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.

Abstract

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.