On the concept of fuzzy order II: Antisymmetry

In the second part of our paper, we explore antisymmetry of fuzzy orders. We provide a unifying definition of antisymmetry, which generalizes three existing variants of antisymmetry examined in the literature, along with the corresponding generalized definition of fuzzy order. We prove that all the particular instances of the generalized definition, which include the three basic ones, are mutually equivalent. We also examine distinctive properties of the three basic notions of fuzzy order.