Parametric sensitivity analysis is one of the most interesting research topics in linear programming with fuzzy variables (FVLP), and it is also a basic tool for studying perturbations in optimization problems, that is perturbation analysis. The focus of this paper is on two kinds of parametric linear programming with fuzzy variables (PFVLP) which can describe the behaviors of the optimal value under parametric perturbations of the objective function coefficients and the right-hand side of constraint equations in a FVLP, respectively. Firstly, for these two kinds of PFVLP, we investigate how to obtain an optimal basis of them from an optimal basis of their corresponding FVLP based on the parameters in them. Then, two algorithms are proposed to solve these two problems. Finally, two examples are illustrated to show that the PFVLP models proposed in this paper can provide more accurate and scientific suggestions for decision-makers.
BelmanR.E. and ZadehL.A., Decision making in a fuzzy environment, Management Science17 (1970), 141–164.
2.
MalekiH.R., TataM. and MashinchiM., Linear programming with fuzzy variables, Fuzzy Sets and Systems109 (2000), 21–33.
3.
NasseriS.H., ArdilE., YazdaniA. and ZaefarianR., Simplex method for solving linear programming problems with fuzzy numbers, Transactions on Engineering, Computing and Technology10 (2005), 284–288.
4.
GanesanK. and VeeramaniP., Fuzzy linear programs with trapezoidal fuzzy numbers, Annals of Operations Research143 (2006), 305–315.
5.
Mahdavi-AmiriN., NasseriS.H. and YazdaniA., Fuzzy primal simplex algorithms for solving fuzzy linear programming problems, Iranian Journal of Operations Research1 (2009), 68–84.
6.
NasseriS.H., AttariH. and EbrahimnejadA., Revised simplex method and its application for solving fuzzy linear programming problems, European Journal of Industrial Engineering6 (2012), 259–280.
7.
NasseriS.H. and KhabiriB., Revised fuzzy simplex algorithm for linear programming problems with fuzzy variables using linear ranking functions, International Journal of Mathematics and Computation6 (2010), 44–55.
8.
NasseriS.H. and AlizadehZ., Solving linear programming problem with fuzzy right hand sides: A penalty method, The Journal of Mathematics and Computer Science3 (2011), 318–328.
9.
SigarpichL.A., AllahviranlooT., HosseinzadehF. and KianiN.A., Degeneracy in fuzzy linear programming and its application, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems19 (2011), 999–1012.
10.
Yi-HuaZ., Yan-LinJ. and YanY., A revised simplex method of solving degenerate linear programming problems with fuzzy variables, Fuzzy Systems and Mathematics28(6) (2014), 98–104. (in Chinese).
11.
EbrahimnejadA., Some new results in linear programs with trapezoidal fuzzy numbers: Finite convergence of the Ganesan and Veeramani’s method and a fuzzy revised simplex method, Applied Mathematical Modelling35 (2011), 4526–4540.
12.
Zhang-XiaZ. and Bing-YuanC., Fuzzy linear programming problems with fuzzy variables, Fuzzy Systems and Mathematics22(1) (2008), 115–119. (In China).
13.
EbrahimnejadA. and NasseriS.H., Using complementary slackness property to solve linear programming with fuzzy parameters, Fuzzy Information and Engineering3 (2009), 233–245.
14.
Mahdavi-AmiriN. and NasseriS.H., Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables, Fuzzy Sets and Systems158 (2007), 1961–1978.
15.
EbrahimnejadA. and NasseriS.H., A dual simplex method for bounded linear programmes with fuzzy numbers, International Journal of Mathematics in Operational Research2 (2010), 762–779.
16.
EbrahimnejadA., NasseriS.H., Hosseinzadeh LotfiF. and
SoltanifarM., A primal-dual method for linear programming problems with fuzzy variables, European Journal of Industrial Engineering4 (2010), 189–209.
17.
NasseriS.H., EbrahimnejadA. and MizunoS., Duality in fuzzy linear programming with symmetric trapezoidal numbers, Applications and Applied Mathematics5 (2010), 1467–1482.
18.
NasseriS.H. and EbrahimnejadA., A new approach to duality in fuzzy linear programming, Fuzzy Engineering and Operations Research147 (2012), 17–29.
19.
EbrahimnejadA., Sensitivity analysis in fuzzy number linear programming problems, Mathematical and Computer Modelling53 (2011), 1878–1888.
20.
FarhadiniaB., Sensitivity analysis in interval-valued trapezoidal fuzzy number linear programming problems, Applied Mathematical Modelling38(1) (2014), 50–62.
21.
KheirfamB. and VerdegayJ.L., The dual simplex method and sensitivity analysis for fuzzy linear programming with symmetric trapezoidal numbers, Fuzzy Optim Decis Making12 (2013), 171–189.
22.
EbrahimnejadA. and VerdegayJ.L., A novel approach for sensitivity analysis in linear programs with trapezoidal fuzzy numbers, Journal of Intelligent & Fuzzy Systems27 (2014), 173–185.
23.
BhatiaN. and KumarA., Mehar’s method for solving fuzzy sensitivity analysis problems with LR flat fuzzy numbers, Applied Mathematical Modelling36(9) (2012), 4087–4095.
24.
Kheirfam and Hasani, Sensitivity analysis for fuzzy linear programming problems with fuzzy variables, Advanced Modeling and Optimization12 (2010), 257–272.
25.
NasseriS.H. and EbrahimnejadA., Sensitivity analysis on linear programming problems with trapezoidal fuzzy variables, International Journal of Operations Research and Information Systems (IJORIS)2 (2011), 22–39.
26.
Kumar and Bhatia, Sensitivity analysis for fuzzy linear programming problems. In Rough Sets, Fuzzy Sets, Data Mining and Granular Computing, SpringerBerlin Heidelberg, 2011, pp. 103–110.
27.
JiaY., YangY. and ZhongY., Parametric study of fuzzy number linear programming, Computational Intelligence and Security (CIS), 2013 9th International Conference on IEEE, 2013, pp. 339–343.
28.
Yi-HuaZ., Yan-LinJ., DandanC. and YanY., Interior point method for solving fuzzy number linear programming problems using linear ranking function, Journal of Applied Mathematics (2013), 9. Article ID 795098.
29.
YagerR.R., A procedure for ordering fuzzy subsets of the unit interval, Information Sciences24(2) (1981), 143–161.
30.
FortempsP. and RoubensM., Ranking and defuzzification methods based on area compensation, Fuzzy Sets and Systems82(3) (1996), 319–330.
