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

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

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.