### Solving Fuzzy Linear Programming Problem Using Defuzzification Method

Nalla Veerraju, V. Lakshmi Prasannam

#### Abstract

Linear Programming (LP) has been one of the efficient, reliable and time tested techniques in Optimization. Conventional LP is not suitable for many real time problems which involve data with inherent vagueness or impreciseness. Fuzzy set theory is proved to be quite good in addressing the inherent vagueness or impreciseness and thus Fuzzy Linear Programming (FLP) is brought to light and developed over the years. A quite good number of techniques have been proposed for solving FLP problems to obtain optimal solution for real world problems involving fuzzy (vague or imprecise) environment. In this paper, “Extended Geometric Mean Defuzzification” is defined and based on it, a method is proposed for solving FLP problems. To showcase the advantages of the proposed method, different problems of FLP, available in the literature, are discussed. Numerical comparisons are also provided to validate the authentication of the proposed method.

#### Keywords

Fuzzy sets; Fuzzy numbers; Geometric mean defuzzification; Fuzzy linear programming

PDF

#### References

T. Allahviranloo, F.H. Lotfi, M.K. Kiasary, N.A. Kiani and L. Alizadeh, Solving full fuzzy linear programming problem by the ranking function, Applied Mathematical Sciences 2(1) (2008), 19 – 32.

R.E. Bellman and L.A. Zadeh, Decision making in a fuzzy environment, Management Science 17 (1970), 141 – 164, DOI: 10.1287/mnsc.17.4.B141.

B. Bhardwaj and A. Kumar, A note on “A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem”, Applied Mathematical Modelling 39(19) (2015), 5982 – 5985, DOI: 10.1016/J.APM.2014.07.033.

J.J. Buckley and T. Feuring, Evolutionary algorithm solution to fuzzy problems: fuzzy linear programming, Fuzzy Sets and Systems 109 (2000), 35 – 53, DOI: 10.1016/S0165-0114(98)00022-0.

S.K. Das, T. Mandal and S.A. Edalatpanah, A mathematical model for solving fully fuzzy linear programming problem with trapezoidal fuzzy numbers, Applied Intelligence 46 (2017), 509 – 519, DOI: 10.1007/s10489-016-0779-x.

M. Dehghan, B. Hashemi and M. Ghatee, Computational methods for solving fully fuzzy linear systems, Applied Mathematics and Computation 179 (2006), 328 – 343, DOI: 10.1016/J.AMC.2005.11.124.

J.Y. Dong and S.P. Wan, A new trapezoidal fuzzy linear programming method considering the acceptance degree of fuzzy constraints violated, Knowledge-Based Systems 148 (2018), 100 – 114, DOI: 10.1016/J.KNOSYS.2018.02.030.

R. Ezzati, E. Khorram and R. Enayati, A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem, Applied Mathematical Modelling 39(12) (2015), 3183 – 3193, DOI: 10.1016/J.APM.2013.03.014.

K. Ganesan and P. Veeramani, Fuzzy linear programs with trapezoidal fuzzy numbers, Annals of Operations Research 143 (2006), 305 – 315, DOI: 10.1007/S10479-006-7390-1.

A. Hosseinzadeh and S.A. Edalatpanah, A new approach for solving fully fuzzy linear programming by using the lexicography method, Advances in Fuzzy Systems 2016 (2016), 1 – 6, DOI: 10.1155/2016/1538496.

A. Kumar and J. Kaur, A new method for solving fuzzy linear programs with trapezoidal fuzzy numbers, Journal of Fuzzy Set Valued Analysis 2011 (2011), Article ID jfsva-00102, 12 pages, https://www.researchgate.net/publication/265975660_A_New_Method_for_Solving_Fuzzy_Linear_Programs_with_Trapezoidal_Fuzzy_Numbers/fulltext/54aade570cf2bce6aa1d75d4/A-New-Method-for-Solving-Fuzzy-Linear-Programs-with-Trapezoidal-Fuzzy-Numbers.pdf.

A. Kumar, J. Kaur and P. Singh, A new method for solving fully fuzzy linear programming problems, Applied Mathematical Modelling 35(2) (2011), 817 – 823, DOI: 10.1016/J.APM.2010.07.037.

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 Modelling 33 (2009), 3151 – 3156, DOI: 10.1016/J.APM.2008.10.020.

F. Mahmoudi and S.H. Nesseri, A new approach to solve fully fuzzy linear programming problem, Journal of Applied Research on Industrial Engineering 6(2) (2019), 139 – 149, DOI: 10.22105/jarie.2019.183391.1090.

H.S. Najafi and S.A. Edalatpanah, A note on “A new method for solving fully fuzzy linear programming problems”, Applied Mathematical Modelling 37 (2013), 7865 – 7867, DOI: 10.1016/J.APM.2013.02.039.

N. Veerraju, V.L. Prasannam and L.N.P.K. Rallabandi, Defuzzification index for ranking of fuzzy numbers on the basis of geometric mean, International Journal of Intelligent Systems and Applications 2020(4) (2020), 13 – 24, DOI: 10.5815/ijisa.2020.04.02.

DOI: http://dx.doi.org/10.26713%2Fcma.v12i2.1510

### Refbacks

• There are currently no refbacks.

eISSN 0975-8607; pISSN 0976-5905