Graphics and representable fuzzifying matroids
Keywords:Fuzzifying matroid, fuzzifying cycle matroid, fuzzifying vector matroid, graphic fuzzifying matroid, representable fuzzifying matroid, matroide difusa, ciclo matroidal de difusión, vector matroidal difuso, matroide gráfica difusa.
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.
A.K. Katsaras and D.B.Liu, Fuzzy vector spaces and fuzzy topological vector spaces, J.Math.Anal.Appl., 58, pp. 135—146, (1977).
P.Lubczonok, Fuzzy vector spaces, Fuzzy Sets and Systems, 38, pp. 329-343, (1990).
C.V. Negoita, D.A. Ralescu, Applications of Fuzzy Sets to Systems Analysis, Interdisciplinary Systems Research Series, vol. 11, Birkhaeuser, Basel, Stuttgart and Halsted Press, New York, (1975).
J.G.Oxley, Matroid Theory, Oxford university press, (1992).
A. Rosenfeld, Fuzzy graphs, in L.A Zadeh, K. S. Fu, and M. Shimura (Eds.), Fuzzy sets and their Applications, Academic Press, New York, pp. 77-95, (1975).
F.-G. Shi, A new approach to the fuzzification of matroids, Fuzzy Sets and Systems, 160, pp. 696-705, (2009).
F.-G. Shi, (L, M)-fuzzy matroids, Fuzzy Sets and Systems, 160, pp. 2387—2400, (2009).
Tutte, W. T., A homotopy theorem for matroids, I, II, Trans. Amer. Math. Soc., 88, pp. 144-174, (1958).
Welsh, D. J. A., Matroid Theory, Acadamic Press, London, (1976).
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