BL-代数的扰动模糊理想

doi:10.6040/j.issn.1671-9352.0.2016.123

摘要/Abstract

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。

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

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.

Key words: 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

中图分类号:

O159

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.

PENG Jia-yin. Disturbing fuzzy ideals of BL-algebras[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(10): 78-94.

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