Adding fuzziness to terms and powerobjects using a monadic approach

Fuzzy mathematics often starts by taking a piece of classical mathematics and introducing fuzziness to existing mathematical concepts, and then proceeds to a more essential adoption of a fuzzy perspective. This paper explores this progression for two important monads: the powerset monad and its generalizations to fuzzy powerobjects, and the term monad and its generalization to using fuzzy sets of operators. This brings together two lines of research previously discussed at the Linz seminars. The powerset and its fuzzy analogs are important in the development of topology in a fuzzy world and the term monad and its fuzzy analogs are vital in understanding fuzzy computer science.