Using fuzzy logic to analyze superscript and subscript relations in handwritten mathematical expressions

Handwritten mathematical notation contains ambiguities of various kinds. Here we focus on ambiguity in spatial relationships; in particular, we use fuzzy logic to treat ambiguity in subscript-or-inline and inline-or-superscript spatial relationships. We extend an existing system for recognizing handwritten mathematical notation, adding the capability of producing a ranked list of interpretations rather than a single top-choice interpretation. Fuzzy membership values are assigned to each spatial relationship; a given pair of symbols can have non-zero membership in fuzzy sets subscript and inline, or in fuzzy sets inline and superscript. These fuzzy membership values are combined to produce an overall confidence value for the entire interpretation. We have modified the user interface of our system so that a user can quickly view and select from the ranked interpretations when the highest confidence interpretation is incorrect.