Affiliations: [a] Department of Mathematics, Faculty of Science, University of Jeddah, Saudi Arabia
| [b] Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
| [c] Department of Mathematicss, Faculty of Science, Sohag University, Sohag, Egypt
Correspondence:
[*]
Corresponding author. Ismail Ibedou, Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt. E-mails: ismail.ibedou@gmail.com, iibedou@jazanu.edu.sa.
Abstract: In this paper, we join the notion of fuzzy ideal to the notion of fuzzy approximation space to define the notion of fuzzy ideal approximation spaces. We introduce the fuzzy ideal approximation interior operator
intΦλ
and the fuzzy ideal approximation closure operator
clΦλ
, and moreover, we define the fuzzy ideal approximation preinterior operator
pintΦλ
and the fuzzy ideal approximation preclosure operator
pclΦλ
with respect to that fuzzy ideal defined on the fuzzy approximation space (X, R) associated with some fuzzy set λ ∈ IX. Also, we define fuzzy separation axioms, fuzzy connectedness and fuzzy compactness in fuzzy approximation spaces and in fuzzy ideal approximation spaces as well, and prove the implications in between.
