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格蕴涵代数的区间值$(\in, \in\vee\,q)$-模糊$LI$-理想格
引用本文:刘春辉.格蕴涵代数的区间值$(\in, \in\vee\,q)$-模糊$LI$-理想格[J].数学研究及应用,2016,36(4):394-406.
作者姓名:刘春辉
作者单位:赤峰学院数学与统计学院, 内蒙古 赤峰 024001
基金项目:国家自然科学基金(Grant No.60774073),内蒙古自治区高等学校科学研究项目(Grant No.NJSY14283).
摘    要:In the present paper, the interval-valued (∈,∈∨q)-fuzzy LI-ideal theory in lattice implication algebras is further studied. Some new properties of interval-valued (∈,∈∨q)-fuzzy LI-ideals are given. Representation theorem of interval-valued (∈,∈∨q)-fuzzy LI-ideal which is generated by an interval-valued fuzzy set is established. It is proved that the set consisting of all interval-valued (∈,∈∨q)-fuzzy LI-ideals in a lattice implication algebra, under the partial order ?, forms a complete distributive lattice.

关 键 词:lattice-valued  logic  lattice  implication  algebra  interval-valued  (∈  ∈∨q)-fuzzy  LI-ideal  complete  distributive  lattice
收稿时间:2015/9/13 0:00:00
修稿时间:3/8/2016 12:00:00 AM

Lattice of Interval-Valued $(\in, \in\vee\,q)$-Fuzzy $LI$-Ideals in Lattice Implication Algebras
Chunhui LIU.Lattice of Interval-Valued $(\in, \in\vee\,q)$-Fuzzy $LI$-Ideals in Lattice Implication Algebras[J].Journal of Mathematical Research with Applications,2016,36(4):394-406.
Authors:Chunhui LIU
Institution:Department of Mathematics and Statistics, Chifeng University, Inner Mongolia 024001, P. R. China
Abstract:In the present paper, the interval-valued $(\in, \in\mspace{-5mu}\vee\,q)$-fuzzy $LI$-ideal theory in lattice implication algebras is further studied. Some new properties of interval-valued $(\in, \in\mspace{-5mu}\vee\,q)$-fuzzy $LI$-ideals are given. Representation theorem of interval-valued $(\in, \in\mspace{-5mu}\vee\,q)$-fuzzy $LI$-ideal which is generated by an interval-valued fuzzy set is established. It is proved that the set consisting of all interval-valued $(\in, \in\mspace{-5mu}\vee\,q)$-fuzzy $LI$-ideals in a lattice implication algebra, under the partial order $\sqsubseteq$, forms a complete distributive lattice.
Keywords:lattice-valued logic  lattice implication algebra  interval-valued $(\in  \in\mspace{-5mu}\vee\  q)$-fuzzy $LI$-ideal  complete distributive lattice
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