying Method for Multi-objective Linear Fractional Programming Problems, Fuzzy Sets and Systems, 28: 129-144.

  16. [16] Tanaka, H., Ichihashi, H., and Asai, K. 1986. A Value of Information in Fuzzy Linear Programming Problems via Sensitivity Analysis, Fuzzy Sets and Systems, 18: 119-129.

  17. [17] Tanaka, H. and Asai, K. 1984. Fuzzy Linear Programming with Fuzzy Number, Fuzzy Sets and Systems, 13: 1-10.

  18. [18] Verdegay, J. L. and Aguado, C. G. 1993. On the Sensitivity of Membership Function for Fuzzy Linear Programming Problem, Fuzzy Sets and Systems, 56: 47-49.

  19. [19] Zadeh, L. A. 1965.  Fuzzy Sets, Information and Control, 8: 338-353.

  20. [20] Zimmerman, H. J. 1976. Description and Optimization of Fuzzy Systems, International Journal of General Systems, 2: 209-215.


Cite this article:

Kumar, A., Bhatia, N. 2011. A new method for solving sensitivity analysis for fuzzy linear programming problems. International Journal of Applied Science and Engineering, 9, 169–176.