A method for solving possibilistic multi-objective linear programming problems with fuzzy decision variables

Document Type : Research Paper

Authors

1 PhD of Operations Research Management, University of Tehran, Tehran, Iran

2 Prof. in Electrical Engineering, Amirkabir University of Technology, Tehran, Iran

3 Assistant Prof., Industrial Management, University of Tehran, Tehran, Iran

Abstract

[Naeini1] In this paper, a new method is proposed to find the fuzzy optimal solution of fuzzy multi-objective linear programming problems (FMOLPp) with fuzzy right hand side and fuzzy decision variables. Due to the imprecise nature of available resources, determination of a definitive solution to the model seems impossible. Therefore, the proposed model is designed in order to make fuzzy decisions. The model resolves the deficiencies of the previous models presented in this field and its main advantage is simplicity. To illustrate the efficiency of the proposed method, it is applied to the problem of allocating orders to suppliers. Due to the nature of the fuzzy solutions obtained from solving the model, the decision maker will be faced with more flexibility in decision making.



 

Keywords


Allahviranloo, T., Lotfi, F.H., Kiasary, M.K., Kiani, N.A. & Alizadeh, L., (2008). Solving full fuzzy linear programming problem by the ranking function. Applied Mathematical Science, 2, 19–32. (In Persian )
 
Buckley, J.J. & Feuring, T. (2000). Evolutionary algorithm solution to fuzzy problems: fuzzy linear programming. Fuzzy Sets and Systems, 109, 35–53.
 
Dehghan, M., Hashemi, B. & Ghatee, M. (2006). Computational methods for solving fully fuzzy linear systems. Applied Mathematics and Computations, 179: 328–343. (In Persian)
 
Farquhar, P. (1984). Utility assessment methods. Management Science, 30: 1283–1300.
 
Harker, P. & Vargas, L. (1987). The theory of ratio scale estimations: Saaty’s analytic hierarchy process. Management Science, 33(11): 1383–1403.
 
Hashemi, S.M., Modarres, M., Nasrabadi, E. & Nasrabadi, M. M. (2006). Fully fuzzified linear programming, solution and duality. Journal of Intelligent Fuzzy Systems, 17, 253–261. (In Persian)
 
Keeney, R. & Raiffa, H. (1976). Decision with Multiple Objectives: Preference and Value Trade-off, John Wiley. New York.
 
Kumar, A., Kaur, J. & Singh, P. (2011). A new method for solving fully fuzzy linear programming problems. Applied Mathematical Modeling. 35, 817–823.
 
Lai, Y. J. & Hwang, C. L. (1992). Fuzzy Mathematical Programming: methods and applications, Springer. Berlin.
 
Lotfi, F. H., Allahviranloo, T., Jondabeha, M. A. & Alizadeh, L. (2009). Solving a fully fuzzy linear programming using lexicography method and fuzzy approximate solution. Applied Mathematical Modeling, 33, 3151–3156. (In Persian)
 
Mahdavi Amiri, N. & 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. (In Persian)
 
Maleki, H. R., Tata, M. & Mashinchi, M. (2000). Linear programming with fuzzy variables. Fuzzy Sets and Systems, 109: 21–33. (In Persian)
 
Menhaj, M. B., (2007). Fuzzy Computations. Daneshnegar Publication, Tehran, 324–329. (In Persian)
 
Saaty, T. (1986). Axiomatic foundation of the analytic hierarchy process. Management Science, 32(7): 841–855.
 
 Shafer, G. A. (1976). Mathematical Theory of Evidence, Princeton University Press.
 
Steuer, R. (1986). Multiple criteria optimization: Theory, Computation and Applications, John Wiley. New York.
 
Tanaka, H., Guo, P. & Zimmermann, H.J. (2000). Possibility distributions of fuzzy decision variables obtained from possibilistic linear programming problems. Fuzzy Sets and Systems, 113: 323-332.
 
Tanaka, H., Okuda, T. & Asai, K. (1973). On fuzzy mathematical programming. Journal of Cybernetics Systems, 3: 37–46.
 
Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8: 338–353.
 
Zimmermann, H.J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1: 45–55.