| 格蕴涵代数的区间值$(in, invee,q)$-模糊$LI$-理想格 |
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| 引用本文： | 刘春辉. 格蕴涵代数的区间值$(in, invee,q)$-模糊$LI$-理想格[J]. 数学研究及应用, 2016, 36(4): 394-406 |
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| 作者姓名： | 刘春辉 |
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| 作者单位： | 赤峰学院数学与统计学院, 内蒙古 赤峰 024001 |
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| 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). |
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| 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.
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| 关 键 词： | lattice-valued logic lattice implication algebra interval-valued (∈,∈∨q)-fuzzy LI-ideal complete distributive lattice |
| 收稿时间： | 2015-09-13 |
| 修稿时间： | 2016-03-08 |
Lattice of Interval-Valued $(in, invee,q)$-Fuzzy $LI$-Ideals in Lattice Implication Algebras |
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| Chunhui LIU. Lattice of Interval-Valued $(in, invee,q)$-Fuzzy $LI$-Ideals in Lattice Implication Algebras[J]. Journal of Mathematical Research with Applications, 2016, 36(4): 394-406 |
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| Authors: | Chunhui LIU |
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| Affiliation: | Department of Mathematics and Statistics, Chifeng University, Inner Mongolia 024001, P. R. China |
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| Abstract: | In the present paper, the interval-valued $(in, inmspace{-5mu}vee,q)$-fuzzy $LI$-ideal theory in lattice implication algebras is further studied. Some new properties of interval-valued $(in, inmspace{-5mu}vee,q)$-fuzzy $LI$-ideals are given. Representation theorem of interval-valued $(in, inmspace{-5mu}vee,q)$-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 $(in, inmspace{-5mu}vee,q)$-fuzzy $LI$-ideals in a lattice implication algebra, under the partial order $sqsubseteq$, forms a complete distributive lattice. |
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| Keywords: | lattice-valued logic lattice implication algebra interval-valued $(in, inmspace{-5mu}vee,q)$-fuzzy $LI$-ideal complete distributive lattice |
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