Measures of fuzzy subgraphs
DOI:
https://doi.org/10.4067/10.4067/S0716-09172010000100005Keywords:
Fuzzy subgroup, implication operator, subgroup degree, subgrupo difuso, operador de implicación, grados de subgrupos.Abstract
In this paper, we introduce the notion of degree to which a fuzzy subset is a fuzzy subgroup by means of the implication operator of [0, 1]. A fuzzy subset µ in a group G is a fuzzy subgroup if and only if its subgroup degree mg(µ) = 1. Some properties of subgroup degrees are investigated.References
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N. Ajmal, Fuzzy groups with sup property, Information Sciences 93, no. 3, pp. 247—264, (1996).
N. Ajmal, Fuzzy group theory: A comparison of different notions of product of fuzzy sets, Fuzzy Sets and Systems 110, no. 3, pp. 437—446, (2000).
J.M. Anthony and H. Sherwood, Fuzzy groups redefined, J. Math. Anal. Appl. 69, no. 1, pp. 124—130, (1979).
J.M. Anthony and H. Sherwood, A characterization of fuzzy subgroups, Fuzzy Sets and Systems 7, no. 3, pp. 297—305, (1982).
I. Chon, Fuzzy subgroups as products, Fuzzy Sets and Systems 141, no. 3, pp. 505—508, (2004).
P.S. Das, Fuzzy groups and level subgroups, J. Math. Anal. Appl. 84, no. 1, pp. 264—269, (1981).
V.N. Dixit et al., Level subgroups and union of fuzzy subgroups, Fuzzy Sets and Systems 37, no. 3, pp. 359—371, (1990).
V.N. Dixit et al., Union of fuzzy subgroups, Fuzzy Sets and Systems 78, no. 1, pp. 121—123, (1996).
M.S. Eroglu, The homomorphic image of a fuzzy subgroup is always a fuzzy subgroup, Fuzzy Sets and Systems 33, no. 2, pp. 255—256, (1989).
W.J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems 8, no. 2, pp. 133—139, (1982).
N.P. Mukherjee and P. Bhattacharya, Fuzzy normal subgroups and fuzzy cosets, Information Sciences 34, no. 3, pp. 225—239, (1984).
A.K. Ray, On product of fuzzy subgroups, Fuzzy Sets and Systems 105, no. 1, pp. 181—183, (1999).
A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35, no. 3, pp. 512—
517, (1971).
H. Sherwood, Products of fuzzy subgroups, Fuzzy Sets and Systems 11, no. 1, 79—89, (1983).
W.-M. Wu, Normal fuzzy subgroups, Fuzzy Math. 1, no. 1, pp. 21—30, (1981).(in Chinese)
Y. Zhang, Some properties on fuzzy subgroups, Fuzzy Sets and Systems 119, no. 3, pp. 427—438, (2001)
Published
2011-01-06
How to Cite
[1]
S. Rui Shi, “Measures of fuzzy subgraphs”, Proyecciones (Antofagasta, On line), vol. 29, no. 1, pp. 41-48, Jan. 2011.
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