Topsis for multiple objective programming with rough decision set
Many optimization problems have competing objectives that require being optimized at the same time. These problems are called ?multiple objective programming problems (MOPPs)?. Real-world MOPPs may have some imprecision (roughness) in the decision set and/or the objective functions. These problems a...
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Published in | Yugoslav Journal of Operations Research p. 3 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
2024
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Online Access | Get full text |
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Summary: | Many optimization problems have competing objectives that require being
optimized at the same time. These problems are called ?multiple objective
programming problems (MOPPs)?. Real-world MOPPs may have some imprecision
(roughness) in the decision set and/or the objective functions. These
problems are known as ?rough MOPPs (RMOPPs)?. There is no unique method able
to solve all RMOPPs. Accordingly, the decision maker (DM) should have more
than one method for solving RMOPPs at his disposal so that he can select the
most appropriate method. To contribute in this regard, we propose a new
method for solving a specific class of RMOPPs in which all the objectives
are precisely defined, but the decision set is roughly defined by its lower
and upper approximations. Our proposed method is a modified version of the
Technique for Order Preference by Similarity to Ideal Solution (TOPSIS).
TOPSIS was chosen as the foundation for our method because it is one of the
most widely applied methods for solving MOPPs. The basic concept underlying
TOPSIS is that the compromise solution is closer to the ideal solution while
also being farther away from the anti-ideal solution. The conventional
TOPSIS can only solve MOPPs with precise (crisp) definitions of the two main
parts of the problem. We extend TOPSIS to optimize multiple precise
objectives over an imprecise decision set. The proposed approach is depicted
in a flowchart. A numerical example is given to demonstrate the
effectiveness of our proposed method to solve RMOPPs with a rough decision
set at different values of objectives? weights and using different
Lp-metrics. |
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ISSN: | 0354-0243 1820-743X |
DOI: | 10.2298/YJOR230614003A |