An insight into the conditional distributivity of nullnorms over uninorms

Conditional distributivity (also called restricted distributivity) is a form of relaxed distributivity on the restricted domain. There are three options for conditional distributivity in literature. In this paper, we focus on type-III conditional distributivity equation involving nullnorms over uninorms. Firstly, we show that it can be transformed into the other two types of conditional distributivity equations involving t-norms/t-conorms over uninorms. Secondly, type-I and type-II conditional distributivity equations involving t-norms/t-conorms over uninorms that are related to our study and remain unknown are investigated. Finally, we show that this new perspective results in not only all known solutions, but new solutions as well.