Verbal Representation for Shape Recognition of Multi-Dimensional Functions

Definition of Words and Its Truth Value

Abstract

This paper describes a verbal representation for shape recognition of multi-dimensional functions. It is expected that the verbalizing of the shape will make it possible to represent shape features, an intelligent shape representation, which can not be represented in multi-dimensional space by contour lines. That is because the verbalizing is one of symbolizing methods of the shape, by which an intelligent processing is executed on a computer. First, the words used for a topographical representation in the geography are discussed. Second, the words used for the verbal representation, TOP, BOT (Bottom), SAD (Saddle), RID (Ridge), VAL (Valley) and SLO (Slope), are defined in n-dimensional space. The truth value of the words is also evaluated based on fuzzy set theory. Finally, shape representations of two-dimensional and three-dimensional functions are shown and compared with those by contour lines.