A survey of categorical properties of L-fuzzy relations

Abstract An L -fuzzy relation is a relation valued on a complete lattice L with a monoidal structure. This paper reviews four categories of L -fuzzy relations each modelling an area where Fuzzy Set Theory can be applied. We review the notions of these multivalued binary relations and present some basic properties of the corresponding categories aiming at applications in areas such as Computing Science, Linear Logic and Quantum Mechanics. The emphasis is on the monoidal aspects of the categories. Monoidal categories are one of the most applied kinds of categories. A monoidal view of Fuzzy Relations may widen the spectrum of applications of Fuzzy Set Theory.