Distributivity of the Ordinal Sum Implications Over t-Norms and t-Conorms

Recently, Su and Liu have introduced a new class of fuzzy implications, called ordinal sum implications, and discussed some of their desirable properties, such as neutrality property, consequent boundary, exchange principle, etc. In this paper, we explore the class of ordinal sum implications with respect to distributivity. Necessary and sufficient conditions, under which ordinal sum implications are distributive over t-norms and t-conorms are given.