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《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (9): 29-35.doi: 10.6040/j.issn.1671-9352.0.2019.131

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否定非对合剩余格的双极值模糊理想格

刘春辉,张海燕,李玉毛   

  1. 赤峰学院数学与统计学院, 内蒙古 赤峰 024001
  • 出版日期:2019-09-20 发布日期:2019-07-30
  • 作者简介:刘春辉(1982— ), 男, 硕士, 副教授, 研究方向为非经典逻辑、 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(NJZY18206)

Lattice of bipolar fuzzy ideals in negative non-involutive residuated lattices

LIU Chun-hui, ZHANG Hai-yan, LI Yu-mao   

  1. School of Mathematics and Statistics, Chifeng University, Chifeng 024001, Inner Mongolia, China
  • Online:2019-09-20 Published:2019-07-30

摘要: 对否定非对合剩余格的双极值模糊理想问题做进一步深入研究,给出了由一个双极值模糊集生成的双极值模糊理想的定义并建立了其两个表示定理,证明了一个否定非对合剩余格L的全体双极值模糊理想之集BFI(L)在偏序下构成完备Heyting代数,为进一步揭示否定非对合剩余格的结构特征拓展了研究思路。

关键词: 模糊逻辑, 逻辑代数, 否定非对合剩余格, 双极值模糊理想, 完备Heyting代数

Abstract: In this paper, the problem of bipolar fuzzy ideals is further studied in negative non-involutive residuated lattices. The definition of bipolar fuzzy ideal which is generated by a bipolar fuzzy set is given and its two representation theorems are established. It is proved that the set BFI(L)which containing of all bipolar fuzzy ideals in a negative non-involutive residuated lattice L, under the partial order, forms a complete Heyting algebra. This work further expands the way for revealing the structural characteristics of negative non-involutive residuated lattices.

Key words: fuzzy logic, logical algebra, negative non-involutive residuated lattice, bipolar fuzzy ideal, complete Heyting algebra

中图分类号: 

  • O141.1
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[1] 刘春辉,李玉毛,张海燕. 否定非对合剩余格的双极值模糊理想[J]. 《山东大学学报(理学版)》, 2019, 54(5): 88-98.
[2] 刘春辉. Heyting代数的扩张模糊滤子[J]. 《山东大学学报(理学版)》, 2019, 54(2): 57-65.
[3] 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.
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[5] 刘春辉. BL代数的(,∨(-overq))-模糊滤子格[J]. 山东大学学报(理学版), 2017, 52(10): 104-110.
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[7] 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.
[8] 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.
[9] 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.
[10] 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.
[11] 刘春辉1,2. Heyting代数的模糊滤子格[J]. J4, 2013, 48(12): 57-60.
[12] 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.
[13] 刘春辉1,2. Fuzzy蕴涵代数的滤子理论刘春辉1,2[J]. J4, 2013, 48(09): 73-77.
[14] 李玲玲, 吴洪博*. BR0-分配性及其推广[J]. J4, 2012, 47(2): 93-97.
[15] 周建仁,吴洪博*. WBR0-代数的正则性及与其他逻辑代数的关系[J]. J4, 2012, 47(2): 86-92.
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