WBR0-代数的Pt-模和Ps-模表示.pdfVIP

Computer Engineering and Applications 计算机工程与应用 2014 ，50（9 ） 49 WBR -代数的Pt-模和Ps-模表示 0 王 娜，吴洪博 WANG Na, WU Hongbo 陕西师范大学 数学与信息科学学院，西安 710062 College of Mathematics and Information Science, Shaanxi Normal University, Xi ’an 710062, China WANG Na, WU Hongbo. Representation of WBR -algebras by Pt-norms and Ps-norms. Computer Engineering and 0 Applications, 2014, 50 （9 ）：49-52. Abstract ：Triangular norms and implication operators are interdependent and basic operators in logic algebras, but WBR -algebras are logic algebras that are defined on general set only using implication operators. The WBR -algebras 0 0 have been studied in depth. The form of Pt-norm （t-norms on posets ）on WBR -algebras is given; the equivalence repre- 0 sentation of WBR -algebras has been obtained on posets through Pt-norms and implication operators; it is proved that the 0 binary operation Å in the original definition of the WBR -algebras is the Ps-norm （s-norm on posets）of WBR -algebras. 0 0 The results of this paper have positive reference value to the further study of WBR -algebras and the relevant logic algebras. 0 Key words ：logic algebra; WBR -algebra; poset; Pt-norm; Ps-norm 0 摘 要：三角模和蕴涵