Two classes of ordinal sum implications

This article aims to contribute to the theory of ordinal sum implications by introducing two new classes: the minor ordinal sum implications and the major ordinal sum implications. The study presents diverse construction methods employed in generating examples of these two new classes. A method of constructing ordinal sums of implications that may be neither major nor minor is also presented. Furthermore, the article extends its contribution by providing examples of major and minor ordinal sum implications within some of the main classes of fuzzy implications, including (S,N)-implications, (T,N)-implications, QL-implications and D-implications. A study of the properties satisfied by the new ordinal sum implications is also presented.