FUZZIFYING CLOSURE SYSTEMS AND CLOSURE OPERATORS

Document Type: Research Paper

Authors

1 Department of Mathematics, Ocean University of China, Qingdao 266071, People’s Republic of China

2 Department of Mathematics, Ocean University of China, Qingdao 266071, People’s Republic of China

Abstract

In this paper, we propose the concepts of fuzzifying closure systems
and Birkhoff fuzzifying closure operators. In the framework of fuzzifying
mathematics, we find that there still exists a one to one correspondence between
fuzzifying closure systems and Birkhoff fuzzifying closure operators as
in the case of classical mathematics. In the aspect of category theory, we prove
that the category of fuzzifying closure system spaces is isomorphic to the category
of Birkhoff fuzzifying closure spaces. In addition, we obtain an important
result that the category of fuzzifying closure spaces and that of fuzzifying closure
system spaces can be both embedded in the category of Birkhoff
𝐼
-closure
spaces. Finally, using fuzzifying closure systems of the paper, we introduce a
 
set of separation axioms in fuzzifying closure system spaces, which offer a try
 
how to research the properties of spaces by fuzzifying closure systems.
 
 

Keywords


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