The cross-migrative property for uninorms (Q727957)

A function \(U: [0, 1]^2 \to [0,1]\) is called a uninorm if it is associative, commutative, increasing with respect to each variable and there exists \(e \in [0, 1]\), called the neutral element, such that \(U(e, x) = x\) for all \(x \in [0, 1]\). Let \(\alpha \in [0, 1]\). A pair \((U, U_0)\) of uninorms \(U\) and \(U_0\) is \(\alpha\)-cross-migrative if \[ U(U_0(\alpha,x),y) = U_0(x,U(\alpha,y)) \] for all \(x,y \in [0, 1]\). The authors find certain conditions equivalent to \(\alpha\)-cross-migrativity of pairs \((U,U_0)\) of uninorms \(U\) and \(U_0\) with the same neutral element.There are numerous results of this kind in the paper.