An $\mathbb{L}$-fuzzy relation is a relation valued on a complete lattice $\mathbb{L}$ with a monoidal structure. This paper reviews four categories of $\mathbb{L}$-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.

中文翻译：

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L-模糊关系的范畴性质综述

一个 $\mathbb{升}$-fuzzy 关系是在完全格上取值的关系 $\mathbb{升}$具有幺半群结构。本文回顾了四类$\mathbb{升}$-模糊关系每个建模一个可以应用模糊集理论的领域。我们回顾了这些多值二元关系的概念，并针对计算科学、线性逻辑和量子力学等领域的应用，介绍了相应类别的一些基本属性。重点是范畴的幺半群方面。幺半群范畴是应用最广泛的范畴之一。模糊关系的幺半群观点可能会拓宽模糊集合论的应用范围。