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

Fuzzy BCI-subalgebras with interval-valued membership functions

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

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.