On solutions of fuzzy multi-objective programming problems through weighted coefficients in two-Phase approach

Document Type: Research Paper

Author

Department of Operations Research, Institute of Statistical Studies and Research, Cairo University, Giza, Egypt.

Abstract

In this paper, a Fuzzy Multi-Objective Linear Programming (FMOLP) problem having both objective functions and constraints fuzzy parameters is introduced. Theses fuzzy parameters are characterized by trapezoidal fuzzy numbers. The FMOLP problem is converted into the corresponding deterministic MOLP problem through the use of intervals arithmetic operations. Then, a two-phase approach having equal weighted coefficients is proposed to generate an efficient solution for the MOLP problem. The major advantage of the new model is that the proposed approach as long as the weighted coefficients not necessarily equal and generates an efficient solution. A numerical example is given to clarify the obtained results.
 

Keywords

Main Subjects


[1]      Bitran, G. R. (1980). Linear multiple objective problems with interval coefficients. Management science26(7), 694-706.

[2]      Dubois, D. J. (1980). Fuzzy sets and systems: Theory and applications. Academic press.

[3]       Garg, H. (2015). Multi-objective optimization problem of system reliability under intuitionistic fuzzy set environment using Cuckoo Search algorithm. Journal of intelligent & fuzzy systems29(4), 1653-1669.

[4]      Garg, H. (2018). Some arithmetic operations on the generalized sigmoidal fuzzy numbers and its application. Granular computing3(1), 9-25.

[5]       Garg, H. (2018). Arithmetic operations on generalized parabolic fuzzy numbers and its application. Proceedings of the national academy of sciences, India section A: Physical sciences88(1), 15-26.

[6]      Garg, H. (2018). Analysis of an industrial system under uncertain environment by using different types of fuzzy numbers. International journal of system assurance engineering and management9(2), 525-538.

[7]       Gasimov, R. R., & Yenilmez, K. (2002). Solving fuzzy linear programming problems with linear membership function. Turkish journal of mathematics26(4), 375-396.

[8]      Hamadameen, A. O. (2017). A novel technique for solving multiobjective fuzzy linear programming problems. ARO-the scientific journal of Koya university5(1), 1-8.

[9]      Kaufmann, A., & Gupta, M. M. (1988). Fuzzy mathematical models in engineering and management science. New York, NY, USA: Elsevier Science Inc.

[10]  Singh, S. K., & Yadav, S. P. (2017). Intuitionistic fuzzy multi-objective linear programming problem with various membership functions. Annals of operations research, 1-15.

[11]  Moore, R. E. (1979). Methods and applications of interval analysis. Siam.

[12]  Philip, J. (1972). Algorithms for the vector maximization problem. Mathematical programming, 2(1): 207- 229.

[13]  Rani, D., Gulati, T. R., & Garg, H. (2016). Multi-objective non-linear programming problem in intuitionistic fuzzy environment: optimistic and pessimistic view point. Expert systems with applications64, 228-238.

[14]  Sakawa, M., & Yano, H. (1985). Interactive decision making for multi-objective linear fractional programmingproblems with fuzzy parameters. Cybernetics and system16(4), 377-394.

[15]  Steuer, R. E. (1986). Multiple criteria optimization. Theory, computation and applications.

[16]   Shaocheng, T. (1994). Interval number and fuzzy number linear programmings. Fuzzy sets and systems66(3), 301-306.

[17]  Veeramani, C., Duraisamy, C., & Nagoorgani, A. (2011). Solving fuzzy multi-objective linear programming problems with linear membership functions. Australian journal of basic and applied sciences5(8), 1163-1171.

[18]   Wang, F. H., & Wang, L. M. (1996). A decision making procedure of a fuzzy multiobjecttive linear problem. Journal of the Chinese institute of industrial engineers, 13(1), 1-10.

[19]  Zadeh, L. A. (1965). Fuzzy sets. Information control, (8) 338- 353.

[20]   Zimmermann, H. J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy sets and systems1(1), 45-55.