| 否定非对合剩余格的双极值模糊素理想 |
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| 引用本文： | 刘春辉.否定非对合剩余格的双极值模糊素理想[J].山东大学学报(理学版),2019,54(11):71-80. |
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| 作者姓名： | 刘春辉 |
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| 作者单位： | 赤峰学院数学与计算机科学学院, 内蒙古 赤峰 024001 |
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| 基金项目： | 内蒙古自治区高等学校科学研究项目(NJZY18206) |
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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。
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| 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 |
Bipolar fuzzy prime ideals in negative non-involutive residuated lattices |
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| LIU Chun-hui.Bipolar fuzzy prime ideals in negative non-involutive residuated lattices[J].Journal of Shandong University,2019,54(11):71-80. |
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| Authors: | LIU Chun-hui |
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| Institution: | School of Mathematics and Computer Science, Chifeng University, Chifeng 024001, Inner Mongolia, China |
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| 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. |
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| Keywords: | fuzzy logic logical algebra negative non-involutive residuated lattice bipolar fuzzy ideal bipolar fuzzy prime ideal |
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