WBR_0-代数的Pt-模和Ps-模表示  

Representation of WBR_0-algebras by Pt-norms and Ps-norms

作　　者：王娜[1] 吴洪博[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710062

出　　处：《计算机工程与应用》2014年第9期49-52,共4页Computer Engineering and Applications

基　　金：国家自然科学基金(No.11171196)

摘　　要：三角模和蕴涵算子是逻辑代数中的一对相互关联的基本算子,而WBR0-代数是仅以蕴涵算子为基本算子定义于一般集合上的逻辑代数。对WBR0-代数进行了再研究。给出了WBR0-代数的Pt-模(偏序集上的t-模)的表现形式;在偏序集上通过Pt-模结合蕴涵算子给出了WBR0-代数的表示形式;证明了WBR0-代数原始定义中的二元运算⊕是WBR0-代数的Ps-模(偏序集上的s-模)。结果对进一步探讨WBR0-代数及其相关的逻辑代数有积极的参考价值。Triangular norms and implication operators are interdependent and basic operators in logic algebras, but WBR0-algebras are logic algebras that are defined on general set only using implication operators. The WBR0-algebras have been studied in depth. The form of Pt-norm（t-norms on posets）on WBR0-algebras is given;the equivalence repre-sentation of WBR0-algebras has been obtained on posets through Pt-norms and implication operators;it is proved that the binary operation ？ in the original definition of the WBR0-algebras is the Ps-norm（s-norm on posets）of WBR0-algebras. The results of this paper have positive reference value to the further study of WBR0-algebras and the relevant logic algebras.

关 键 词：逻辑代数 WBR0-代数 偏序集 Pt-模 Ps-模 

分 类 号：O141.1[理学—数学]