伪BCI-代数的导出半群与T-部分（英文）

Derived Semi-group and T-part of Pseudo-BCI Algebras

伪BCI-代数是一类非经典逻辑代数,它是伪BCK-代数的推广,而伪BCK-代数与各种非可换模糊逻辑代数有密切关系。本文从任意伪BCI-代数出发,构造了两种加法运算,进而得到两个导出半群。同时,本文引入强伪BCI-代数、伪BCI-代数的T-部分等概念,给出伪BCI-代数的T-部分成为伪BCI-滤子的一些等价条件。

Pseudo-BCI algebra is a kind of non-classical logicalgebra; it is a generalization of pseudo-BCK algebra which is close connection with various non-commutative fuzzy logical algebras. In this paper, from any pseudo-BCI algebra, two addition operations are established, and two derived semi-groups are obtained. Moreover, the notions of strong pseudo-BCI algebra and T-part of pseudo-BCI algebra are introduced, and some equivalent conditions for the T-part to be a pseudo-BCI filter are proved.