# α-Pareto Optimal Solutions for Fuzzy Multiple Objective Optimization Problems Using MATLAB

α-Pareto Optimal Solutions for Fuzzy Multiple Objective Optimization Problems Using MATLAB

Tarek H.M. Abou-El-Enien

Department of Operations Research & Decision Support, Faculty of Computers & Information, Cairo University, Giza 12613, Egypt

Corresponding Author Email:
t.hanafy@fci-cu.edu.eg
Page:
53-59
|
DOI:
https://doi.org/10.18280/ama_c.730204
18 March 2018
|
Accepted:
2 May 2018
|
Published:
30 June 2018
| Citation

OPEN ACCESS

Abstract:

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.
Keywords:

fuzzy sets, fuzzy Parameters, MATLAB, multiple objective optimization problems, weighting method

1. Introduction
2. Basic Definitions
3. Linear Multiple Objective Optimization Problems with Fuzzy Parameters in the Right Hand Side of the Constraints
4. Linear Multiple Objective Optimization Problems with Fuzzy Parameters in the Objective Functions
5. Conclusions
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