تعداد نشریات | 31 |
تعداد شمارهها | 714 |
تعداد مقالات | 6,952 |
تعداد مشاهده مقاله | 11,426,609 |
تعداد دریافت فایل اصل مقاله | 7,804,647 |
Equivalent axioms of M-fuzzifying convex matroids | ||
Iranian Journal of Fuzzy Systems | ||
دوره 20، شماره 7، بهمن و اسفند 2023، صفحه 101-109 اصل مقاله (175.02 K) | ||
نوع مقاله: Original Manuscript | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2023.7633 | ||
نویسنده | ||
F. G. Shi* | ||
School of Mathematics and Statistics, Beijing Institute of Technology | ||
چکیده | ||
In this paper, our aim is to present some characterizations of M-fuzzifying convex matroids. First we discuss the relation between M-fuzzifying convex matroids and M-fuzzy families of dependent sets. Secondly, we give characterizations of M-fuzzifying convex matroids by M-fuzzifying rank functions. Finally we discuss the relation between two concept of M-fuzzifying hull (closure) operators. | ||
کلیدواژهها | ||
M-fuzzifying convex matroid؛ M-fuzzifying hull operator؛ M-fuzzy family of dependent sets؛ M-fuzzifying circuit map؛ M-fuzzifying rank function | ||
مراجع | ||
[1] P. Dwinger, Characterizations of the complete homomorphic images of a completely distributive complete lattice I, Indagationes Mathematicae (Proceedings), 85 (1982), 403-414.
[2] C. Z. Fan, F. G. Shi, M-fuzzifying span mappings in M-fuzzifying matroids, Journal of Intelligent and Fuzzy Systems, 37(3) (2019), 4157-4169.
[3] G. Gierz, et al., A compendium of continuous lattices, Springer Verlag, Berlin, 1980.
[4] R. Goetschel, W. Voxman, Fuzzy matroids, Fuzzy Sets and Systems, 27 (1988), 291-302.
[5] H. L. Huang, F. G. Shi, L-fuzzy numbers and their properties, Information Sciences, 178 (2008), 1141-1151.
[6] C. E. Huang, F. G. Shi, Bases of [0, 1]-matroids, Hacettepe Journal of Mathematics and Statistics, 39 (2010), 233-240.
[7] E. Q. Li, F. G. Shi, Minors of M-fuzzifying matroids, Journal of Intelligent and Fuzzy Systems, 28 (2015), 1213- 1224.
[8] E. Q. Li, F. G. Shi, The free product of M-fuzzifying matroids, Journal of Intelligent and Fuzzy Systems, 30 (2016), 679-690.
[9] S. G. Li, X. Xin, Y. L. Li, Closure axioms for a class of fuzzy matroids and co-towers of matroids, Fuzzy Sets and Systems, 158 (2007), 1246-1257.
[10] X. N. Li, H. J. Yi, Fuzzy bases of fuzzy independent set systems, Fuzzy Sets and Systems, 311 (2017), 99-111.
[11] H. Lian, X. Xin, The nullity for M-fuzzifying matroids, Applied Mathematics Letters, 39 (2010), 31-39.
[12] L. Novák, A comment on bases of fuzzy matroids, Fuzzy Sets and Systems, 87 (1997), 251-252.
[13] L. Novák, On fuzzy independence set systems, Fuzzy Sets and Systems, 91 (1997), 365-374.
[14] J. Oxley, Matroid theory, Oxford University Press, Second Edition, 2011.
[15] F. G. Shi, A new approach to the fuzzification of matroids, Fuzzy Sets and Systems, 160 (2009), 696-705.
[16] F. G. Shi, (L, M)-fuzzy matroids, Fuzzy Sets and Systems, 160 (2009), 2387-2400.
[17] F. G. Shi, L. Wang, Characterizations and applications of M-fuzzifying matroids, Journal of Intelligent and Fuzzy Systems, 25 (2013), 919-930.
[18] F. G. Shi, Z. Y. Xiu, A new approach to the fuzzification of convex structures, Journal of Applied Mathematics, 2014 (2014), 1-12.
[19] L. J. V. D. Vel, Theory of convex structures, North Holland, Amsterdam, 1993.
[20] D. J. A. Welsh, Matroid theory, Academic Press Inc. (London) LTD., 1976.
[21] H. Whitney, On the abstract properties of linear dependence, American Journal of Mathematics, 57(3) (1935), 509-533.
[22] X. Y. Wu, B. Davvaz, S. Z. Bai, On M-fuzzifying convex matroids and M-fuzzifying independent structures, Journal of Intelligent and Fuzzy Systems, 33 (2017), 269-280.
[23] X. Xin, F. G. Shi, Categories of bi-fuzzy pre-matroids, Computers and Mathematics with Applications, 59 (2010), 1548-1558.
[24] X. Xin, F. G. Shi, Rank functions for closed and perfect [0, 1]-matroids, Hacettepe Journal of Mathematics and Statistics, 39 (2010), 31-39.
[25] X. Xin, F. G. Shi, S. G. Li, M-fuzzifying derived operators and difference derived operators, Iranian Journal of Fuzzy Systems, 7(2) (2010), 71-81.
[26] Z. Y. Xiu, F. G. Shi, M-fuzzifying submodular functions, Journal of Intelligent and Fuzzy Systems, 27 (2014), 1243-1255.
[27] S. J. Yang, F. G. Shi, M-fuzzifying independence spaces, Journal of Intelligent and Fuzzy Systems, 34 (2018), 11-21.
[28] S. J. Yang, F. G. Shi, Bases and circuits of fuzzifying matroids, Iranian Journal of Fuzzy Systems, 15(2) (2018), 41-52.
[29] W. Yao, F. G. Shi, Basis axioms and circuits axioms for fuzzifying matroids, Fuzzy Sets and Systems, 161 (2010), 3155-3165. | ||
آمار تعداد مشاهده مقاله: 325 تعداد دریافت فایل اصل مقاله: 565 |