A note on fuzzy neighbourhood base spaces

Fuzzy neighbourhood base spaces (FNBS), introduced by Morsi, are a special type of stratified I-topological spaces (SI-TOP), previously denoted as fuzzy topological spaces (FTS). We introduce further characterizations of FNBS in terms of level sets. Also, we construct stable subconstructs of SI-TOP, in the sense of Lowen and Wuyts [Stable subconstructs of FTS: I, J. Fuzzy Math. 1(3) (1993) 475–489], whose corresponding total stratified I-topologies are generated by elements of II which are greater than idI. The maximal objects of such stable subconstructs have weaker properties than that of the ascending chain property, and then these objects give rise to fuzzy neighbourhood base spaces. Therefore, special types of fuzzy neighbourhood base spaces are constructed.