In generalizing constructions of N.V. Veli£ko, the paper starts from two generalized topologies μ and μ′ on a set X and introduces two more generalized topologies δ(μ, μ′) and θ(μ, μ′) with the examination of their properties.

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 t...