On the classes of uninorms Umin and Umax on bounded trellises

Recently, the concept of a uninorm on a bounded lattice has been generalized to bounded trellises. A fundamental distinction between lattices and trellises lies in the fact that the underlying pseudo-order relation of a trellis does not need to be transitive. In this paper, we undertake an in-depth dissection of certain types of uninorms on bounded trellises, both from a construction and a characterization point of view. We begin by introducing the uninorms in the classes $U_{\min }$ and $U_{\max }$ on a bounded trellis and provide necessary and sufficient conditions for their characterization. Subsequently, we present two approaches for constructing uninorms on a bounded trellis by utilizing a uninorm defined on a closed subinterval of that bounded trellis. It is shown that these approaches yield uninorms on a bounded trellis that not only differ from the ones obtainable through existing methods, but also generalize those on a bounded lattice constructed via a uninorm defined on a closed subinterval of that bounded lattice.