| 预线性与对合非结合剩余格 |
| |
| 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 |
| |
| 作者姓名： | 梁聪 张小红 |
| |
| 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 |
| |
| 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 |
| |
| 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。
|
| 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 |
| |
| LIANG Cong , ZHANG Xiao-hong. Prelinear and Involution Non-associative Residuated Lattices[J]. Fuzzy Systems and Mathematics, 2012, 26(3): 17-23 |
| |
| Authors: | LIANG Cong ZHANG Xiao-hong |
| |
| Affiliation: | 1.Department of Mathematics,Ningbo University,Ningbo 315211,China;2.Department of Mathematics,Shanghai Maritime University,Shanghai 201306,China) |
| |
| 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. |
| |
| Keywords: | Fuzzy Logic Non-associative Residuated Lattice Prelinear Involution Implication Lattice |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
