Journal of Frontiers of Computer Science and Technology ›› 2016, Vol. 10 ›› Issue (10): 1493-1500.DOI: 10.3778/j.issn.1673-9418.1507060

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(α,β)-Soft BCK Algebras

LI Qiaoyan1,2, LIAO Zuhua1,2,3+, LIU Weilong1   

  1. 1. School of Science, Jiangnan University, Wuxi, Jiangsu 214122, China
    2. Honors School, Jiangnan University, Wuxi, Jiangsu 214122, China
    3. Institute of Intelligence System & Network Computing, Jiangnan University, Wuxi, Jiangsu 214122, China
  • Online:2016-10-01 Published:2016-09-29

(α,β)-软BCK代数

李巧燕1,2,廖祖华1,2,3+,刘维龙1   

  1. 1. 江南大学 理学院,江苏 无锡 214122
    2. 江南大学 至善学院,江苏 无锡 214122
    3. 江南大学 智能系统与网络计算研究所,江苏 无锡 214122

Abstract: Firstly, by endowing a parameter set with the algebra structure of BCK algebras, this paper introduces the concept of (α,β)-soft BCK algebras, and verifies that the (α,β)-soft BCK algebras is a non-trivial generalization of the intersectional soft BCK algebras and the α-intersectional soft BCK algebras. Then this paper reaches the conclusions that two (α,β)-soft BCK algebras are still (α,β)-soft BCK algebras under the intersection, union and the AND operation of soft sets, and investigates the properties of the homomorphism image and inverse image of the (α,β)-soft BCK algebras. At last, by applying the dual soft sets, this paper gives the equivalent characterizations of the (α,β)-soft BCK algebras.

Key words: 软集;软集运算;对偶软集;BCK代数;(&alpha, ,&beta, )-软BCK代数

摘要: 将软集的参数集赋予BCK代数的代数结构,给出了(α,β)-软BCK代数的概念,并验证了得到的(α,β)-软BCK代数是交软BCK代数和α-交软BCK代数的非平凡推广;得到了两个(α,β)-软BCK代数在软集的交、并、且等运算下仍然是(α,β)-软BCK代数的结论,并讨论了(α,β)-软BCK代数的同态像和原像的性质;最后运用对偶软集的方法给出了(α,β)-软BCK代数的等价刻画。

关键词: soft set, soft set operation, dual soft set, BCK algebra, (&alpha, , &beta, )-soft BCK algebra