# TOPSIS for Multiple Objective Programming With Rough Decision Set

• Tarek Abou-El-Enien Department of O.R. & D.S., Faculty of Computers and Artificial Intelligence, Cairo University, Giza 12613, Egypt
• Y. Abo-Elnaga Department of Basic Science, Higher Technological Institute, Tenth of Ramadan City, Egypt
• Kamilia Mohammad Department of Physics and Engineering Mathematics, Faculty of Engineering, Tanta University, Tanta, Egypt

### Abstract

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.

Published
Jan 29, 2024
How to Cite
ABOU-EL-ENIEN, Tarek; ABO-ELNAGA, Y.; MOHAMMAD, Kamilia. TOPSIS for Multiple Objective Programming With Rough Decision Set. Yugoslav Journal of Operations Research, [S.l.], jan. 2024. ISSN 2334-6043. Available at: <https://yujor.fon.bg.ac.rs/index.php/yujor/article/view/1253>. Date accessed: 09 aug. 2024. doi: http://dx.doi.org/10.2298/YJOR230614003A.
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