### δβ-I APPROXIMATION SPACES

**DOI Number**

**First page**

**Last page**

#### Abstract

In this paper, we generalize rough set theory by introducing concepts of δβ-I lower and δβ-I -upper approximation for any ideal I on X which depends on the concept δβ-I -open sets. Some of their basic properties with the help of examples are investigated and the interrelation between them are obtained. Also, the connections between the rough approximations de_ned in [2] and our new approximations are studied.

#### Keywords

#### Keywords

#### Full Text:

PDF#### References

M. E. Abd El-Monsef; S. N. El-Deeb, R. A. Mahmoud, -opensets and -continuous mappings, Bull. Fac. Sci. Assiut Univ., 12(1983), 77–90.

H. M. Abu-Donia, A. S. Salama, Generalization of Pawlaks rough approximation spaces by using -open sets, International Journal of Approximate Reasoning, 53(7)(2012), 1094–1105.

D. Andrijević, Semi-preopensets, Mat. Vesnik., 38(1986), 24–32.

D. Ciucci; T. Mihalydeak, Z. E.Csajbk, On exactness, definability and vagueness in partial approximation spaces, Tech. Sci. 18(3)(2015), 203-212.

Deepmala, L. N. Mishra, Differential operators over modules and rings as a path to the generalized differential geometry, FACTA Univ. (NIŠ ) Ser. Math. Inform., 30(5)(2015), 753–764.

Deepmala, A Study on Fixed Point Theorems for Nonlinear Contractions and its Applications, Ph. D. Thesis, Pt. Ravishankar Shukla University, Raipur 492 010, Chhatisgarh, India, (2014).

E. Ekici, On e-open sets and (D, S)-sets and decompositions of continuous functions, Math. Moravica, 13(1)(2009), 29–36.

M. E. El-Shafei, A. M. Kozae, M. Abo-elhamayel, Semi ordered topologi-calapproximations of rough sets, Ann. of fuzzy sets, fuzzy logic and fuzzy syst., 2(2013) 61–72.

T. R. Hamlett, D. Rose, -topological properties, Internat J. Math. and Math. Sci., 13(3)(1990), 507–512.

E. Hatir, T. Noiri, On -continuous functions, Chaos, Solitons Fractals, 42(2009), 205–211.

E. Hatir, T. Noiri, Decompositions of continuity and complete continuity, Acta Math. Hungary, 11(3)(2006), 281–287.

E. Hatir, T. Noiri, On descompositions of continuity via idealization, Acta Math. Hungar., 96(2002), 341–349.

E. Hayashi, Topologies defined by local properties, Mathematische Annalen, 156(1964), 205–215.

D. Jankovic, T. R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97(1990), 295–310.

K. Kuratowski, Topology, Vol. I, Academic Press, New York, (1966).

N. Levine, Semi open sets and semi continuity topological spaces, Amer. Math. Monthly, 70(1963), 24–32.

T. Y. Lin, An overview of rough set theory from the Point of View of Relational Databases, Bull. Int. Rough Set Soc., 1(1)(1997) 30–34.

V. N. Mishra, Some Problems on Approximations of Functions in Banach Spaces, Ph. D. Thesis, Indian Institute of Technology, Roorkee 247 667, Uttarakhand, India, (2007).

Z. Pawlak, Rough Sets, Internat. J. Comput. Inform. Sci., 11(1982), 341–356.

Z. Pawlak, Rough Sets, Theoretical Aspects of Reasoning about Data, Kluwer Academic, Boston, (1991).

M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41(1937), 375–481.

R. Vaidyanathaswamy, The localisation theory in set Topology, Proc. Indian Acad. Sci. Math. Sci., 20(1945), 51–61.

N. V. Velicko, H-closed topological spaces, Amer. Math. Soc. Transl., 78(1968), 103–118.

W. Zhu, Topological approaches to covering rough sets, Inf. Sci. 177(15)(2007), 1499-1508.

### Refbacks

- There are currently no refbacks.

ISSN 0352-9665 (Print)