您的位置:山东大学 -> 科技期刊社 -> 《山东大学学报(理学版)》

山东大学学报(理学版) ›› 2017, Vol. 52 ›› Issue (10): 104-110.doi: 10.6040/j.issn.1671-9352.0.2016.400

• • 上一篇    

BL代数的(,∨(-overq))-模糊滤子格

刘春辉   

  1. 赤峰学院数学与统计学院, 内蒙古 赤峰 024001
  • 收稿日期:2016-08-24 出版日期:2017-10-20 发布日期:2017-10-12
  • 作者简介:刘春辉(1982— ), 男, 硕士, 副教授, 研究方向为非经典数理逻辑、Domain理论与拓扑学.E-mail:chunhuiliu1982@163.com
  • 基金资助:
    内蒙古自治区高等学校科学研究项目(NJSY14283)

Lattice of(,∨(-overq))-fuzzy filters in a BL-algebra

LIU Chun-hui   

  1. Department of Mathematics and Statistics, Chifeng University, Chifeng 024001, Inner Mongolia, China
  • Received:2016-08-24 Online:2017-10-20 Published:2017-10-12

摘要: 对BL代数的(,∨(-overq))-模糊滤子理论作进一步深入研究给出了(,∨(-overq))-模糊滤子的若干新性质, 定义了由BL代数上的一个模糊集生成的(,∨(-overq))-模糊滤子并建立了其表示定理, 证明了BL代数的全体(,∨(-overq))-模糊滤子之集构成一个完备的分配格。

关键词: BL代数, (, ∨(-overq))-模糊滤子, 分配格, 完备格, 模糊逻辑

Abstract: (,∨(-overq))-fuzzy filter theory in BL-algebras is further studied. Some new properties of(,∨(-overq))-fuzzy filters are given. The notion of(,∨(-overq))-fuzzy filter which is generated by a fuzzy set is defined and its representation theorem is established. It is proved that the set of all(,∨(-overq))-fuzzy filters in a BL-algebra forms a complete distributive lattice.

Key words: distributive lattice, fuzzy logic, BL-algebra, complete lattice, (,∨(-overq))-fuzzy filter

中图分类号: 

  • O141.1
[1] WANG Guojun, ZHOU Hongjun. Introduction to mathematical logic and resolution principle[M]. 2nd. Beijing: Science Press, 2009.
[2] HÁJEK P. Metamathematics of fuzzy logic[M]. Dordrecht: Kluwer Academic Publishers, 1998.
[3] TURUNEN E. BL-algebras of basic fuzzy logic[J]. Mathware and Soft Computing, 1999, 6(1):49-61.
[4] XU Yang, RUAN D, QIN Keyun, et al. Lattice-valued logic[M]. Berlin: Springer, 2004.
[5] TURUNEN E. Boolean deductive systems of BL-algebras[J]. Archive Mathematical Logic, 2001, 40(6):467-473.
[6] HAVESHKY M, SAEID A B, ESLAMI E. Some type of filters in BL-algebras[J]. Soft Computing, 2006, 10(8):657-664.
[7] KONDO M, DUDEK W A. Filter theory of BL-algebras[J]. Soft Computing, 2008, 12(5):419-423.
[8] ZHU Yiquan, XU Yang. On filter theory of residuated lattice[J]. Information Sciences, 2010, 180(19):3614-3632.
[9] BORZOOEI R A, SHOAR S K, AMERI R. Some types of filters in MTL-algebras[J]. Fuzzy Sets and Systems, 2012, 187(1):92-102.
[10] BUSNEAG D, PICIU D. Some types of filters on residuated lattices[J]. Soft Computing, 2014, 18(5):825-837.
[11] LIU Lianzhen, LI Kaitai. Fuzzy filters of BL-algebras[J]. Information Sciences, 2005, 173(1-3):141-154.
[12] LIU Lianzhen, LI Kaitai. Fuzzy Boolean and positive implicative filters of BL-algebras[J]. Fuzzy Sets and Systems, 2005, 152(2):333-348.
[13] ZADEH L A. Fuzzy sets[J]. Informtion and Control, 1965, 8:338-352.
[14] MA Xueling, ZHAN Jianming. On(∈,∈∨q)-fuzzy filters of BL-algebras[J]. Journal of Systems Sciences and Complexity, 2008, 21(1):144-158.
[15] MA Xueling, ZHAN Jianming, DUDEK W A. Some kinds of(,∨(-overq))-fuzzy filters of BL-algebras[J]. Computers and Mathematics with Applications, 2009, 58(2):248-256.
[1] 刘春辉. 可换BR0-代数在一般集合上的蕴涵表示形式[J]. 山东大学学报(理学版), 2018, 53(6): 86-94.
[2] 刘春辉. 关于格蕴涵代数的(∈,∈∨q(λ, μ))-模糊LI-理想[J]. 山东大学学报(理学版), 2018, 53(2): 65-72.
[3] 邵勇. 半格序完全正则周期半群[J]. 山东大学学报(理学版), 2018, 53(10): 1-5.
[4] 梁颖,崔艳丽,吴洪博. 基于BL系统的演绎系统集代数的剩余格属性[J]. 山东大学学报(理学版), 2017, 52(11): 65-70.
[5] 乔希民,吴洪博. 区间集上非交换剩余格的〈,(-overQ)〉-fuzzy滤子及其特征刻画[J]. 山东大学学报(理学版), 2016, 51(2): 102-107.
[6] 周建仁, 吴洪博. IMTL逻辑系统的一种新扩张形式[J]. 山东大学学报(理学版), 2015, 50(12): 28-34.
[7] 卢涛, 王习娟, 贺伟. Topos中选择公理的一个等价刻画[J]. 山东大学学报(理学版), 2015, 50(12): 54-57.
[8] 沈冲, 姚卫. 模糊完备格上模糊G-理想和模糊Galois伴随之间的一一对应[J]. 山东大学学报(理学版), 2015, 50(04): 36-41.
[9] 寇海燕, 吴洪博. MTL代数的Wajsberg形式及其应用[J]. 山东大学学报(理学版), 2015, 50(02): 75-82.
[10] 鲁静, 赵彬. 模糊Quantale范畴中的投射对象[J]. 山东大学学报(理学版), 2015, 50(02): 47-54.
[11] 刘春辉. 正则剩余格的模糊超⊙-理想[J]. 山东大学学报(理学版), 2014, 49(12): 87-94.
[12] 刘春辉. BL代数的区间值(∈,∈∨q)-模糊滤子理论[J]. 山东大学学报(理学版), 2014, 49(10): 83-89.
[13] 周建仁1,2,吴洪博2*. IMTL逻辑代数的一种新强化形式[J]. 山东大学学报(理学版), 2014, 49(04): 84-89.
[14] 罗清君1,2, 王国俊1*. BL代数中极大滤子的拓扑性质[J]. J4, 2013, 48(12): 47-51.
[15] 刘春辉1,2. 正则剩余格的素模糊⊙理想及其拓扑性质[J]. J4, 2013, 48(12): 52-56.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!