Hostname: page-component-77f85d65b8-6c7dr Total loading time: 0 Render date: 2026-03-29T05:59:30.467Z Has data issue: false hasContentIssue false
  • English
  • Français

Computable soft separation axioms

Published online by Cambridge University Press:  12 October 2023

S. M. Elsayed Open the ORCID record for S. M. Elsayed [Opens in a new window]  and
Keng Meng Ng
S. M. Elsayed*
Affiliation:
Maths Department, Faculty of Science, Aswan University, Aswan, Egypt
Keng Meng Ng
Affiliation:
SPMS School, NTU University, Jurong West, Singapore
*
Corresponding author: S. M. Elsayed; Email: profsalah55@yahoo.com
Get access Rights & Permissions [Opens in a new window]

Abstract

Soft sets were introduced as a means to study objects that are not defined in an absolute way and have found applications in numerous areas of mathematics, decision theory, and in statistical applications. Soft topological spaces were first considered in Shabir and Naz ((2011). Computers & Mathematics with Applications 61 (7) 1786–1799) and soft separation axioms for soft topological spaces were studied in El-Shafei et al. ((2018). Filomat 32 (13) 4755–4771), El-Shafei and Al-Shami ((2020). Computational and Applied Mathematics 39 (3) 1–17), Al-shami ((2021). Mathematical Problems in Engineering 2021). In this paper, we introduce the effective versions of soft separation axioms. Specifically, we focus our attention on computable u-soft and computable p-soft separation axioms and investigate various relations between them. We also compare the effective and classical versions of these soft separation axioms.

Keywords

Soft setscomputable soft topological spacescomputable soft separation axioms

Information

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 33 , Issue 9 , October 2023 , pp. 781 - 808
Check for updates
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Acar, U., Koyuncu, F. and Tanay, B. (2010). Soft sets and soft rings. Computers & Mathematics with Applications 59 (11) 3458–3463.CrossRefGoogle Scholar
Aktaş, H. and Çağman, N. (2007). Soft sets and soft groups. Information Sciences 177 (13) 2726–2735.CrossRefGoogle Scholar
Al-shami, T. (2020). Comments on some results related to soft separation axioms. Afrika Matematika 31 (7)1105–1119.CrossRefGoogle Scholar
Al-shami, T. (2021). On soft separation axioms and their applications on decision-making problem. Mathematical Problems in Engineering 2021 1–12.Google Scholar
Ali, M. I., Feng, F., Liu, X., Min, W. K. and Shabir, M. (2009). On some new operations in soft set theory. Computers & Mathematics with Applications 57 (9) 1547–1553.CrossRefGoogle Scholar
El-Shafei, M., Abo-Elhamayel, M. and Al-Shami, T. (2018). Partial soft separation axioms and soft compact spaces. Filomat 32 (13) 4755–4771.CrossRefGoogle Scholar
El-Shafei, M. and Al-Shami, T. (2020). Applications of partial belong and total non-belong relations on soft separation axioms and decision-making problem. Computational and Applied Mathematics 39 (3) 1–17.CrossRefGoogle Scholar
Elsayed, S. M. M. (2022). Applications of effective methods in computable mathematics. PhD thesis. NTU University.Google Scholar
Feng, F., Li, Y. and Leoreanu-Fotea, V. (2010). Application of level soft sets in decision making based on interval-valued fuzzy soft sets. Computers & Mathematics with Applications 60 (6) 1756–1767.CrossRefGoogle Scholar
Gorzałczany, M. B. (1987). A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets and Systems 21 (1) 1–17.CrossRefGoogle Scholar
Jaynes, E. T. (2003). Probability Theory: The Logic of Science, Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Jun, Y. B. and Park, C. H. (2008). Applications of soft sets in ideal theory of bck/bci-algebras. Information Sciences 178 (11) 2466–2475.Google Scholar
Maji, P., Roy, A. R. and Biswas, R. (2002). An application of soft sets in a decision making problem. Computers & Mathematics with Applications 44 (8-9) 1077–1083.CrossRefGoogle Scholar
Matejdes, M. (2021). Methodological remarks on soft topology. Soft Computing 25 (5) 4149–4156.CrossRefGoogle Scholar
Molodtsov, D. (1999). Soft set theory–first results. Computers & Mathematics with Applications 37 (4-5) 19–31.CrossRefGoogle Scholar
Nazmul, S. and Samanta, S. (2013). Neighbourhood properties of soft topological spaces. Ann. Fuzzy Math. Inform 6 (1) 1–15.Google Scholar
Pawlak, Z. (1982). Rough sets. International journal of computer & information sciences, 11(5) 341–356.CrossRefGoogle Scholar
Pei, D. and Miao, D. (2005). From soft sets to information systems. In: 2005 IEEE International Conference on Granular Computing, vol. 2, IEEE, 617–621.Google Scholar
Peng, X., Yang, Y., Song, J. and Jiang, Y. (2015). Pythagorean fuzzy soft set and its application. Computer Engineering 41(7) 224–229.Google Scholar
Peyghan, E. (2013). About soft topological spaces. Journal of New Results in Science 2(2) 60–75.Google Scholar
Shabir, M., Ali, M. I. and Shaheen, T. (2013). Another approach to soft rough sets. Knowledge-Based Systems 40 72–80.CrossRefGoogle Scholar
Shabir, M. and Naz, M. (2011). On soft topological spaces. Computers & Mathematics with Applications 61 (7) 1786–1799.CrossRefGoogle Scholar
Turing, A. M. et al. (1936). On computable numbers, with an application to the entscheidungsproblem. Journal of Mathematics 58 (345–363) 5.Google Scholar
Weihrauch, K. (2000). Computable Analysis: An Introduction, Germany: Springer Science & Business Media.CrossRefGoogle Scholar
Weihrauch, K. (2010). Computable separation in topology, from t0 to t2. Journal of Universal Computer Science 16 (18) 2733–2753.Google Scholar
Weihrauch, K. (2012). Computability, vol. 9, Germany: Springer Science & Business Media.Google Scholar
Weihrauch, K. and Grubba, T. (2009). Elementary computable topology. Journal of Universal Computer Science 15 (6) 1381–1422.Google Scholar
Xiao, Z., Gong, K. and Zou, Y. (2009). A combined forecasting approach based on fuzzy soft sets. Journal of Computational and Applied Mathematics 228 (1) 326–333.CrossRefGoogle Scholar
Yang, Y., Tan, X. and Meng, C. (2013). The multi-fuzzy soft set and its application in decision making. Applied Mathematical Modelling 37 (7) 4915–4923.CrossRefGoogle Scholar
Zadeh, L. A. (1965). Fuzzy sets. Information and Control 8 338–353.CrossRefGoogle Scholar