Fuzzy Goal Programming to Optimization the Multi-Objective Problem

Azzabi Lotfi; Ayadi Dorra; Bachar Kaddour; Kobi Abdessamad

doi:doi:10.11648/j.sjams.20140201.12

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Fuzzy Goal Programming to Optimization the Multi-Objective Problem

Azzabi Lotfi, Ayadi Dorra, Bachar Kaddour, Kobi Abdessamad

Published in Science Journal of Applied Mathematics and Statistics (Volume 2, Issue 1)

Received: 13 November 2013 Accepted: Published: 20 February 2014

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Abstract

Many present-day problems are multi-objective in nature and their solution requires consideration of conflicting objectives. Usually, they have a number of potentially Pareto-optimal solutions. An extensive knowledge of the problem is required in discriminating between solutions, eliminating the unwanted ones and accepting the required solution(s) by a decision making process. It is well known that multi-objective optimization model had found a lot of important applications in decision making problems such as in economics theory, management science and engineering design. Because of these applications, a lot of literatures have been published to study optimality conditions, duality theories and topological properties of solutions of multi-objective optimization problems. In the case of optimization problems, the idea of regularizing a problem by adding a strongly convex term to the objective function can actually be treated back at least. The regularization technique proved to be an invaluable tool in the solution of ill-posed problems, and an enormous amount of work has been devoted to its study. In this paper, a Multi-objective Optimization Problems formulation based on a Goal Programming Methods solves the multi-objective problem which can tackle relatively large test systems. This method is based on optimization of the most preferred objective and considering the other objectives as constraints.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 2, Issue 1)
DOI	10.11648/j.sjams.20140201.12
Page(s)	14-19
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Multicriteria Approach, Multi-Objective Optimization Problems, Fuzzy Goal Programming

References

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APA Style

Azzabi Lotfi, Ayadi Dorra, Bachar Kaddour, Kobi Abdessamad. (2014). Fuzzy Goal Programming to Optimization the Multi-Objective Problem. Science Journal of Applied Mathematics and Statistics, 2(1), 14-19. https://doi.org/10.11648/j.sjams.20140201.12

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ACS Style

Azzabi Lotfi; Ayadi Dorra; Bachar Kaddour; Kobi Abdessamad. Fuzzy Goal Programming to Optimization the Multi-Objective Problem. Sci. J. Appl. Math. Stat. 2014, 2(1), 14-19. doi: 10.11648/j.sjams.20140201.12

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AMA Style

Azzabi Lotfi, Ayadi Dorra, Bachar Kaddour, Kobi Abdessamad. Fuzzy Goal Programming to Optimization the Multi-Objective Problem. Sci J Appl Math Stat. 2014;2(1):14-19. doi: 10.11648/j.sjams.20140201.12

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@article{10.11648/j.sjams.20140201.12,
  author = {Azzabi Lotfi and Ayadi Dorra and Bachar Kaddour and Kobi Abdessamad},
  title = {Fuzzy Goal Programming to Optimization the Multi-Objective Problem},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {2},
  number = {1},
  pages = {14-19},
  doi = {10.11648/j.sjams.20140201.12},
  url = {https://doi.org/10.11648/j.sjams.20140201.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20140201.12},
  abstract = {Many present-day problems are multi-objective in nature and their solution requires consideration of conflicting objectives. Usually, they have a number of potentially Pareto-optimal solutions. An extensive knowledge of the problem is required in discriminating between solutions, eliminating the unwanted ones and accepting the required solution(s) by a decision making process. It is well known that multi-objective optimization model had found a lot of important applications in decision making problems such as in economics theory, management science and engineering design. Because of these applications, a lot of literatures have been published to study optimality conditions, duality theories and topological properties of solutions of multi-objective optimization problems. In the case of optimization problems, the idea of regularizing a problem by adding a strongly convex term to the objective function can actually be treated back at least. The regularization technique proved to be an invaluable tool in the solution of ill-posed problems, and an enormous amount of work has been devoted to its study. In this paper, a Multi-objective Optimization Problems formulation based on a Goal Programming Methods solves the multi-objective problem which can tackle relatively large test systems. This method is based on optimization of the most preferred objective and considering the other objectives as constraints.},
 year = {2014}
}

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TY  - JOUR
T1  - Fuzzy Goal Programming to Optimization the Multi-Objective Problem
AU  - Azzabi Lotfi
AU  - Ayadi Dorra
AU  - Bachar Kaddour
AU  - Kobi Abdessamad
Y1  - 2014/02/20
PY  - 2014
N1  - https://doi.org/10.11648/j.sjams.20140201.12
DO  - 10.11648/j.sjams.20140201.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 14
EP  - 19
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20140201.12
AB  - Many present-day problems are multi-objective in nature and their solution requires consideration of conflicting objectives. Usually, they have a number of potentially Pareto-optimal solutions. An extensive knowledge of the problem is required in discriminating between solutions, eliminating the unwanted ones and accepting the required solution(s) by a decision making process. It is well known that multi-objective optimization model had found a lot of important applications in decision making problems such as in economics theory, management science and engineering design. Because of these applications, a lot of literatures have been published to study optimality conditions, duality theories and topological properties of solutions of multi-objective optimization problems. In the case of optimization problems, the idea of regularizing a problem by adding a strongly convex term to the objective function can actually be treated back at least. The regularization technique proved to be an invaluable tool in the solution of ill-posed problems, and an enormous amount of work has been devoted to its study. In this paper, a Multi-objective Optimization Problems formulation based on a Goal Programming Methods solves the multi-objective problem which can tackle relatively large test systems. This method is based on optimization of the most preferred objective and considering the other objectives as constraints.
VL  - 2
IS  - 1
ER  -

