Abstract :
Powerset structures of extensional fuzzy sets in sets with similarity
relations are investigated. It is proved that extensional fuzzy sets have powerset
structures which are powerset theories in the category of sets with similarity
relations, and some of these powerset theories are dened also by algebraic
theories (monads). Between Zadeh's fuzzy powerset theory and the classical
powerset theory there exists a strong relation, which can be represented as a
homomorphism. Analogical results are also proved for new powerset theories
of extensional fuzzy sets.
