TOPSIS for Multiple Objective Programming With Rough Decision Set
DOI:
https://doi.org/10.2298/YJOR230614003AKeywords:
TOPSIS, Rough programming, Rough decision set, Multiple objective programmingAbstract
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.References
C.-L. Hwang and A. S. M. Masud, Methods for Multiple Objective Decision Making. Springer Berlin Heidelberg, 1979, p. 21-283.
Z. Pawlak, “Granularity of knowledge, indiscernibility and rough sets,” in 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228), ser. FUZZY-98. IEEE. doi: 10.1109/fuzzy.1998.687467
Y. Yao, “Granular computing: basic issues and possible solutions,” in Proceedings of the 5th Joint Conference on Information Sciences, 2000.
T. Atteya, “Rough multiple objective programming,” European Journal of Operational Research, vol. 248, no. 1, p. 204-210, Jan. 2016. doi: 10.1016/j.ejor.2015.06.079
L. A. Zadeh, “Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic,” Fuzzy Sets and Systems, vol. 90, no. 2, p. 111-127, Sep. 1997. doi: 10.1016/s0165-0114(97)00077-8
Z. Pawlak, “Rough sets,” International Journal of Computer amp; Information Sciences, vol. 11, no. 5, p. 341-356, Oct. 1982. doi: 10.1007/bf01001956
E. A. Youness, “Characterizing solutions of rough programming problems,” European Journal of Operational Research, vol. 168, no. 3, p. 1019-1029, Feb. 2006. doi: 10.1016/j.ejor.2004.05.019
M. S. Osman, E. F. Lashein, E. A. Youness, and T. E. Atteya, “Mathematical programming in rough environment,” Optimization, vol. 60, no. 5, p. 603-611, May 2011. doi: 10.1080/02331930903536393
“Compromise solutions for rough multiple objective decision making problems,” AUSTRALIAN JOURNAL OF BASIC AND APPLIED SCIENCES, 2018. doi: 10.22587/ajbas.2018.12.7.18
Shivani and E. A. Rani, Deepika, “An approach to solve an unbalanced fully rough multiobjective fixed-charge transportation problem,” Computational and Applied Mathematics, vol. 41, no. 4, Apr. 2022. doi: 10.1007/s40314-022-01830-5
Shivani, D. Rani, and A. Ebrahimnejad, “On solving fully rough multi-objective fractional transportation problem: development and prospects,” Computational and Applied Mathematics, vol. 42, no. 6, Aug. 2023. doi: 10.1007/s40314-023-02400-z
N. Gunantara, “A review of multi-objective optimization: Methods and its applications,” Cogent Engineering, vol. 5, no. 1, p. 1502242, Jan. 2018. doi: 10.1080/23311916.2018.1502242
F. Aydin and B. Gümüş, “Comparative analysis of multi-criteria decision making methods for the assessment of optimal svc location,” Bulletin of the Polish Academy of Sciences Technical Sciences, p. 140555-140555, Jan. 2024. doi: 10.24425/bpasts.2022.140555
C.-L. Hwang and K. Yoon, Multiple Attribute Decision Making. Springer Berlin Heidelberg, 1981. ISBN 9783642483189
Y.-J. Lai, T.-Y. Liu, and C.-L. Hwang, “Topsis for modm,” European Journal of Operational Research, vol. 76, no. 3, p. 486-500, Aug. 1994. doi: 10.1016/0377-2217(94)90282-8
Y. Wang, P. Liu, and Y. Yao, “Bmw-topsis: A generalized topsis model based on three-way decision,” Information Sciences, vol. 607, p. 799-818, Aug. 2022. doi: 10.1016/j.ins.2022.06.018
R. E. Bellman and L. A. Zadeh, “Decision-making in a fuzzy environment,” Management Science, vol. 17, no. 4, pp. B-141-B-164, Dec. 1970. doi: 10.1287/mnsc.17.4.b141
Y. Yao and J. Yang, “Granular rough sets and granular shadowed sets: Three-way approximations in pawlak approximation spaces,” International Journal of Approximate Reasoning, vol. 142, p. 231-247, Mar. 2022. doi: 10.1016/j.ijar.2021.11.012
Y. Yao, A Partition Model of Granular Computing. Springer Berlin Heidelberg, 2004, p. 232-253. ISBN 9783540277941
T. Y. Lin, Topological and Fuzzy Rough Sets. Springer Netherlands, 1992, p. 287-304. ISBN 9789401579759
T. Y. Lin and Q. Liu, Rough Approximate Operators: Axiomatic Rough Set Theory. Springer London, 1994, p. 256-260. ISBN 9781447132387
Y. Y. Yao, “Information granulation and rough set approximation,” International Journal of Intelligent Systems, vol. 16, no. 1, p. 87-104, 2000. doi: 10.1002/1098- 111x(200101)16:1<87::aid-int7>3.0.co;2-s
K. Elbess, “A study of some uncertain rough mathematical programming problems,” 2017.
B. Wang, J. Liang, and Y. Yao, “A trilevel analysis of uncertainty measuresin partition-based granular computing,” Artificial Intelligence Review, vol. 56, no. 1, p. 533-575, Apr. 2022. doi: 10.1007/s10462-022-10177-6
Y. Yao, “Perspectives of granular computing,” in 2005 IEEE International Conference on Granular Computing. IEEE, 2005. doi: 10.1109/grc.2005.1547239
Y. Yao, C.-J. Liau, and N. Zhong, Granular Computing Based on Rough Sets, Quotient Space Theory, and Belief Functions. Springer Berlin Heidelberg, 2003, p. 152-159. ISBN 9783540395928
D. DUBOIS and H. PRADE, “Rough fuzzy sets and fuzzy rough sets
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) YUJOR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
