On uninorms with fixed values along their border

Abstract. Since their introduction, uninorms have been studied deeply by numerous authors from theoretical and also from application points of view. Recently, a characterization of the class of uninorms with strict underlying t-norm and t-conorm was presented. It is also known that uninorms with nilpotent underlying t-norm and t-conorm belong to \(U_{min}\) or \(U_{max}\). In this paper, some further construction methods of uninorms with fixed values along the borders are discussed and sufficient and necessary conditions are presented.