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Abstract: 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. [Copyright &y& Elsevier]

Abstract: This paper presents, by means of Alexandrov topology for fuzzy preordered sets and specialization order for fuzzy topological spaces, a systematic investigation of the interrelationship between fuzzy preordered sets, topological spaces, and fuzzy topological spaces. [Copyright &y& Elsevier]