IJPAM: Volume 23, No. 2 (2005)

SOME SUBCATEGORIES OF THE CATEGORY ${\bf IRel_R}(H)$

Young Sin Ahn$^1$, Kul Hur$^2$, Jang Hyun Ryou$^3$
$^1$Department of Computer Information Science
Dong Kang College
Kwang-Ju, 500-714, KOREA
e-mail: yongsin@dongkang.ac.kr
$^2$Division of Mathematics and Informational Statistics
Institute of Basic Natural Science
Wonkwang University
Iksan, Chonbuk, 570-749, KOREA
e-mail: kulhur@wonkwang.ac.kr
$^3$Bong Young Girls' Middle School 325-8
Shinjung, 7 Dong, Yangchongu, Seoul, KOREA
e-mail: donggni@hanmail.net


Abstract.We introduce the subcategories ${\bf
IRel_{PR}}(H)$, ${\bf IRel_{P}}(H)$ and ${\bf IRel_{E}}(H)$ of ${\bf IRel_R}(H)$ and study their structures in a viewpoint of the topological universe introduce by Nel. In particular, the category ${\bf
IRel_{PR}}(H)$ (resp. ${\bf IRel_{P}}(H)$ and ${\bf IRel_{E}}(H)$) is a topological universe over Set. Moreover, we show that ${\bf IRel_{E}}(H)$ has exponential objects.

Received: June 24, 2005

AMS Subject Classification: 04A72, 18B10, 18D15, 03F55

Key Words and Phrases: intuitionistic H-fuzzy proximity (resp. preorder, equivalence) relation, Cartesian closed category, topological universe

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 23
Issue: 2