Applications of Rough Set Theory to Power Mappings and Their Related Spaces

Document Type : Original Manuscript

Authors

Department of Mathematical Sciences, Yazd University, Yazd, Iran.

10.22044/jas.2025.14834.1868

Abstract

In this paper, we first introduce the concept of a power mapping and demonstrate the existence of a natural one-to-one correspondence between all relations from $A$ to $B$ and all power mappings from $A$ to $\mathcal{P}(B)$. Then, we define several binary operations on a power mapping and investigate their fundamental properties. Next, we investigate the power space $ \langle U, W \mid K = \overline{S} \rangle $ and prove that it admits a unique basis. Finally, we define several important subsets of a power mapping, prove fundamental results and provide a variety of examples.

Keywords

References

1. N. Bagirmaz and A. F. Ozcan, Rough semigroups on approximation space, International Journal of Algebra, 9(7) (2015), 339–350.
 
2. R. Biswas and S. Nanda, Rough groups and rough subgroups, Bull. Pol. AC. Math., 42(3) (1994), 251–254.
 
3. B. Davvaz, Approximations in hyperrings, J. Mult.-Valued Logic Soft Comput., 15 (2009), 471–488.
 
4. B. Davvaz, A short note on algebraic T-rough sets, Inform. Sci., 178 (2008), 3247–3252.
 
5. B. Davvaz, Roughness based on fuzzy ideals, Inform. Sci., 164 (2004), 2417–2437.
 
6. B. Davvaz, Roughness in rings, Inform. Sci., 164 (2004), 147–163.
 
7. B. Davvaz and M. Mahdavipour, Roughness in modules, Inform. Sci., 176 (2006), 3658– 3674.
 
8. A. A. Estaji, M. R. Hooshmandasl and B. Davvaz, Rough Set theory applied to lattice theory, Inform. Sci., 200 (2012), 108–122.
 
9. A. A. Estaji, S. Khodaii and S. Bahrami, On Rough Set and fuzzy sublattice, Inform. Sci., 181 (2011), 3981–3994.
 
10. S. B. Hosseini, N. Jafarzadeh and A. Gholami, T-rough ideal and T-rough fuzzy ideal in a semigroup, Advanced Materials Research, 433-440 (2012), 4915–4919.
 
11. S. B. Hosseini, N. Jafarzadeh and A. Gholami, Some results on T-rough (prime, primary) ideal and T-rough fuzzy (prime, primary) ideal on commutative rings, Int. J. Contempt. Math. Sci., 7(7) (2012), 337–350.
 
12. O. Kazanci and B. Davvaz, On the structure of rough prime (primary) ideals and rough fuzzy prime (primary) ideals in commutative rings, Inform. Sci., 178 (2008), 1343–1354.
 
13. N. Kuroki, Rough ideals in semigroups, Inform. Sci., 100 (1997), 139–163.
 
14. J. N. Mordeson, Rough set theory applied to (fuzzy) ideal theory, Fuzzy Sets and Systems, 121 (2001), 315–324.
 
15. Z. Pawlak, Rough sets basic notions, Ics Pas Rep., 436 (1981), 1–12.
 
16. Z. Pawlak, Some remarks on rough sets, Bull. Pol. Acad. Tech., 33 (1985), 567–572.
 
17. Z. Pawlak and A. Skowron, Rudiments of rough sets, Inform. Sci., 177 (2007), 3–27.
 
18. S. Yamak, O. Kazanca and B. Davvaz, Generalized lower and upper approximations in a ring, Inform. Sci., 180 (2010), 1759–1768. 
Journal of Algebraic Systems
Volume 14, Issue 4
September 2026
Pages 649-669

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