Images and preimages of \(L\)-filterbases
The paper is concerned with the notion of \(L\)-filterbase formed on a strictly two-sided, commutative quantale lattice \(L\). Considering that \(L\) is a complete lattice and \(\phi\) is a function \(\phi: X\to Y\), the Zadeh image and preimage operators are defined in the form \[ \phi^{\rightarrow}_L(f)(y)= \bigvee\{f(x)\mid\phi(x)= y\},\qquad \phi^{\leftarrow}_L(g)= g\circ\phi. \] Second-order powerset operators are introduced (the image and preimage operators \(\phi^{\rightrightarrows}\) and \(\phi^{\leftleftarrows}\)) and their properties studied.
scientific article; zbMATH DE number 5073274