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We consider the concept of fuzzy order in which antisymmetry is intrinsically connected to a many-valued equality on the underlying universe. We examine the origins of this concept, provide remarks and observations on the existing studies, and prove new results. In part I, we scrutinize the existing approaches to the examined concept of fuzzy order and present remarks and results to elucidate the available notions and findings, as well as to provide a deeper insight into several issues. In part II, we explore antisymmetry.

On the concept of fuzzy order I: Remarks and observations