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| 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L-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. |
| 关键词: 左连续t-模 模糊理想 模格 T-直积 |
| DOI： |
| 分类号:O159 |
| 基金项目:Supported by Graduate Independent Innovation Foundation of Northwest Uni-versity (YZZ12061); Scientific Research Program Funded by Shaanxi Provincial Education Department (2013JK0562). |
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| ON TL-FUZZY IDEALS IN LATTICES |
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HE Peng-fei,YANG Yong-wei
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| Abstract: |
| In this paper, we study TL-fuzzy ideals in lattices. By a TL-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 TL-fuzzy ideal of a Cartesian product of lattices to be a T-product of TL-fuzzy ideals of lattices. Our results generalize and develop the fuzzy ideal theory in lattices. |
| Key words: left continuous t-norm TL-fuzzy ideal modular lattice T-product |
