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
格蕴涵代数的区间值$(\in, \in\vee\,q)$-模糊$LI$-理想格
Lattice of Interval-Valued $(\in, \in\vee\,q)$-Fuzzy $LI$-Ideals in Lattice Implication Algebras
投稿时间:2015-09-13  最后修改时间:2016-03-08
DOI:10.3770/j.issn:2095-2651.2016.04.002
中文关键词:  格值逻辑  格蕴涵代数  区间值$(\in, \in\vee\,q)$-模糊$LI$-理想  完备分配格
英文关键词:lattice-valued logic  lattice implication algebra  interval-valued $(\in, \in\mspace{-5mu}\vee\,q)$-fuzzy $LI$-ideal  complete distributive lattice
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).
作者单位
刘春辉 赤峰学院数学与统计学院, 内蒙古 赤峰 024001 
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中文摘要:
      本文深入研究了格蕴涵代数的区间值$(\in, \in\mspace{-5mu}\vee\,q)$-模糊$LI$-理想理论. 给出了区间值$(\in, \in\mspace{-5mu}\vee\,q)$-模糊$LI$-理想的若干新的性质. 建立了由一个模糊集生成的区间值$(\in, \in\mspace{-5mu}\vee\,q)$-模糊$LI$-理想的表示定理. 证明了一个格蕴涵代数的全体区间值$(\in, \in\mspace{-5mu}\vee\,q)$-模糊$LI$-理想之集在偏序$\sqsubseteq$下构成一个完备的分配格.
英文摘要:
      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.
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