International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 567482, 16 pages
Research Article

Connecting Fuzzifying Topologies and Generalized Ideals by Means of Fuzzy Preorders

Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt

Received 17 February 2009; Accepted 25 May 2009

Academic Editor: Etienne Kerre

Copyright © 2009 G. Elsalamony. 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.


The present paper investigates the relations between fuzzifying topologies and generalized ideals of fuzzy subsets, as well as constructing generalized ideals and fuzzifying topologies by means of fuzzy preorders. Furthermore, a construction of generalized ideals from preideals, and vice versa, is obtained. As a particular consequence of the results in this paper, a construction of fuzzifying topology generated by generalized ideals of fuzzy subsets via a given I-topology is given. The notion of σ-generalized ideal is introduced and hence every σ-generalized ideal is shown to be a fuzzifying topology induced by some fuzzy preorder.