Isolated Monad Points on Amply Soft Topological Spaces

Öz

In this study, isolated monad points are introduced. For any amply soft set, an amply soft set of isolated monad points on amply soft topological spaces is defined. The relationship between limit monad points, closure points and isolated monad points is mentioned and some properties related to these are given. While creating amply soft sets in the given examples, special focus is given to amply soft topologies that are created by selecting real numbers from both universal and parametric spaces, unlike traditional soft sets.

Anahtar Kelimeler

• A new extended soft set
• Amply soft set
• Amply soft topology
• Isolated monad point
• Limit monad point

Amply Soft Topolojik Uzaylar Üzerinde İzole Monad Noktaları

Öz

Bu çalışmada, izole monad noktaları tanıtılmıştır. Herhangi bir amply soft küme için, amply soft topolojik uzaylar üzerindeki izole monad noktalarının amply soft kümesi oluşturulmuştur. Limit monad noktaları ve kapanış noktaları ile izole monad noktaları arasındaki ilişkiye değinilmiş ve bununla ilgili bazı özellikler verilmiştir. Verilen örneklerde amply soft kümeler oluşturulurken, geleneksel soft kümelerden farklı olarak hem evrensel hem de parametrik uzaylardan reel sayılar seçilerek oluşturulan amply soft topolojilere özel olarak odaklanılmıştır.

Anahtar Kelimeler

• Bir yeni genelleştirilmiş soft küme
• Amply soft küme
• Amply soft topoloji
• İzole monad nokta
• Limit monad nokta

Kaynakça

1. Atanassov K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems; 20, 87-96.
2. Çağman, N., Enginoğlu, S. (2010). Soft set theory and uni-int decision making. European Journal of Operational Research; 207, 848-855.
3. Çağman, N., Enginoğlu, S., Çıtak, F. (2011). Fuzzy soft set theory and its applications. International Journal of Fuzzy Systems; 8, 137-147.
4. Dalkılıç, O., Demirtaş, N. (2022). Decision analysis review on the concept of class for bipolar soft set theory. Computational and Applied Mathematics; 41, 205.
5. Dalkılıç, O. (2022). On topological structures of virtual fuzzy parametrized fuzzy soft sets. Complex Intell. Syst., 8, 337–348.
6. Fatimah, F., Rosadi, D., Hakim, R.B.F. (2018). N-Soft Sets and Decision Making Algorithms. Soft Computing; 22, 3829-3842.
7. Gau W.L., Buehrer D.J. (1993). Vague sets. IEEE Transactions on Systems, Man, and Cybernetics, 23(2), 610-614.
8. Gorzalzany M. B. (1987). A method of inference in approximate reasoning based on interval valued fuzzy sets. Fuzzy Sets and Systems; 21, 1- 17.

9. Göçür, O. (2020). Monad metrizable space. Mathematics, 8, 1891.
10. Göçür, O. (2021). Amply soft set and its topologies: AS and PAS topologies. AIMS Mathematics, 6, 3121-3141.
11. Göçür, O. (2022). Neighbourhoods on Amply Soft Topological Spaces. World Scientific News, 172, 105-117.
12. Göçür, O. (2025). On limit monad points over any amply soft topological spaces. Filomat, in review.
13. Jyothis, T., Sunil, J.J. (2016). A note on soft topology. Journal of New Results in Science; 11: 24-29.
14. Maji P.K., Biswas R., Roy R. (2003). Soft set theory. Computers and Mathematics with Applications, 45: 555-562.
15. Molodtsov D. (1999). Soft set theory: First results. Computers and Mathematics with Applications, 37, 19-31.
16. Musa, S.Y., Asaad, B.A. (2021). Bipolar hypersoft sets. Mathematics, 9, 1826.
17. Musa, S.Y., Mohammed, R.A., Asaad, B.A. (2023). N-hypersoft sets: An innovative extension of hypersoft sets and their applications. Symmetry, 15, 1795.
18. Musa, S.Y. (2024). N-bipolar hypersoft sets: Enhancing decision-making algorithms. PLOS One, 19, 1.
19. Pawlak. Z. (1982). Rough sets. International Journal of Computer and Information Sciences; 11, 341-356.
20. Smarandache F. (2005). Neutrosophic set, a generalisation of the generalized fuzzy sets, International Journal of Pure and Applied Mathematics; 24, 287-297.
21. Smarandache, F. (2018). Extension of soft set to hypersoft set, and then to plithogenic hypersoft set. Neutrosophic Sets and Systems; 22, 168-170.
22. Zadeh. L. A. (1965). Fuzzy sets. Information and Control; 8: 338-353.
23. Zhu, P., Wen, Q. (2013). Operations on Soft Sets Revisited. Journal of Applied Mathematics; 213, 1-7.