预线性与对合非结合剩余格  

Prelinear and Involution Non-associative Residuated Lattices

作　　者：梁聪[1] 张小红[2] 

机构地区：[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

出　　处：《模糊系统与数学》2012年第3期17-23,共7页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61175044);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。Non-associative residuated lattice is a common algebraic abstract of various non-assoctauve lattice-valued logic systems. In this paper, the algebraic properties o{ 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 su{ficient 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.

关 键 词：模糊逻辑 非结合剩余格 预线性 对合 蕴涵格 

分 类 号：O141[理学—数学]