BCI-代数的 Fuzzy α-理想(英文)  

Fuzzy a-Ideals of BCI-Algebras

作　　者：刘用麟[1] 张小红[2] 

机构地区：[1]南平师范高等专科学校数学系 [2]汉中师范学院数学系

出　　处：《数学进展》2002年第1期65-73,共9页Advances in Mathematics（China）

基　　金：the Natural Sicence Foundation of Fujian Educational Commission ;the Natural Science Foundation of Shaanxi.

摘　　要：本文的目的是引进 ＢＣＩ－代数的 ｆｕｚｚｙ ａ－理想的概念与探讨它的性质．给出了 ｆｕｚｚｙ ａ－理想的特征与Ｍｅｎｇ’ｓ扩张定理．讨论了 ＢＣＩ－代数中 ｆｕｚｚｙ ａ－理想，ｆｕｚｚｙ ｑ－理想与ｆｕｚｚｙ ｐ－理想之间的关系，从而得到一个 ＢＣＩ－代数的 ｆｕｚｚｙ子集是 ｆｕｚｚｙ ａ－理想当且仅当它是 ｆｕｚｚｙ ｙ－理想与 ｆｕｚｚｙｐ－理想，利用 ｆｕｚｚｙ ａ－理想与 ｆｕｚｚｙｐ－理想分别刻画了结合 ＢＣＩ－代数与ｐ－半单 ＢＣＩ－代数．此外，亦给出了 ｆｕｚｚｙ ａ－理想的其他性质．The aim of this paper is to introduce the concpet of fuzzy a-ideals in BCI--algebras and investigate its properties. The characterizations and the Meng's extension the-orem about fuzzy a-ideals are given. We discuss the connects among fuzzy a-ideals, fuzzy q-ideals and fuzzy p-ideals in BCI-algebras and show that a fuzzy set of a BCI-algebra is fuzzy a-ideal if and only if it is both fuzzy q-ideal and fuzzy p-ideal. Using fuzzy a-ideals (p-ideals) we characterize associative (p-semisimple) BCI-algebras. Moreover, other properties of fuzzy a-ideals are obtained.

关 键 词：零fuzzy理想 BCI-代数 模糊α-理想 模糊q-理想 模糊p-理想 

分 类 号：O153.3[理学—数学] O159[理学—基础数学]