The conditional distributivity, also called restricted distributivity, is crucial for many different areas such as utility theory and integral theory. This is the because it weakens distributivity on the domain. This paper is focused on and fully characterizes the conditional distributivity for a uni-nullnorm with continuous and Archimedean underlying t-norms and t-conorm over a continuous t-conorm or a uninorm from Umin ∪ Umax with continuous underlying operators.
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