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《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (11): 71-80.doi: 10.6040/j.issn.1671-9352.0.2019.245

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否定非对合剩余格的双极值模糊素理想

刘春辉   

  1. 赤峰学院数学与计算机科学学院, 内蒙古 赤峰 024001
  • 发布日期:2019-11-06
  • 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)

Bipolar fuzzy prime ideals in negative non-involutive residuated lattices

LIU Chun-hui   

  1. School of Mathematics and Computer Science, Chifeng University, Chifeng 024001, Inner Mongolia, China
  • Published:2019-11-06

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摘要： 对否定非对合剩余格的双极值模糊理想问题作进一步深入研究。引入双极值模糊素理想(简称BF-素理想)概念并考察其性质特征。获得了BF-素理想的一些等价刻画, 建立了预线性否定非对合剩余格中的BF-素理想定理, 证明了BF-素理想的NRL-同态像与原像仍为BF-素理想。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, 双极值模糊素理想

Abstract: The problem of bipolar fuzzy ideals is further studied in negative non-involutive residuated lattices. The concept of bipolar fuzzy prime ideal(BF-prime ideal for short)is introduced and its properties are investigated. Some equivalent characterizations of BF-prime ideal are obtained. The BF-prime ideal theorem in a prelinearity negative non-involutive residuated lattice is established. It is proved that the NRL-homomorphism image and the inverse image of a BF-prime ideal are also BF-prime ideals. 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, bipolar fuzzy prime ideal

中图分类号: 

  • O141.1
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[2] 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.
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[8] 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.
[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] 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.
[11] 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.
[12] 刘春辉1,2. Heyting代数的模糊滤子格[J]. J4, 2013, 48(12): 57-60.
[13] 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.
[14] 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.
[15] 李玲玲, 吴洪博*. BR0-分配性及其推广[J]. J4, 2012, 47(2): 93-97.
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