Fang investigated \(\alpha \) -cross-migrativity of t-conorms over fuzzy implications, which opens a new direction for the relationships between disjunctive connectives and fuzzy implications. Our work is dedicated to the further study of \(\alpha \) -cross-migrativity involving disjunctive uninorms and fuzzy implications with certain properties of either uninorms or fuzzy implications. The investigation is presented in two parts. The first part focuses on the connections between \(\alpha \) -cross-migativitity of disjunctive uninorms over fuzzy implications and other properties, such as \(\alpha \) -mutual exchangeability of fuzzy implications, \(\alpha \) -cross-law of importation of fuzzy implications and uninorms, and \(\alpha \) -cross-migrative property of conjunctive uninorms. The second part deals with fuzzy implications satisfying ordering property.
