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I present a computational view to generate α-Pareto optimal solutions for the fuzzy multiple objective optimization problems based on the α-Level sets method and the weighting method using
. In this paper, two MATLAB codes based on two hybrid algorithms for solving linear multiple objective programming problems involving fuzzy parameters in: (1) The right hand side of the constraints, and (2) The objective functions are introduced. These fuzzy parameters are characterized as fuzzy numbers. For such problems, the α-Pareto optimality is introduced by extending the ordinary Pareto optimality on the basis of the α-Level sets of fuzzy numbers. Also, two numerical examples are given to clarify the main results developed in the paper. The hand solutions of the numerical examples and the solutions by the MATLAB codes are identical.fuzzy sets, fuzzy Parameters, MATLAB, multiple objective optimization problems, weighting method
[1] Chankong V, Haimes YY. (1983). Multiobjective decision making: Theory and methodology. North- Holand. Series in Science and Engineering, New York.
[2] Hwang CL, Masud ASM. (1979). Multiple objective decision making methods and applications. Springer-Verlag, New York, USA. https://doi.org/10.1007/978-3-642-45511-7
[3] Zeleny M. (1982). Multiple criteria decision making. McGraw-Hill, New York.
[4] Branch MA, Grace A. (1996). Optimization Toolbox, User's Guide. The MathWorks Inc.
[5] Lopez CP. (2014). MATLAB Optimization Techniques. Apress Academic, Springer, New York, USA.
[6] Math W. (2010). MATLAB Reference Guide. The MathWorks Inc., Natick.
[7] Venkataraman P. (2009). Applied Optimization with MATLAB Programming. 2ed, John Wiley & Sons, Inc, New Jersey, USA.
[8] Bellman RE, Zadeh LA. (1970). Decision-making in fuzzy environment. Management Science B 17: 141-164. https://doi.org/10.1287/mnsc.17.4.B141
[9] Dubois D, Prade A. (1980). Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York.
[10] El-Sawy AA, El-Khouly NA, Abou-El-Enien THM. (2000). An algorithm for decomposing the parametric space in large scale linear vector optimization problems: A fuzzy approach. AMSE Journals, Advances in Modelling and Analysis C 55(2): 1-16.
[11] Sakawa M, Yano H. (1989). Interactive decision-making for multiobjective programming problems with fuzzy parameters. Fuzzy Sets and Systems 29: 315-326.
[12] Zimmermann HJ. (1987). Fuzzy Sets, Decision Making, and Expert Systems. Kluwer Academic Publishers, Boston, USA.
[13] Sharma S, Bhattacharjee S, Bhattacharya A. (2015). Solution of multi-objective optimal DG placement problems using swine influenza model based optimization (SIMBO). AMSE Journals, Advances C 70(1): 46-70.