I-fuzzy Alexandrov topologies and specialization orders

The aim of this paper is to investigate the relationships between certain generalized topological structures and fuzzy order structures on a universe set X. In details, a fuzzy preordered relation induces an I-fuzzy Alexandrov topology; and an I-fuzzy topology induces a fuzzy preordered relation, which turns out to be a specialization order in I-fuzzy setting. In addition, the Representation Theorem of fuzzy preorders by I-fuzzy topologies is obtained. These results coincide with the conclusions obtained in literature in the version of two-valued logic.