Characterizations for the migrativity of uninorms over N -ordinal sum implications

The migrative equations offer an important tool to characterize new fuzzy logic connectives, and play a significant role in image processing. The migrative equations of disjunctive aggregation functions over fuzzy implications, together with their dualities, provide a unified framework for the study of migrativity between fuzzy logic connectives which will include, as special cases, the migrative equations studied in the literature. In this paper, we focus on the migrativity of uninorms over N -ordinal sum implications due to the respective fundamental roles of them in aggregation functions and fuzzy implications. We characterize the α -migrativity of uninorms over N -ordinal sum implications depending on the position where α lies in the range of N . The necessary and sufficient conditions under which a uninorm is α -migrative over an N -ordinal sum implication are obtained by giving ordinal sum representations of the underlying t-norms or t-conorms of the uninorm and the representations of the α -vertical section of the implication function.