摘要
本文研究了格的TL-模糊理想.利用生成TL-模糊理想,证明了一个模格的全体TM-模糊理想形成一个完备的模格.此外,利用L-模糊集的投影和截影,获得了将直积格的TL-模糊理想表示成分量格的TL-模糊理想的T-直积的一个充分必要条件.所得结果进一步推广和发展了格的模糊理想的理论.
In this paper,we study T L-fuzzy ideals in lattices.By a T L-fuzzy ideal generated by an L-fuzzy subset,we prove that the lattice of TM-fuzzy ideals in a modular lattice is a complete modular lattice.Moreover,using the projection and the cut shadow of an L-fuzzy set,we obtain necessary and sufficient conditions for a T L-fuzzy ideal of a Cartesian product of lattices to be a T-product of T L-fuzzy ideals of lattices.Our results generalize and develop the fuzzy ideal theory in lattices.
出处
《数学杂志》
CSCD
北大核心
2015年第6期1341-1352,共12页
Journal of Mathematics
基金
Supported by Graduate Independent Innovation Foundation of Northwest University(YZZ12061)
Scientific Research Program Funded by Shaanxi Provincial Education Department(2013JK0562)
关键词
左连续t-模
模糊理想
模格
T-直积
left continuous t-norm
T L-fuzzy ideal
modular lattice
T-product
