IJPAM: Volume 60, No. 3 (2010)

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

Kul Hur$^1$, Wang Ro Lee$^2$
$^1$Division of Mathematics and Informational Statistics
Nanoscale Science and Technology Institute
Wonkwang University
Iksan, Chonbuk, 570-749, KOREA
e-mail: kulhur@wonkwang.ac.kr
$^2$Faculty of Liberal Education
Cheonbuk National University
Jeonju, Cheonbuk, 561-756, KOREA
e-mail: wrlee@jbun.ac.kr


Abstract.We introduce the subcategory ${\bf IVRel_R}(H)$ of ${\bf IVRel}(H)$ consisting of interval-valued H-fuzzy reflexive relational space on sets and we study structures of ${\bf IVRel_R}(H)$ in a viewpoint of the topological universe introduce by Nel. We show that ${\bf IVRel_R}(H)$ is a topological universe over Set. Moreover, we show that exponential objects in ${\bf IVRel_R}(H)$ are quite different from those in ${\bf IVRel}(H)$. Also we introduce the subcategories ${\bf IVRel_{PR}}(H)$, $\bf {IV}{\bf Rel_P}(H)$ and ${\bf IVRel_E}(H)$ of ${\bf IVRel_R}(H)$ and investigate their structures in the sense of a topological universe.

Received: March 3, 2010

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

Key Words and Phrases: interval-valued H-fuzzy reflexive (resp. symmetric, transitive, proximity, preorder and equivalence) relation, (co)topological category, Cartesian closed category, topological universe

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 60
Issue: 3