| 强Ockham代数与剩余格 |
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| 引用本文： | 张隆传,张小红. 强Ockham代数与剩余格[J]. 纯粹数学与应用数学, 2010, 26(1): 123-130,145. DOI: 10.3969/j.issn.1008-5513.2010.01.021 |
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| 作者姓名： | 张隆传 张小红 |
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| 作者单位： | 宁波大学数学系,浙江,宁波,315211;宁波大学数学系,浙江,宁波,315211 |
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| 基金项目： | 国家自然科学基金(60775038);;宁波市自然科学基金(2009A610078);;宁波大学王宽诚幸福基金 |
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| 摘 要： | 首先讨论了Ockham代数与剩余格的关系，引入了强Ockham代数的概念，并讨论了它的基本性质．然后，将著名的风蕴涵和风算子推广到Ockham代数上，证明了添加广义R0蕴涵和广义风算子后的Ockham代数L成为剩余格的充要条件是L为强Ockham代数．最后给出若干重要例子，以此来说明强Ockham代数的条件是独立的．
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| 关 键 词： | 模糊逻辑 强De Morgan代数 Ockham代数 剩余格 强Ockham代数 |
Strong Ockham algebra and residuated lattice |
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| ZHANG Long-chuan,ZHANG Xiao-hong. Strong Ockham algebra and residuated lattice[J]. Pure and Applied Mathematics, 2010, 26(1): 123-130,145. DOI: 10.3969/j.issn.1008-5513.2010.01.021 |
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| Authors: | ZHANG Long-chuan ZHANG Xiao-hong |
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| Affiliation: | Department of Mathematics;Ningbo University;Ningbo 315211;China |
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| Abstract: | Firstly,the relation between Ockham algebras and residuated lattice are investigated,and the notion of Strong Ockham algebras is introduced,and its elementary properties are given.Secondly,the famous R_0 implication and R_0 operator are developed to Ockham algebras,which are called general R0 implication and general R_0 operator.And the necessary and sufficient condition is proved as following:a Ockham algebra L with general R_0 implication and general R_0 operator becomes a Residuated lattice if and only i... |
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| Keywords: | fuzzy logic strong De Morgan algebras Ockham algebras residuated lattices strong Ockham algebras |
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