Pareto-optimal solution for multiple objective linear programming problems with fuzzy goals

Several methods have been addressed to attain fuzzy-efficient solution for the multiple objective linear programming problems with fuzzy goals (FMOLP) in the literature. Recently, Jimenez and Bilbao showed that a fuzzy-efficient solution may not guarantee to be a Pareto-optimal solution in the case...

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Bibliographic Details
Published in:Fuzzy optimization and decision making Vol. 14; no. 1; pp. 43 - 55
Main Authors: Wu, Yan-Kuen, Liu, Chia-Cheng, Lur, Yung-Yih
Format: Journal Article
Language:English
Published: Boston Springer US 01.03.2015
Springer Nature B.V
Subjects:
Artificial Intelligence
Calculus of Variations and Optimal Control; Optimization
Decision making
Fuzzy
Fuzzy logic
Fuzzy set theory
Fuzzy sets
Linear programming
Mathematical analysis
Mathematical Logic and Foundations
Mathematical models
Mathematics
Mathematics and Statistics
Multiple objective
Operations Research/Decision Theory
Optimization
Pareto optimum
Probability Theory and Stochastic Processes
Production planning
Simplex method
Studies
Fuzzy-efficient solution
Pareto-optimal solution
Multiple objective linear programming problems
Two-phase approach
ISSN:1568-4539, 1573-2908
Online Access:Get full text
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Summary:Several methods have been addressed to attain fuzzy-efficient solution for the multiple objective linear programming problems with fuzzy goals (FMOLP) in the literature. Recently, Jimenez and Bilbao showed that a fuzzy-efficient solution may not guarantee to be a Pareto-optimal solution in the case that one of fuzzy goals is fully achieved. To show this point they employ Guu and Wu’s two-phase approach to obtain a fuzzy-efficient solution first, then a model like a conventional goal programming problem is proposed to find a Pareto-optimal solution. In this study, a new simplified two-phase approach is proposed to find a Pareto-optimal solution for FMOLP without relying on the results of Guu and Wu’s two-phase approach. This new simplified two-phase approach not only obtains the Pareto-optimal solution but also provides more potential information for decision makers. Precisely, decision makers can find out whether the fuzzy goals of objective function are overestimated or not and the amount of overestimation can easily be computed if it exists.
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ISSN:1568-4539
1573-2908
DOI:10.1007/s10700-014-9192-2