Goal Programming Approach to Solve Multi-Objective Intuitionistic Fuzzy Non- Linear Programming Models

S.Rukmani; R.Sophia Porchelvi

doi:https://doi.org/10.14445/22315373/IJMTT-V53P562

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 53 | Number 7 | Year 2018 | Article Id. IJMTT-V53P562 | DOI : https://doi.org/10.14445/22315373/IJMTT-V53P562

Goal Programming Approach to Solve Multi-Objective Intuitionistic Fuzzy Non- Linear Programming Models

S.Rukmani, R.Sophia Porchelvi

Citation :

S.Rukmani, R.Sophia Porchelvi, "Goal Programming Approach to Solve Multi-Objective Intuitionistic Fuzzy Non- Linear Programming Models," International Journal of Mathematics Trends and Technology (IJMTT), vol. 53, no. 7, pp. 505-514, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V53P562

Abstract

In this Paper Multi-objective Intuitionistic Fuzzy Non-linear Programming Problem has been solved through goal programming approach. Solving non-linear programming problem straightaway is quite difficult. So, the Multi-objective Intuitionistic Fuzzy Non-linear Programming Problem is transformed into Multi-objective Intuitionistic Fuzzy Linear Programming Problem by the use of Taylor Polynomial Series. Intuitionistic fuzzy goal programming approach is discussed by forming suitable membership and non-membership function in which the aspiration level and the tolerance levels are fixed by the decision maker or by finding the best and worst solution of each objective function. Using the membership and non-membership function of each objective, the given problem was formulated and the solutions are found by various approaches and the obtained solutions are identical. Numerical example will illustrate the efficiency of the proposed approach.

Keywords

PNon-Linear Programming, Goal Programming, Intuitionistic Fuzzy Set.

References

[1] H.J. Zimmermann (1978), “ Fuzzy programming and linear programming with several objective functions”, Fuzzy Sets and Systems, vol.1, 45-55
[2] P.P.Angelov (1997), “Optimization in intuitionistic fuzzy environment”, Fuzzy Sets and Systems, vol.86, 299-306
[3] R. Sophia Porchelvi (2010), “An Algorithmic approach to Multi-objective fuzzy linear programming problem”, International Journal of Algorithms, Computing & Mathematics, Eashwar Publications, 3(4),61-66
[4] Rajesh Dangwal(2012), “Taylor series solution of multi-objective linear fractional programming problem by vague set”, International Journal of Fuzzy Mathematics and Systems, Vol.2, No.3, 245-253
[5] Mahapatra.G.S(2010), “Intuitionistic fuzzy multi-objective mathematical programming on reliability optimization model”, International Journal of Fuzzy Systems, Vol-12, No-3, pp.259-266
[6] Samir Dey and Tapan Kumar Roy(2015), “Intutionistic Fuzzy Goal Programming Technique for Solving Non-Linear Multi-Objective Structural Problem”, Journal of Fuzzy Set Valued Analysis, No.3, pp.179-193
[7] Pramanik.S and Roy.T.K(2005), “An intuitionistic fuzzy goal programming approach to vector oprimization problem”, Notes on Intuitionistic Fuzzy sets, Vol-11, No-1, pp.1-14.
[8] Attanassov.K.T. (1986) , “Intuitionistic fuzzy sets”, Fuzzy Sets and Systems, Vol-20, pp.87-96.