Optical music recognition aims at reading automatically scanned scores in order to convert them in an electronic format, such as a midi ÿle. We only consider here classical monophonic music: we exclude any music written on several staves, but also any music that contains chords. In order to overcome recognition failures due to the lack of methods dealing with structural information, non-local rules and corrections, we propose a recognition approach integrating structural information in the form of relationships between symbols and of musical rules. Another contribution of this paper is to solve ambiguities by accounting for sources of imprecision and uncertainty, within the fuzzy set and possibility theory framework. We add to a single symbol analysis several rules for checking the consistency of hypotheses: graphical consistency (compatibility between accidental and note, between grace note and note, between note and augmentation dot, etc.), and syntactic consistency (accidentals, tonality, metric). All these rules are combined in order to lead to better decisions. Experimental results on 65 music sheets show that our approach leads to very good results, and is able to correct errors made by other approaches, such as the one of SmartScore.