Categories with fuzzy sets and relations.

We define a 2-category whose objects are fuzzy sets and whose maps are relations subject to certain natural conditions. We enrich this category with additional monoidal and involutive structure coming from t-norms and negations on the unit interval. We develop the basic properties of this category and consider its relation to other familiar categories. A discussion is made of extending these results to the setting of type-2 fuzzy sets. [ABSTRACT FROM AUTHOR]