Document Type : Review Paper
Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood Road, Pretoria 0002, South Africa.
Department of Computer Science, University of Illinois at Springfield,, One University Plaza, Springfield, IL 62703, USA.
Department of Mathematics, School of Sciences, University of Management and Technology, Lahore 54000, Pakistan.
The aim of this paper is to investigate different definitions of soft points in the existing literature on soft set theory and its extensions in different directions. Then limitations of these definitions are illustrated with the help of examples. Moreover, the definition of soft point in the setup of fuzzy soft set, intervalvalued fuzzy soft set, hesitant fuzzy soft set and intuitionistic soft set are also discussed. We also suggest an approach to unify the definitions of soft point which is more applicable than the existing notions.
- Murtaza, G., Abbas, M., & Ali, M. I. (2019). Fixed points of interval valued neutrosophic soft mappings. Filomat, 33(2), 463-474.
- Abbas, M., Murtaza, G., & Smarandache, F. (2020). Basic operations on hypersoft sets and hypersoft point. Neutrosophic sets and systems, 35, 407-421. http://fs.unm.edu/NSS2/index.php/111/article/view/34
- Smarandache, F. (2018). Extension of soft set to hypersoft set, and then to plithogenic hypersoft set. Neutrosophic sets and systems, 22, 168-170.
- Molodtsov, D. (1999). Soft set theory—first results. Computers & mathematics with applications, 37(4-5), 19-31.
- Maji, P. K., Roy, A. R., & Biswas, R. (2002). An application of soft sets in a decision making problem. Computers & mathematics with applications, 44(8-9), 1077-1083.
- Ali, M. I., Feng, F., Liu, X., Min, W., & Shabir, M. (2009). On some new operations in soft set theory. Computers & mathematics with applications, 57(9), 1547-1553.
- Aygünoğlu, A., & Aygün, H. (2012). Some notes on soft topological spaces. Neural computing and applications, 21(1), 113-119.
- Das, S., & Samanta, S. K. (2013). Soft metric. Ann. Fuzzy Math. Inform. 6 (1), 77—94.
- Das, S., & Samanta, S. K. (2012). Soft real sets, soft real numbers and their properties. fuzzy Math, 20(3), 551-576.
- Mishra, S., & Srivastava, R. (2015). Hausdorff fuzzy soft topological spaces. Fuzzy Math. Inform, 9(2), 247-260.
- Neog, T. J., Sut, D. K., & Hazarika, G. C. (2012). Fuzzy soft topological spaces. J. Latest Trend Math, 2(1), 54-67.
- Osmanoglu, I., & Tokat, (2013). On intuitionistic Fuzzy soft topology. General mathematics notes, 19(2), 59-70.
- Senel, G. (2017). A comparative research on the definition of soft point. International journal of computer applications, 163(2), 1-5.
- El-Shafei, M. E., Abo-Elhamayel, M., & Al-Shami, T. M. (2018). Partial soft separation axioms and soft compact spaces. Filomat, 32(13), 4755-4771.
- Al-Shami, T. M., & Abo-Tabl, E. A. (2021). Soft a-separation axioms and a-fixed soft points. AIMS mathematics, 6(6), 5675-5694.
- Shabir, M., & Naz, M. (2011). On soft topological spaces. Computers & mathematics with applications, 61(7), 1786-1799.
- Wardowski, D. (2013). On a soft mapping and its fixed points. Fixed point theory and applications, 2013(1), 1-11.
- Zorlutuna, İ., Akdag, M., Min, W. K., & Atmaca, S. (2012). Remarks on soft topological spaces. Annals of fuzzy mathematics and informatics, 3(2), 171-185.