Proximity Measures for the Classification of Geometric Figures

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Abstract
A proximity relation is a fuzzy relation which is reflexive, symmetric, but not necessarily transitive. A quantitative measure of the proximity of two n-sided polygons is defined. Various properties of angular and dimensional proximities of triangles are investigated. A method for classifying a triangle as an “approximate right triangle,” “approximate isosceles triangle,” “approximate isosceles right triangle,” “approximate equilateral triangle” or “ordinary triangle” is presented. A method used to classify a quadrangle as “approximate square,” “approximate rectangle,” “approximate rhombus,” “approximate parallelogram,” “approximate trapezoid” or “ordinary quadrangle” is also presented. The measures of proximity employed for this purpose have an intuitive interpretation. The results may be of use in pattern recognition, information retrieval and artificial intelligence.

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