IJPAM: Volume 80, No. 1 (2012)

FUZZY DECOMPOSITION ON
THE AFFINE KAC-MOODY ALGEBRAS

A. Uma Maheswari
Department of Mathematics
Quaid-E-Millat Government College (Autonomous)
Chennai, 600002, INDIA


Abstract. Kac-Moody algebras is one of the modern fields of Mathematical research which has got interesting connections and applications to other fields of Mathematics and Mathematical Physics. On the other hand fuzzy theory has been finding deep rooted applications in all walks of life. In this paper, we define fuzzy sets on the Cartesian product of the simple roots of some of the affine type of Kac-Moody algebras. The fundamental fuzzy properties like normality, convexity and cardinality are studied for these affine Kac-Moody algebras. The $\alpha$-level, strong $\alpha$-level sets and $\alpha$-cut decomposition for these fuzzy sets, associated with the affine Kac-Moody algebras are computed.

Received: June 9, 2012

AMS Subject Classification: 17B67, 03E72

Key Words and Phrases: generalized Cartan matrix, Kac-Moody algebra, simple roots, affine type, fuzzy set, $\alpha$-cut decomposition, $\alpha$-level sets, convexity

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 80
Issue: 1