| 预线性与对合非结合剩余格 |
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| 引用本文： | 梁聪,张小红.预线性与对合非结合剩余格[J].模糊系统与数学,2012,26(3):17-23. |
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| 作者姓名： | 梁聪 张小红 |
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| 作者单位： | 1. 宁波大学数学系,浙江宁波,315211
2. 上海海事大学文理学院,上海,201306 |
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| 基金项目： | 国家自然科学基金资助项目，上海海事大学科研基金资助项目 |
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| 摘 要： | 非结合剩余格是非结合格值逻辑系统的代数抽象,本文研究几类特殊非结合剩余格的代数性质。证明了满足预线性条件的非结合剩余格必是分配格,并给出预线性非结合剩余格的充分必要条件。同时,引入对合和强对合非结合剩余格的概念,研究了它们的基本性质,并分别给出对合和强对合非结合剩余格的等价条件。最后,通过反例说明强对合预线性非结合剩余格不一定是蕴涵格。
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| 关 键 词： | 模糊逻辑 非结合剩余格 预线性 对合 蕴涵格 |
Prelinear and Involution Non-associative Residuated Lattices |
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| LIANG Cong
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ZHANG Xiao-hong.Prelinear and Involution Non-associative Residuated Lattices[J].Fuzzy Systems and Mathematics,2012,26(3):17-23. |
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| Authors: | LIANG Cong ZHANG Xiao-hong |
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| Institution: | 1.Department of Mathematics,Ningbo University,Ningbo 315211,China;2.Department of Mathematics,Shanghai Maritime University,Shanghai 201306,China) |
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| Abstract: | Non-associative residuated lattice is a common algebraic abstract of various non-associative lattice-valued logic systems.In this paper,the algebraic properties of several special non-associative residuated lattices are studied.It is proved that every prelinear non-associative residuated lattice is a bounded distributive lattice,and a necessary and sufficient condition for non-associative residuated lattice to be prelinear is given.The notions of involution and strong involution non-associative residuated lattice are introduced,and their basic properties are studied.Moreover,the equivalence conditions for involution non-associative residuated lattices and strong involution non-associative residuated lattices are given respectively.Finally a counter example is given to show that there is a strong involution and prelinear non-associative residuated lattice which is not an implication lattice. |
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| Keywords: | Fuzzy Logic Non-associative Residuated Lattice Prelinear Involution Implication Lattice |
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