IJPAM: Volume 60, No. 3 (2010)

INTERVAL-VALUED H-FUZZY RELATIONS

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 category ${\bf IVRel}(H)$ consisting of interval-valued H-fuzzy relational spaces and relation preserving mappings between them and we study structures of the category ${\bf IVRel}(H)$ in the viewpoint of the topological universe introduced by Nel. Thus we show that ${\bf IVRel}(H)$ satisfies all the conditions of a topological universe over Set except the terminal separator property and ${\bf IVRel}(H)$ is Cartesian closed over Set. Further more, we study some relations among ${\bf Rel}(H)$, ${\bf IRel}(H)$ and ${\bf IVRel}(H)$.

Received: March 3, 2010

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

Key Words and Phrases: interval-valued H-fuzzy 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