On defining and computing fuzzy kernels on L-valued simple graphs

In this paper we introduce the concept of fuzzy kernels defined on valued-finite simple graphs in a sense close to fuzzy preference modelling. First we recall the classic concept of kernel associated with a crisp binary relation defined on a finite set. In a second part, we introduce fuzzy binary relations. In a third part, we generalize the crisp kernel concept to such fuzzy binary relations and in a last part, we present an application to fuzzy choice functions on fuzzy outranking relations