J4 ›› 2012, Vol. 47 ›› Issue (2): 93-97.
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李玲玲, 吴洪博*
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国家自然科学基金资助项目(10871121)
LI Ling-ling, WU Hong-bo*
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摘要：
在BR0-代数结构中,BR0-分配性a→b∨c=(a→b)∨(a→c)具有十分重要的地位。本文证明了具有BR0-分配性的剩余格同样具备十分良好的性质。首先将BR0-分配性引入到剩余格中,并给出了BR0-分配性的等价形式。其次,在完备剩余格中将BR0-分配性进行了推广,提出了BR0-第一无限分配性和BR0-第二无限分配性。最后,分别在正则完备剩余格,单位区间［0,1］中讨论了两种BR0-无限分配性的关系及性质。
关键词: 模糊逻辑;剩余格;BR0-代数;BR0-分配性;无限分配性
Abstract:
BR0-distributivity has an important position in the structure of BR0algebras which says a→b∨c=(a→b)∨(a→c). It is proved that residuated lattices with BR0-distributivity also have good properties. BR0-distributivity is introduced in residuated lattices, and its equivalent form is given. Then the BR0-distributivity is generalized in complete residuated lattices, and BR0-first infinite distributivity and BR0-second infinite distributivity are obtained. Finally, the properties and relationship between two kinds of BR0-infinite distributivity are discussed in regular complete residuated lattices and the unite interval ［0,1］, respectively.
Key words: fuzzy logic; residuated lattice; BR0-algebras; BR0-distributivity; infinite distributivit
李玲玲, 吴洪博*. BR0-分配性及其推广[J]. J4, 2012, 47(2): 93-97.
LI Ling-ling, WU Hong-bo*. BR0-distributivity and its generalization[J]. J4, 2012, 47(2): 93-97.
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http://lxbwk.njournal.sdu.edu.cn/CN/Y2012/V47/I2/93
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