On The Investigation Of The Distributivity Property For T-uninorms

In this paper,we investigate the distributivity between T-uninorms and aggregation operators.Firstly,we investigate the distributivity for some special aggregation operators over T-uninorms with the underlying uninorms in U_max.We obtain the necessary conditions or sufficient conditions for t-(co)norms distributive over T-uninorms.On the basis of discussions mentioned above,the distributivity betweenT-uninorms is discussed.Secondly,the distributivity between semi-t-operators and T-uninorms with the underlying uninorms in U_maxis investigated.We study the necessary conditions or sufficient conditions when T-uninorms are distributive over semi-t-operators.Moreover,we characterize the left and right dis-tributivity equations for semi-t-operators over T-uninorms.Especially,the algebraic characterizations of the distributivity betweenT-uninorms and semi-t-operators are obtained.Finally,we investigate the distributivity for T-uninorms over uninorms,where uninorms are assumed to be arbitrary.Especially,the underlying uninorms of T-uninorms are not only assumed to be in U_maxbut also some other types of T-uninorms,that is,the underlying uninorms of T-uninorms in U_cos,max.