BL代数滤子公开问题的进一步求解(英文)Further solution to open problems of filters in BL-algebras
王伟;杨鹏煕;徐扬;
摘要(Abstract):
基于之前的工作,进一步刻画了BL代数的fantastic和normal滤子的等价条件,得到了两种滤子之间的条件等价关系,全面地解决了关于这两种滤子之间关系的两个公开问题:"在什么样的合适条件下,一个normal滤子成为一个fantastic滤子?"和"在什么合适的条件下, normal滤子的拓展性成立?"
关键词(KeyWords): 滤子;normal滤子;fantastic滤子;BL代数
基金项目(Foundation): 国家自然科学基金(11571281,61673320);; 国家空间动力重点实验室基础项目(202300006);; 中央大学基础研究基金(2682017ZT12);; 陕西省大学生创新创业训练计划资助项目(201819062)
作者(Authors): 王伟;杨鹏煕;徐扬;
参考文献(References):
- [1] Haveshki M, Saeid A B, Eslami E. Some types of filters in BL algebras[J]. Soft Comput., 2006,10:657-664.
- [2] Guo Y M, Zhao K K, Wang W. Open problems on implicative pseudo-filters and Boolean filters[J].Proc. 12th International Conference on Intelligent Systems and Knowledge Engineering, 2017,4:1-4.
- [3] H′ajek P. Observations on non-commutative fuzzy logic[J]. Soft Computing, 2003,8:38-43.
- [4] H′ajek P. Metamathematics of Fuzzy Logic[M]. Kluwer:Dordrecht, 1998.
- [5] Kondo M, Dudek W A. Filter theory of BL algebras[J]. Soft Comput., 2008,12:419-423.
- [6] Saeid A B, Motamed S. A new filter in BL-algebras[J]. Journal of Intelligent&Fuzzy Systems,2014,27:2949-2957.
- [7] Saeid A B, Motamed S. Normal filters in BL-algebras[J]. World Applied Sciences Journal, 2009,7:70-76.
- [8] Zhang X H. Fuzzy Logic and Its Algebric Analysis[M]. Beijing:Science Press, 2008.
- [9] Wang W, Xin X L. On fuzzy filters of pseudo BL-algebras[J]. Fuzzy Sets and Systems, 2011,162:27-38.
- [10] Wang W, Wan H, Du K, et al. On open problems based on fuzzy filters of pseudo BCK-algebras[J].Journal of Intelligent&Fuzzy Systems, 2015,29:2387-2395.
- [11] Wang W, Saeid A B. Solutions to open problems on fuzzy filters of BL-algebras[J]. International Journal of Computational Intelligence Systems, 2015,8:106-113.
- [12] Wang W. Solution to open problems on fuzzy filters in logical algebras and secure communication encoding scheme on filters[J]. Filomat, 2018,32(5):1679-1686.
- [13] Wang W, Yang L, Shi Z, et al. On fantastic filters and normal filters in BL algebras[J]. Pure and Applied Mathematics, 2012,28(5):595-598.