Hierarchical generation of α-Pareto optimal solutions in large-scale multi-objective non-linear systems with fuzzy parameters

This paper proposes a decomposition method for hierarchical generation of α-Pareto optimal solutions in large-scale multi-objective non-linear programming (MONLP) problems with fuzzy parameters in the objective functions and in the constraints (FMONLP). These fuzzy parameters are characterized by fu...

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Bibliographic Details
Published in:Applied mathematical modelling Vol. 32; no. 6; pp. 930 - 957
Main Authors: Abo-Sinna, Mahmoud A., Amer, Azza H., Ibrahim, Ashraf S.
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 01.06.2008
Elsevier Science
Subjects:
Applied sciences
Decision theory. Utility theory
Decomposition method
Exact sciences and technology
Fuzzy multi-objective non-linear programming problem
Fuzzy set theory
Interactive decision-making
Lagrangian function and Kuhn–Tucker conditions
Operational research and scientific management
Operational research. Management science
Weighting method
α-Pareto optimality
Fuzzy multi-objective non-linear programming problem
Decomposition method
Interactive decision-making
Fuzzy set theory
Weighting method
Lagrangian function and Kuhn–Tucker conditions
α-Pareto optimality
Interactive programming
Pareto optimum
Decision support system
Decision making
Multiobjective programming
Non linear programming
Fuzzy set
Non linear system
Global solution
Fuzzy logic
Multiscale method
Kuhn Tucker condition
Fuzzy decision
Large scale
Objective function
Fuzzy number
Lagrangian function
Lagrangian function and Kuhn-Tucker conditions
ISSN:0307-904X
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Summary:This paper proposes a decomposition method for hierarchical generation of α-Pareto optimal solutions in large-scale multi-objective non-linear programming (MONLP) problems with fuzzy parameters in the objective functions and in the constraints (FMONLP). These fuzzy parameters are characterized by fuzzy numbers. For such problems, the concept of α-Pareto optimality introduced by extending the ordinary Pareto optimality based on the α-level sets of fuzzy numbers. The decomposition method is based on the principle of decompose the original problem into interdependent sub-problems. In this method, the global multi-objective non-linear problem is decomposed into smaller multi-objective sub-problems. The smaller sub-problems, which obtained solved separately by using the weighting method and through an operative procedure. All these solution are coordinates in such a way that an optimal solution for the global problem achieved. In addition, an interactive fuzzy decision-making algorithm for hierarchical generation of α-Pareto optimal solution through the decomposition method is developed. Finally, two numerical examples given to illustrate the results developed in this paper.
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ISSN:0307-904X
DOI:10.1016/j.apm.2007.02.035