The ACID (Atomicity, Consistency, Isolation, andDurability) model has played a cornerstone role in servicecomposition to guarantee that Composite Services (CSs) havetransactional support and consistent outcomes ("all-or-nothing" property). However, the classical "all-or-nothing" model is toorestrictive for loosely coupled and distributed environments asInternet. Some approaches have been proposed to relax atomicitybased on transactional properties of services, using compensationmechanisms or providing checkpointing techniques. In this article, we propose a model that measures the fuzzy atomicity of acomposite service based on transactional properties and on thecheckpointing mechanism, relaxing the "all-or-nothing" propertyinto a new a fuzzy "all-something-or-(almost) nothing" property. The proposed measure takes into account the acceptable fuzzyatomicity expressed in the user requirements (i.e., the minimumresult that user can accept), but also the state of the compositeservice execution. As far as we know, no such a model exists.