Stratified simplex method for solving fuzzy multi-objective linear programming problem
Abstract: The objective of this paper is to deal with a kind of fuzzy multi-objective linear programming(FMOLP)problems involving symmetric trapezoidal fuzzy numbers. Several methods has been proposed in the literature in order to obtain fuzzy efficient solution to FMOLP problem. In this paper, we change the FMOLP problem into the complete stratified fuzzy linear programming problem, then use the stratified simplex method to obtain the fuzzy optimal solution directly without converting them to crisp linear programming problem. We then prove that this fuzzy optimal solution is the fuzzy efficient solution of the original FMOLP problem. A numerical example is given to illustrate the proposed method.
Keywords: fuzzy multi-objective linear programming, symmetric trapezoidal fuzzy numbers, fuzzy efficient solution, stratified simplex method
Category 1: Linear, Cone and Semidefinite Programming
Category 2: Linear, Cone and Semidefinite Programming (Linear Programming )
Citation:  R.E.Bellman, L.A.Zadeh, Decision making in a fuzy envionment, Management Sci. 17(1970),141-164.  M.Duran Toksar, Taylor series approach to fuzzy multiobjective linear fractional programming, Information Sciences 178(2008),1189-1204.  A.Ebrahimnejad, Some new results in linear programs with trapezoidal fuzzy num- bers:Finite convergence of the Ganesan and Veeramani’s method and a fuzzy revised simplex method, Applied Mathematical Modelling 35(2011),4526-4540.  K.Ganesan, P.Veeramani, Fuzzy linear programs with trapezolidal fuzzy numbers, Ann Oper Res 143(2006),305-315.  Hong-Zhong Huang, Wei-Dong Wu and Chun-Sheng Liu, A coordination method for fuzzy multi-objective optimization of system reliability, Journal of Intelligent Fuzzy Systems 16(2005),213-220.  Ibrahim A.Baky, Fuzzy goal programming algorithm for solving decentralized bi-level multi-objective programming problems, Fuzzy Set and Systems 160(2009),2701-2713.  Mariano Jiménez, Amelia Bilbao, Pareto-optimal solutions in fuzzy multi-objective linear programming, Fuzzy Set and Systems 160(2009),2714-2721.  Sukhpreet Kaur Sidhu, Amit Kumar, S.S.Appadoo, Mehar Methods for Fuzzy Optimal Solution and Sensitivity Analisis of Fuzzy Linear Programming with Symmetric Trapezoidal Fuzzy Numbers, Mathematical Problems in Engineering (2014),http://dx.doi.org/10.1155/2014/697085  Behrouz Kherirfam, José-Luis Verdegay, The dual simplex method and sensitivity analysis for fuzzy linear programming with symmetric trapezoidal numbers, Fuzzy Optim Decis Making (2012).DOI 10.1007/s 10700-012-9152-7  Amit Kumar, Pushpinder Singh, Parmpreet Kuar, Amarpreet Kuar, A new ap- proach for ranking of L-R tyre generalized fuzzy number, Expert Systems with Ap- plications 38(2011),10906-10910.  Amit Kumar, Jagdeep Kaur, Pushpinder Singh, A new method for solving fully fuzzy linear programming problems, Applied Mathematical Modelling 35(2011),817- 823.  Y.J.Lai and C.L.Hwang, A new approach to some possibilistic linear programming problems, Fuzzy Sets and Systems 49(1992),121-133.  Jie Lu, Fengjie Wu and Guangquan Zhang, On a generalized fuzzy goal optimization for solving fuzzy multi-objective linear programming problems, Journal of Intelligent Fuzzy Systems 18(2007),83-97.  M.K.Luhandjula, Multiple objective programming problems with possibilistic coef- ficients, Fuzzy Set and Systems 21(1987),135-145.  N.Mahdavi-Amiri, S.H.Nasseri, Duality results and a dual simplex method for lin- ear programming problems with trapezoidal fuzzy variables, Fuzzy Set and Systems 158(2007),1961-1978.  Masatoshi Sakawa, Kosuke Kato, Interactive decision making for large-scale multi- objective linear programs with fuzzy number, Fuzzy Set and Systems 88(1997),161- 172.  Tong Shaocheng, Interval number and fuzzy number linear programming, Fuzzy Set and Systems 66(1994),301-306.  H.Tanaka, K.Asai, Fuzzy linear programming problems with fuzzy numbers, Fuzzy Set and Systems 13(1984),1-10.  H.Tanaka, T.Okudo, K.Asai, On fuzzy mathematical programming, J.Cybernet. 3(1974),37-46.  F.J.Wu, J.Lu, G.Q.Zhang, A new approximate algorithm for solving multiple ob- jective linear programming problems with fuzzy parameters, Appl. Math. Comput. 174(2006),524-544.  H.J.Zimmermann, Fuzzy programming and linear programming with sveral objec- tive functions , Fuzzy Sets and Systems 1(1978),45-55.
Entry Submitted: 01/14/2015
Modify/Update this entry
|Visitors||Authors||More about us||Links|
Search, Browse the Repository
Give us feedback
|Optimization Journals, Sites, Societies|