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CATEGORICAL RELATIONS AMONG MATROIDS, FUZZY MATROIDS AND FUZZIFYING MATROIDS | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 8، دوره 7، شماره 1، اردیبهشت 2010، صفحه 81-89 اصل مقاله (185.47 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2010.163 | ||
| نویسندگان | ||
Ling-Xia Lu  1؛ Wei-Wei Zheng2
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| 1School of Mathematics and Science, Shijiazhuang University of Technology, Shijiazhuang 050031, P.R. China | ||
| 2School of Science, Xi’an Polytechnic University, Xi’an 710048, P.R. China | ||
| چکیده | ||
| The aim of this paper is to study the categorical relations between matroids, Goetschel-Voxman’s fuzzy matroids and Shi’s fuzzifying matroids. It is shown that the category of fuzzifying matroids is isomorphic to that of closed fuzzy matroids and the latter is concretely coreflective in the category of fuzzy matroids. The category of matroids can be embedded in that of fuzzifying matroids as a simultaneously concretely reflective and coreflective subcategory. | ||
| کلیدواژه‌ها | ||
| Matroid؛ Fuzzy matroid؛ Closed fuzzy matroid؛ Fuzzifying matroid. This paper is supported by the national natural science foundation of china(10926055) | ||
| مراجع | ||
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[1] J. Ad´amek, H. Herrlich and G. E. Strecker, Abstract and concrete categories, Wiley, New York, 1990. [2] K. R. Bhutani, J. Mordeson and A. Rosenfeld, On degrees of end nodes and cut nodes in fuzzy graphs, Iranian Journal of Fuzzy Systems, 1 (2004), 57-64. [3] J. Edmonds, Matroids and the greedy algorithm, Mathematical Programming, 1 (1971), 125- 136. [4] D. Gale, Optimal assignments in an ordered set: an application of matroid theory, Journal of Combinatoral Theory, 4 (1968), 176-180. [5] R. Goetschel and W. Voxman, Bases of fuzzy matroids, Fuzzy Sets and Systems, 31 (1989), 253-261. [6] R. Goetschel and W. Voxman, Fuzzy circuits, Fuzzy Sets and Systems, 32 (1989), 35-43. [7] R. Goetschel and W. Voxman, Fuzzy matroids, Fuzzy Sets and Systems, 27 (1988), 291-302. [8] R. Goetschel and W. Voxman, Fuzzy rank functions, Fuzzy Sets and Systems, 42 (1991), 245-258. [9] S. G. Li, X. Xin and Y. L. Li, Closure axioms for a class of fuzzy matroids and the co-tower of matroids, Fuzzy Sets and Systems, 158 (2007), 1246-1257. [10] J. G. Oxley, Matroid Theory, Oxford Universty Press, 1992. [11] F. G. Shi, A new approach to the fuzzification of matroids, Fuzzy Sets and Systems, 160 (2009), 696-705. [12] M. S. Ying, A new approach to fuzzy topologies (I), Fuzzy Sets and Systems, 39 (1991), 373-380. | ||
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