| BL-代数的扰动模糊理想 |
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| 引用本文： | 彭家寅. BL-代数的扰动模糊理想[J]. 山东大学学报(理学版), 2016, 51(10): 78-94. DOI: 10.6040/j.issn.1671-9352.0.2016.123 |
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| 作者姓名： | 彭家寅 |
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| 作者单位： | 内江师范学院数学与信息科学学院, 四川 内江 641199 |
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| 基金项目： | 国家自然科学基金(11071178);教育部数学与应用数学专业综合改革(ZG0464);四川省科技厅重点科技项目(2006J13-035);四川省数学与应用数学专业综合改革(01249);内江师范学院应用数学重点学科、四川省教育厅和内江师范学院卓越中学教师协同培养计划 |
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| 摘 要： | 利用扰动模糊集概念,研究BL-代数的扰动模糊理想的性质。引入了扰动模糊理想的概念并研究它的一些性质。通过扰动模糊理想构造了商BL-代数,并给出了扰动模糊同态基本定理。此外,给出了由扰动模糊集生成扰动模糊理想的方法。定义了扰动模糊理想的一些类型,研究它们间的一些关系。给出了扰动模糊Boolean理想、扰动模糊素理想、扰动模糊既约理想、扰动模糊超理想及扰动模糊Godel理想的一些刻画。
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| 关 键 词： | 扰动模糊Boolean理想 扰动模糊素理想 扰动模糊超理想 扰动模糊固执理想 扰动模糊Godel理想 扰动模糊理想 扰动模糊既约理想 BL-代数 |
| 收稿时间： | 2016-03-25 |
Disturbing fuzzy ideals of BL-algebras |
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| PENG Jia-yin. Disturbing fuzzy ideals of BL-algebras[J]. Journal of Shandong University, 2016, 51(10): 78-94. DOI: 10.6040/j.issn.1671-9352.0.2016.123 |
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| Authors: | PENG Jia-yin |
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| Affiliation: | School of Mathematics and Information Science, Neijiang Normal University, Neijiang 641199, Sichuan, China |
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| Abstract: | Utilizing the notion of disturbing fuzzy sets, the properties of disturbing fuzzy ideals of BL-algebras are investigated. The concept of disturbing fuzzy ideal is introduced and its several properties are studied. A quotient BL-algebra via a disturbing fuzzy ideal is constructed, and the disturbing fuzzy homomorphism fundamental theorem is given. Moreover, a procedure to generate a disturbing fuzzy ideal is given by a disturbing fuzzy set. Some classes of disturbing fuzzy ideals are defined and the relations of them are investigated. Some characterizations of disturbing fuzzy Boolean ideals, disturbing fuzzy prime ideals, disturbing fuzzy irreducible ideals, disturbing fuzzy ultra ideals, disturbing fuzzy Godel ideals are established. |
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| Keywords: | disturbing fuzzy ultra ideal disturbing fuzzy obstinate ideal disturbing fuzzy ideal disturbing fuzzy irreducible ideal disturbing fuzzy Godel ideal disturbing fuzzy Boolean ideal BL-algebra disturbing fuzzy prime ideal |
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