Distributivity And Conditional Distributivity For Uni-Nullnorms

At first,in this paper,we studied the distributivity and conditional distribu-tivity of the proper conjunctive uni-nullnorm over a t-norm or a t-conorm or a uninorm fromU_min?U_max.According to the results what we have obtained,it is easily shown that,as for the existence of the solution,the distributivity equa-tion and the conditional distributivity equation are equivalent for all the cases considered in this part.That is,if the conditional distributivity equation has a solution,then the distributivity equation also has a solution and vice versa.More-over,if the solution exists,then the number of solutions of the two equations is not equal except the case whenbeing a t-norm.Obviously,that of solutions of the conditional distributivity equation is much more.And then,we study and full 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 fromU_min?U_maxwith continuous underlying operators.In this case,it is interesting to find that when the internal operator is a uninorm fromU_min?U_maxwith continuous underlying operators,then there is only one form satisfies conditional distributivity,respectively.