International Journal of Mathematics and Mathematical Sciences 
Volume 25 (2001), Issue 2, Pages 135-143
doi:10.1155/S0161171201005087

Fuzzy BCI-subalgebras with interval-valued membership functions

Sung Min Hong,1 Young Bae Jun,2 Seon Jeong Kim,1 and Gwang Il Kim1

 1Department of Mathematics, Gyeongsang National University, Chinju 660-701, South Korea
2Department of Mathematics Education, Gyeongsang National University, Chinju 660-701, South Korea
Received 3 May 2000

Abstract

The purpose of this paper is to define the notion of an interval-valued fuzzy BCI-subalgebra (briefly, an i-v fuzzy BCI-subalgebra) of a BCI-algebra. Necessary and sufficient conditions for an i-v fuzzy set to be an i-v fuzzy BCI-subalgebra are stated. A way to make a new i-v fuzzy BCI-subalgebra from old one is given. The images and inverse images of i-v fuzzy BCI-subalgebras are defined, and how the images or inverse images of i-v fuzzy BCI-subalgebras become i-v fuzzy BCI-subalgebras is studied.