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Author Information

Azzabi Lotfi

LASQUO/ISTIA/ University of Angers France
Ayadi Dorra

LASQUO/ISTIA/ University of Angers France
Bachar Kaddour

ESSCA Angers France
Kobi Abdessamad

LASQUO/ISTIA/ University of Angers France

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Plain Text BibTeX RIS

APA Style

Azzabi Lotfi, Ayadi Dorra, Bachar Kaddour, Kobi Abdessamad. (2014). Fuzzy Goal Programming to Optimization the Multi-Objective Problem. Science Journal of Applied Mathematics and Statistics, 2(1), 14-19. https://doi.org/10.11648/j.sjams.20140201.12

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ACS Style

Azzabi Lotfi; Ayadi Dorra; Bachar Kaddour; Kobi Abdessamad. Fuzzy Goal Programming to Optimization the Multi-Objective Problem. Sci. J. Appl. Math. Stat. 2014, 2(1), 14-19. doi: 10.11648/j.sjams.20140201.12

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AMA Style

Azzabi Lotfi, Ayadi Dorra, Bachar Kaddour, Kobi Abdessamad. Fuzzy Goal Programming to Optimization the Multi-Objective Problem. Sci J Appl Math Stat. 2014;2(1):14-19. doi: 10.11648/j.sjams.20140201.12

Copy | Download

@article{10.11648/j.sjams.20140201.12,
  author = {Azzabi Lotfi and Ayadi Dorra and Bachar Kaddour and Kobi Abdessamad},
  title = {Fuzzy Goal Programming to Optimization the Multi-Objective Problem},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {2},
  number = {1},
  pages = {14-19},
  doi = {10.11648/j.sjams.20140201.12},
  url = {https://doi.org/10.11648/j.sjams.20140201.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20140201.12},
  abstract = {Many present-day problems are multi-objective in nature and their solution requires consideration of conflicting objectives. Usually, they have a number of potentially Pareto-optimal solutions. An extensive knowledge of the problem is required in discriminating between solutions, eliminating the unwanted ones and accepting the required solution(s) by a decision making process. It is well known that multi-objective optimization model had found a lot of important applications in decision making problems such as in economics theory, management science and engineering design. Because of these applications, a lot of literatures have been published to study optimality conditions, duality theories and topological properties of solutions of multi-objective optimization problems. In the case of optimization problems, the idea of regularizing a problem by adding a strongly convex term to the objective function can actually be treated back at least. The regularization technique proved to be an invaluable tool in the solution of ill-posed problems, and an enormous amount of work has been devoted to its study. In this paper, a Multi-objective Optimization Problems formulation based on a Goal Programming Methods solves the multi-objective problem which can tackle relatively large test systems. This method is based on optimization of the most preferred objective and considering the other objectives as constraints.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Fuzzy Goal Programming to Optimization the Multi-Objective Problem
AU  - Azzabi Lotfi
AU  - Ayadi Dorra
AU  - Bachar Kaddour
AU  - Kobi Abdessamad
Y1  - 2014/02/20
PY  - 2014
N1  - https://doi.org/10.11648/j.sjams.20140201.12
DO  - 10.11648/j.sjams.20140201.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 14
EP  - 19
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20140201.12
AB  - Many present-day problems are multi-objective in nature and their solution requires consideration of conflicting objectives. Usually, they have a number of potentially Pareto-optimal solutions. An extensive knowledge of the problem is required in discriminating between solutions, eliminating the unwanted ones and accepting the required solution(s) by a decision making process. It is well known that multi-objective optimization model had found a lot of important applications in decision making problems such as in economics theory, management science and engineering design. Because of these applications, a lot of literatures have been published to study optimality conditions, duality theories and topological properties of solutions of multi-objective optimization problems. In the case of optimization problems, the idea of regularizing a problem by adding a strongly convex term to the objective function can actually be treated back at least. The regularization technique proved to be an invaluable tool in the solution of ill-posed problems, and an enormous amount of work has been devoted to its study. In this paper, a Multi-objective Optimization Problems formulation based on a Goal Programming Methods solves the multi-objective problem which can tackle relatively large test systems. This method is based on optimization of the most preferred objective and considering the other objectives as constraints.
VL  - 2
IS  - 1
ER  -

Copy | Download