We present a quantum framework for coarse graining and fuzzy measurements in a multiparticle system, based solely on what might be physically measured.  For the case of coarse graining, we assume that the detectors can measure only randomly selected particles with a physically motivated distribution. For the case of fuzzy measurements, we assume that the detectors might be placed incorrectly, leading to misidentification of some particles. In the space of states, both situations induce completely positive maps that lead to a shrinking of the state space.