Energy of a fuzzy soft set and its application in decision-making

Document Type : Research Paper

Authors

1 Faculty of Engineering, University of Kragujevac

2 Faculty of Science, University of Kragujevac

Abstract

In our paper, we continue the study of the theory of fuzzy soft sets and their properties. Based on the singular values of the corresponding matrix, we define the energy of a fuzzy soft set, as well as the $\lambda$-energy of a fuzzy soft set, allowing us to introduce an effective method for decision-making. Then, we consider the limits of the defined energies, which are essentially non-negative numerical values. The paper demonstrates through examples how the introduced method can be successfully applied to many problems containing uncertainties. Additionally, the paper includes comparisons of the introduced method with other methods addressing similar problems.

Keywords

Main Subjects

References

C. C. Aggarwal, Linear algebra and optimization for machine learning, Springer Nature Switzerland AG, 2020.
https://doi.org/10.1007/978-3-030-40344-7
[2] H. Akta¸s, N. C¸ a˘gman, Soft sets and soft groups, Information Sciences, 177 (2007), 2726-2735. https://doi.org/
10.1016/j.ins.2006.12.008
[3] T. M. Al-shami, J. C. R. Alcantud, A. Mhemdi, New generalization of fuzzy soft sets: (a, b)–Fuzzy soft sets, AIMS
Mathematics, 8(2) (2023), 2995-3025. https://doi.org/10.3934/math.2023155
[4] J. C. R. Alcantud, A novel algorithm for fuzzy soft set based decision making from multiobserver input parameter
data set, Information Fusion, 29 (2016), 142-148. https://doi.org/10.1016/j.inffus.2015.08.007
[5] J. C. R. Alcantud, Soft open bases and a novel construction of soft topologies from bases for topologies, Mathematics,
8(5) (2020), 672. https://doi.org/10.3390/math8050672
[6] M. I. Ali, F. Feng, X. Y. Liu, W. K. Min, M. Shabir, On some new operations in soft set theory, Computers and
Mathematics with Applications, 57(9) (2009), 1547-1553. https://doi.org/10.1016/j.camwa.2008.11.009
[7] S. Barik, S. Pati, B. K. Sarma, The spectrum of the corona of two graphs, SIAM Journal on Discrete Mathematics,
21(1) (2007), 47-56. https://doi.org/10.1137/05062402
[8] N. C¸ a˘gman, F. Citak, S. Enginoglu, Fuzzy parametrized fuzzy soft set theory and its applications, Turkish Journal
of Fuzzy Systems, 1(1) (2010), 21-35.
[9] N. C¸ a˘gman, S. Enginoglu, Soft matrix theory and its decision making, Computers and Mathematics with Applications,
59(10) (2010), 3308-3314. https://doi.org/10.1016/j.camwa.2010.03.015
[10] N. C¸ a˘gman, S. Enginoglu, Soft set theory and uni-int decision making, European Journal of Operational Research,
207 (2010), 848-855. https://doi.org/10.1016/j.ejor.2010.05.004
[11] N. C¸ a˘gman, S. Enginoglu, F. Citak, Fuzzy soft set theory and its applications, Iranian Journal of Fuzzy Systems,
8(3) (2011), 137-147. https://doi.org/10.22111/ijfs.2011.292
[12] N. C¸ a˘gman, S. Karatas, S. Enginoglu, Soft topology, Computers and Mathematics with Applications, 62(1) (2011),
351-358. https://doi.org/10.1016/j.camwa.2011.05.016
[13] J. Day, W. So, Singular value nequality and graph energy change, Electronic Journal of Linear Algebra, 16 (2007),
291-299. https://doi.org/10.13001/1081-3810.1202
[14] F. Feng, J. B. Jun, X. Liu, L. Li, An adjustable approach to fuzzy soft set based decision making, Journal of
Computational and Applied Mathematics, 234 (2010), 10-20. https://doi.org/10.1016/j.cam.2009.11.055
[15] S. Filipovski, R. Jajcay, New upper bounds for the energy and spectral radius of graphs, MATCH Communications
in Mathematical and in Computer Chemistry, 84 (2020), 335-343.
[16] S. Filipovski, R. Jajcay, Bounds for the energy of graphs, Mathematics, 9(14) (2021), 1687. https://doi.org/10.
3390/math9141687
[17] I. Gutman, The energy of a graph, Ber. Math. Statist. Sekt. Forschungsz. Graz, 103 (1978), 1-22.
[18] I. Gutman, D. Kiani, M. Mirzakhah, B. Zhou, On incidence energy of a graph, Linear Algebra and its Applications,
431 (2009), 1223-1233. https://doi.org/10.1016/j.laa.2009.04.019
[19] M. Jooyandeh, D. Kiani, M. Mirzakhah, Incidence energy of a graph, MATCH Communications in Mathematical
and in Computer Chemistry, 62 (2009), 561-572.
[20] Z. Liu, K. Qin, Z. Pei, A method for fuzzy soft sets in decision-making based on an ideal solution, Symmetry, 9(10)
(2017), 246. https://doi.org/10.3390/sym9100246
[21] P. K. Maji, R. Biswas, A. R. Roy, Fuzzy soft sets, Journal of Fuzzy Mathematics, 9(3) (2001), 598-602.
