软环的T-模糊软理想
T-Fuzzy Soft Ideals of Soft Rings
DOI: 10.12677/PM.2013.35050, PDF, 下载: 2,748  浏览: 8,141  科研立项经费支持
作者: 李文婷*:西北大学数学系
关键词: 软集模糊软集软环T-模糊软理想模糊软同态Soft Set; Fuzzy Soft Set; Soft Ring; T-Fuzzy Soft Ideal; Fuzzy Soft Homomorphism
摘要: 为了进一步研究模糊软集理论,通过将软集与模糊理想结合,给出了T-模糊软理想的定义,并在一定程度上推广了模糊软集。然后给出了软环的T-模糊软理想在模糊软运算和模糊软同态下像的相关性质。
Abstract: In order to investigate fuzzy soft sets further more, T-fuzzy soft ideal, as a generalization of a fuzzy soft set, is initiated by the combination of soft sets and fuzzy sets. Several relevant properties of T-fuzzy soft ideals under fuzzy soft operations and fuzzy soft homomorphisms are also discussed.
文章引用:李文婷. 软环的T-模糊软理想[J]. 理论数学, 2013, 3(5): 321-325. http://dx.doi.org/10.12677/PM.2013.35050

参考文献

[1] L. A. Zadeh. Fuzzy sets. Information and Control, 1965, 8(3): 338-353.
[2] Z. Pawlak. Rough sets. International Journal of Information and Computer Science, 1982, 11(5): 341-356.
[3] D. Molodstov. Soft set theory—First results. Computers & Mathematics with Applications, 1999, 37(4): 19-31.
[4] P. K. Maji, A. R. Roy and R. Biswas. An application of soft sets in a decision making problem. Computers & Mathematics with Applications, 2002, 44(8): 1077-1083.
[5] M. I. Ali, F. Feng, et al. On some new operations in soft set theory. Computers & Mathematics with Applications, 2009, 57(9): 1547-1553.
[6] H Aktaş, N Çağman. Soft sets and soft groups. Information Sciences, 2007, 177(13): 2726-2735.
[7] U. Acar, F. Koyuncu and B. Tanay. Soft sets and soft rings. Computers & Mathematics with Applications, 2010, 59(11): 3458-3463.
[8] P. K. Maji, R. Biswas and A. R. Roy. Fuzzy soft sets. Journal of Fuzzy Mathematics, 2001, 9(3): 589-602.
[9] K. Menger. Statistical metrics. Proceedings of the National Academy of Sciences of the United States of America, 1942, 8: 535-537.
[10] E. P. Klement, R. Mesiar and E. Pap. Triangular norms. Dordreclot: Klmver Academic Publishers, 2000: 13-29.
[11] T. Whaler. Paranieteilized R-implications. Fuzzy Sets and Systems, 2003, 134: 231-281.
[12] 张小红, 何华灿, 徐扬. 基于Schweizer-Sklar -范数的模糊逻辑系统[J]. 中国科学E辑 信息科学, 2005, 35(12): l314-1326.
[13] 苗明力, 廖祖华, 胡森菌, 陆金花. 关于 范数的广义模糊子坡(理想)[J]. 山东人学学报(工学版), 2010, 40(5): 28-33.
[14] 谭宜家. Fuzzy群中的Fuzzy同余关系与正规Fuzzy子群[J]. 福州大学学报(自然科学版), 1995, 23(2): 1-6.
[15] S. L. Li, Y. D. Yu and Z. D. Wang. -congruence -relations on groups and rings. Fuzzy Sets and Systems, 1997, 92: 365-381.
[16] 姚炳学. 群与环上的模糊理论[M]. 北京: 科学出版社, 2008.
[17] A. Aygünoğlu, H. Aygün. Introduction to fuzzy soft groups. Computers & Mathematics with Applications, 2009, 58(6): 1279-1286.