Volume 25 , Issue 3 , PP: 435-449, 2025 | Cite this article as | XML | Html | PDF | Full Length Article
Jawaher Al-Mufarrij 1 , Samer Al-Ghour 2 *
Doi: https://doi.org/10.54216/IJNS.250337
The object of the present paper is to introduce a new class of soft functions called soft regular-closed functions. This class contains the class of soft closed functions. Numerous theorems that give properties of such soft functions are presented. Moreover, sufficient conditions for a soft function to be soft regular-closed are given. In addition, several preservation theorems of soft separations axioms using soft regular-closed are given. Finally, the correspondence between this class of soft functions and the class of regular-closed functions in classical topology is studied.
Soft closed functions , Soft compactness , Soft separation axioms , Generated soft topology
[1] Prade, H., & Dubois, D. (1980), Fuzzy Sets and Systems Theory and Applications, Aca demic Press, London.
[2] Zadeh, L. A. (1965), Fuzzy Sets. Infor. and Control, 8, 338-353.
[3] Zimmermann, H. J. (1996), Fuzzy Set Theory and Its Applications. Kluwer Academic, Boston, MA, .
[4] Atanassov, K. (1986), Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87-96.
[5] Atanassov, K. (1994), Operators over interval valued intuitionstic fuzzy sets. Fuzzy Sets and Systems, 64, 159-174.
[6] Gau, W. L.; Buehrer, D.J. (1993), Vague sets. IEEE Trains System Man Cybernet, 23, 610-614.
[7] Gorzalzany, M. B. (1987), A method of inference in approximate reasoning based on interval valued fuzzy sets. Fuzzy Sets and Systems, 21, 1-17.
[8] Pawlak, Z. (1982), Rough sets. International Journal of Information and Computer Sciences, 11, 341-356.
[9] Molodtsov, D. (1999), Soft set theory-first results. Computers Math. Applic., 37, 19-31.
[10] Nasef, A. A., & El-Sayed, M. K. (2017), Molodtsov’s Soft Set Theory and its Applications in Decision Making. Inter. Jour. of Eng. Sci. Inve., 6, 86-90.
[11] Alqahtani, M. H., & Ameen, Z. A. (2024), Soft nodec spaces. AIMS Mathematics, 9, 3289-3302.
[12] Ameen, Z. A., & Alqahtani, M. H. (2023), Baire category soft sets and their symmetric local properties, Symmetry, 15,1810.
[13] Al-shami, T. M., Mhemdi, A., & Abu-Gdairi, R. (2023), A Novel framework for generalizations of soft open sets and its applications via soft topologies. Mathematics, 11, 840.
[14] Mhemdi, A. (2023), Novel types of soft compact and connected spaces inspired by soft Q-sets. Filomat, 37, 9617-9626.
[15] Guan, X. (2023), Comparison of two types of separation axioms in soft topological spaces. Journal of Intelligent and Fuzzy Systems, 44, 2163-2171.
[16] Al-shami, T. M. (2022), Soft somewhat open sets: Soft separation axioms and medical application to nutrition. Comput. Appl. Math., 41, 2016.
[17] Al Ghour, S. (2022), Between the Classes of soft open sets and soft omega open sets. Mathematics, 10, 719.
[18] Al Ghour, S. (2022), Boolean algebra of soft Q-Sets in soft topological spaces. Appl. Comput. Intell. Soft Comput., 2022, 5200590.
[19] Al-shami, T. M. (2021), On soft separation axioms and their applications on decision-making problem. Mathematical Problems in Engineering, 2021, 1-12.
[20] Al-shami, T. M., Kocinac, L. D. R., & Asaad, B. A. (2020), Sum of soft topological spaces. Mathematics, 8, 990.
[21] Al-shami, T. M., & El-Shafei, M. E. (2020), Partial belong relation on soft separation axioms and decision-making problem, two birds with one stone. Soft Comput., 24, 5377-5387.
[22] Alcantud, J. C. R. (2020), Soft Open Bases and a Novel construction of soft topologies from bases for topologies. Mathematics, 8, 672.
[23] Al Ghour, S., & Bin-Saadon, A. (2019), On some generated soft topological spaces and soft homogeneity. Heliyon, 5, e02061.
[24] Al Ghour, S., & Hamed, W. (2020), On two classes of soft sets in soft topological spaces. Symmetry, 12, 265.
[25] Stone, M. H. (1937), Applications of the theory of Boolean rings to general topology. Trans. Am. Math. Soc., 41, 375-481.
[26] Singal, M. K., & Singal, A. R. (1968), Almost-continuous mappings, Yokohama Math. J., 16, 63-73.
[27] Yuksel, S., Tozlu, N., & Ergul, Z. G. S(2014), oft regular generalized closed sets in soft topological spaces. Int. J. Math. Anal., 8, 355-367.
[28] Georgiou, D. N., Megaritis, A. C., & Petropoulos, V. I. (2013), On soft topological spaces. Appl. Math. Inf. Sci., 7, 1889-1901.
[29] Demir, I., & Ozbakır, O. B. (2014), Soft Hausdorff spaces and their some properties. Ann. Fuzzy Math. Inform., 8, 769-783.
[30] Thakur, S. S., & Rajput, A. S. (2017), Soft almost continuous mappings. J. Adv. Stud. Topol., 2017, 23-29.
[31] Mohammed, R. A., Sayed, O. R., & Eliow, A. (2019), Some properties of soft delta-topology. Acad. J. Nawroz Univ., 8, 352-361.
[32] Aygunoglu, A., & Aygun, H. (2012), Some notes on soft topologicalspaces. Neural Computing and Applications, 21, (SUPPL. 1), S113-S119.
[33] Hussain, S., & Ahmad, B. (2015), Soft separation axioms in soft topological spaces. Hacet. J. Math. Stat., 44, 559-568.
[34] Prasad, A. K., & Thakur, S. S.(2019), Soft almost regular spaces. Malaya J. Mat., 7, 408-411.
[35] Ramkumar, S., & Subbiah, V. 2020), Soft separation axioms and soft product of soft topological spaces. Maltepe J. Math., 2, 61-75.
[36] Debnath, B. (2017), A note on soft nearly compact and soft nearly paracompactness in soft topological spaces. Int. J. Innov. Res. Sci. Eng. Technol., 6, 15906-15914.
[37] Al Ghour, S. (2022), Soft Rω-open sets and the soft topology of soft δω-open sets. Axioms, 11, 177.
[38] Al-Omeri, W. F. (2023), The property (P) and new fixed point results on ordered metric spaces in neutrosophic theory. Neutrosophic Sets and Systems, 56, 261-275.
[39] Al-Omeri, W. F. (2023), Neutrosophic g˚-closed sets in Neutrosophic topological spaces. International Journal of Neutrosophic Science, 20, 210-222.
