International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 36, Pages 2303-2313

On an equivalence of fuzzy subgroups III

V. Murali1 and B. B. Makamba2

1Department of Mathematics (Pure and Applied), Faculty of Science, Rhodes University, Grahamstown 6140, South Africa
2Department of Mathematics, Faculty of Science, University of Fort Hare, Alice 5700, South Africa

Received 29 May 2002

Copyright © 2003 V. Murali and B. B. Makamba. 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.


This paper is the third in a series of papers studying equivalence classes of fuzzy subgroups of a given group under a suitable equivalence relation. We introduce the notion of a pinned flag in order to study the operations sum, intersection and union, and their behavior with respect to the equivalence. Further, we investigate the extent to which a homomorphism preserves the equivalence. Whenever the equivalences are not preserved, we have provided suitable counterexamples.