Vol. 29, N° 1, pp. 17-30, May 2010.

Universidad Católica del Norte

Antofagasta - Chile

**GRAPHIC AND REPRESENTABLE FUZZIFYING MATROIDS***

**Chun-E Huang**]]> Beijing Institute Of Technology, China

HUNAN UNIVERSITY OF SCIENCE AND TECH., CHINA

Correspondencia a:

**Abstract**

In this paper, a fuzzifying matroid is induced respectively from a fuzzy graph and a fuzzy vector subspace. The concepts of graphic fuzzifying matroid and representable fuzzifying matroid are presented and some properties of them are discussed. In general, a graphic fuzzifying matriod can not be representable over any field. But when a fuzzifying matroid is isomorphic to a fuzzifying cycle matroid which is induced by a fuzzy tree, it is a representable over any field.

**Keywords : **fuzzifying matroid, fuzzifying cycle matroid, fuzzifying vector matroid, graphic fuzzifying matroid, representable fuzzifying matroid.

**2000 Mathematics Subject Classification : **05C50, 15A03, 52B40.

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Received : December 2009. Accepted : January 2010

**Chun-E Huang
** Department of Mathematics

School of Science

Beijing Institute of Technology

Beijing 100081

P. R. China

e-mail :

__hchune@yahoo.com__]]>