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M-FUZZIFYING MATROIDS INDUCED BY M-FUZZIFYING CLOSURE OPERATORS | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 10، دوره 14، شماره 3، تابستان 2017، صفحه 139-149 اصل مقاله (371.85 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2017.3260 | ||
| نویسندگان | ||
Xiu Xin1؛ Shao-Jun Yang  2
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| 1Department of Mathematics, Tianjin University of Technology, Tianjin 300384, P.R.China | ||
| 2School of Mathematics and Statistics, Beijing Institute of Tech- nology, Beijing 100081, P.R.China and Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing 100081, P.R.China | ||
| چکیده | ||
| In this paper, the notion of closure operators of matroids is generalized to fuzzy setting which is called $M$-fuzzifying closure operators, and some properties of $M$-fuzzifying closure operators are discussed. The $M$-fuzzifying matroid induced by an $M$-fuzzifying closure operator can induce an $M$-fuzzifying closure operator. Finally, the characterizations of $M$-fuzzifying acyclic matroids are given. | ||
| کلیدواژه‌ها | ||
| M$-fuzzifying matroids؛ $M$-fuzzifying closure operators؛ $M$-fuzzifying exchange law | ||
| مراجع | ||
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[1] H. L. Huang and F. G. Shi, L-fuzzy numbers and their properties, Information Sciences, 178 (2008), 1141{1151. [2] H. Lian and X. Xin, The nullities for M-fuzzifying matroids, Applied Mathematics Letters, 25(3) (2012), 279{286. [3] J. Oxley, Matroid Theory, Oxford University Press, 1992. [4] F. G. Shi, A new approach to fuzzi cation of matroids, Fuzzy Sets and Systems, 160(5) (2009), 696{705. [5] F. G. Shi, (L,M)-fuzzy matroids, Fuzzy Sets and Systems, 160(16) (2009), 2387{2400. [6] F. G. Shi and B. Pang, Categories isomorphic to the category of L-fuzzy closure system spaces, Iranian Journal of Fuzzy Systems, 10(5) (2013), 127{146. [7] F. G. Shi and L. Wang, Characterizations and applications of M-fuzzifying matroids, Journal of Intelligent and Fuzzy Systems, 25 (2013), 919{930. [8] G. J. Wang, Theory of topological molecular lattices, Fuzzy Sets and Systems, 47(3) (1992), 351{376. [9] L. Wang and F. G. Shi, Characterization of L-fuzzifying matroids by M-fuzzifying families of - ats, Advances of Fuzzy Sets and Systems, 2 (2009), 203{213. [10] L. Wang and F. G. Shi, Characterization of L-fuzzifying matroids by L-fuzzifying closure operators, Iranian Journal of Fuzzy Systems, 7(1) (2010), 47{58. [11] L. Wang and Y. P. Wei, M-fuzzifying P-closure operators, Advances in Intelligent and Soft Computing, 62 (2009), 547{554. [12] X. Xin and F. G. Shi, M-fuzzifying bases, Proyecciones, 28(3) (2009), 271{283. [13] X. Xin and F. G. Shi, Categories of bi-fuzzy pre-matroids, Computer and Mathematics with Applications, 59 (2010), 1548{1558. [14] X. Xin and F. G. Shi, Rank functions for closed and perfect [0,1]-matroids, Hacettepe Journal of Mathematics and Statistics, 39(1) (2010), 31{39. [15] X. Xin, F. G. Shi and S. G. Li, M-fuzzifying derived operators and di erence derived operators, Iranian Journal of Fuzzy Systems, 7(2) (2010), 71{81. [16] Z. Y. Xiu and F. G. Shi, M-fuzzifying submodular functions, Journal of Intelligent and Fuzzy Systems, 27 (2014), 1243{1255. [17] W. Yao and F. G. Shi, Base axioms and circuits axioms for fuzzifying matroids, Fuzzy Sets and Systems, 161 (2010), 3155{3165. | ||
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