[22] P. K. Maji, R. Biswas, A. R. Roy, An application of soft sets in decision making problem, Computer and Mathematics
with Applications, 44 (2002), 1077-1083. https://doi.org/10.1016/S0898-1221(02)00216-X
[23] P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Computers and Mathematics with Applications, 45 (2003),
555-562. https://doi.org/10.1016/S0898-1221(03)00016-6
[24] P. Majumdar, S. K. Samanta, On soft mappings, Computer and Mathematics with Applications, 60 (2010), 2666-
2672. https://doi.org/10.1016/j.camwa.2010.09.004
[25] M. Matejdes, Soft topological space and topology on the Cartesian product, Hacettepe Journal of Mathematics and
Statistics, 45(4) (2016), 1091-1100. https://doi.org/10.15672/HJMS.20164513117
[26] D. Molodtsov, Soft set theory-first results, Computers and Mathematics with Applications, 37 (1999), 19-31.
https://doi.org/10.1016/S0898-1221(99)00056-5
[27] D. Molodtsov, The theory of soft sets, URSS Publishers, Moscow (in Russian), 2004.
[28] A. Mukherjee, A. Saha, A. K. Das, Measurable soft sets, International Journal of Open Problems in Computer
Science and Mathematics, 8(4) (2015), 12-25. https://doi.org/10.12816/0023170
[29] V. Nikiforov, The energy of graphs and matrices, Journal of Mathematical Analysis and Applications, 326 (2007),
1472-1475. https://doi.org/10.1016/j.jmaa.2006.03.072
[30] V. Nikiforov, Beyond graph energy: Norms of graphs and matrices, Linear Algebra and its Applications, 506
(2016), 82-138. https://doi.org/10.1016/j.laa.2016.05.011
[31] D. Pei, D. Miao, From soft sets to information systems, in: X. Hu, Q. Liu, A. Skowron, T. Y. Lin, R. R. Yager,
B. Zhang (Eds.), Proceedings of Granular Computing IEEE, 2 (2005), 617-621. https://doi.org/10.1109/GRC.
2005.1547365
[32] S. K. Pezuk, G. Senel, An application of soft multisets to a decision-making problem concerning side effects of
COVID-19 vaccines, Journal of New Theory, 35 (2021), 103-113. https://doi.org/10.53570/jnt.949227
[33] X. S. Qin, G. H. Huang, A. Chakma, X. H. Nie, Q. G. Lin, A MCDM-based expert system for climate-change impacy
assessment and adaptation planning-A case study for the georgia basin, Canada, Expert Systems with Applications,
34(3) (2008), 2164-2179. https://doi.org/10.1016/j.eswa.2007.02.024
[34] M. Riaz, N. C¸ a˘gman, N. Wali, A. Mushtaq, Certain properties of soft multi-set topology with applications in multicriteria decision making, Applications in Management and Engineering, 3(2) (2020), 70-96. https://doi.org/10. 31181/dmame2003070r
[35] M. Riaz, K. Naeem, Measurable soft mappings, Punjab University Journal of Mathematics, 48(2) (2016), 19-34.
[36] M. Riaz, K. Naeem, M. Ozair Ahmad, Novel concepts of soft sets with applications, Annals of Fuzzy Mathematics
and Informatics, 13(2) (2017), 239-251.
[37] A. R. Roy, P. K. Maji, A fuzzy soft set theoretic approach to decision making problems, Journal of Computational
and Applied Mathematics, 203 (2007), 412-418. https://doi.org/10.1016/j.cam.2006.04.008
[38] A. Sezgin, S. Ahmad, A. Mehmood, A new operation on soft sets: Extended difference of soft sets, Journal of New
Theory, 27 (2019), 33-42.
[39] A. Sezgin, A. O. Atagun, On operations of soft sets, Computers and Mathematics with Applications, 61 (2011),
1457-1467. https://doi.org/10.1016/j.camwa.2011.01.018
[40] M. Shabir, M. Naz, On soft topological spaces, Computers and Mathematics with Applications, 61 (2011), 1786-
1799. https://doi.org/10.1016/j.camwa.2011.02.006
[41] T. Som, On the theory of soft sets, soft relation and fuzzy soft relation, Proc. of the National Conference on
Uncertainty: A Mathematical Approach, UAMA-06, Burdwan, (2006), 1-9.
[42] E. Szmidt, Distances and similarities in intuitionistic fuzzy sets, Studies in Fuzziness and Soft Computing, No.
307, Springer, Berlin, (2014). https://doi.org/10.1007/978-3-319-01640-5
[43] P. Vassilev, K. T. Atanassov, Extensions and modifications of intuitionistic fuzzy sets, “Prof. Marin Drinov”
Academic Publishing House, Sofia, Bulgaria, 2019.
[44] C. F. Yang, A note on “Soft Set Theory” [Comput. Math. Appl. 45(4-5) (2003) 555-562], Computers and Mathematics
with Applications, 56 (2008), 1899-1900. https://doi.org/10.1016/j.camwa.2008.03.019
[45] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)
90241-X
[46] J. Zhang, J. Li, New results on the incidence energy of graphs, MATCH Communications in Mathematical and in
Computer Chemistry, 68 (2012), 777-803.
 
Iranian Journal of Fuzzy Systems
Volume 21, Issue 2
March and April 2024
Pages 35-49

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