Page 80 - programme book

OT-007
New Generalized Closed Concepts in Fuzzy Bitopological Spaces.

Adem Kilicman 1, a) and Ahlam Alharbi 2, b)

1 Department of Mathematics and Statistics, Faculty of Science, University Putra Malaysia,
43400 UPM Serdang, Selangor, Malaysia.
2 Department of Mathematics, Faculty of Science, Taibah University,
Madinah, Kingdom of Saudi Arabia.

a) Corresponding author: akilic@upm.edu.my
b) dreams.alsehli@hotmail.com

Abstract. This paper is focused on Fuzzy Bitopology. Zadeh (1965) introduced and laid out landmark
papers concerning introduction to fuzzy topology. Subsequently several authors generalized various
basic concepts from general topology to fuzzy sets and developed the theory of fuzzy topological
space. The idea of this work is to contribute and improve several mathematical topics in fuzzy
bitopological spaces. This study is considered new science and has many applications, such as applying
the concept of closure, opening and separation in fuzzy bitopological spaces to expanding and
narrowing the cancer cell and controlling its content. Also, in artificial intelligence and in making a
mathematical model or database. The importance of this work is evident through that it will be a fertile
reference not only for the fuzzy bitopology field, but for all branches of mathematics. The problem
statement of this study lies in the definition of generalized closed set to fuzzy bitopological spaces by
let the first factor of it is fixed on fuzzy open set from the first fuzzy space , then by making the

second factor diversified to includes the types: β closed, semi closed, preclosed, and α-closed from the
second fuzzy space . So, we introduce and develop basic notions of generalized closed sets in fuzzy

bitopological spaces. In addition, some basic theorems are studied, and we found the relations between
them in fuzzy bitopological spaces. We also pointed out many interesting examples and counter
examples which explain that the inverse relation is not correct. In addition, we defined some basic
definitions like closure, interior, neighborhood, quasi-neighborhood on these sets.

Keywords: Fuzzy bitopological spaces, fuzzy generalized closed sets, fuzzy generalized
neighborhoods, fuzzy closure operator, fuzzy interior operator.

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