Abstract Four advantages of storing and retrieving geometric figures and chromosome images through the use of shape-oriented similarity measures are presented. A complemented but not distributive lattice and a distributive but not complemented lattice are found. Answers to triangle related fuzzy queries such as “retrieve the triangles which are very similar to isosceles triangles but not similar to a given triangle Δ x ”, and chromosome related fuzzy queries such as “retrieve the chromosomes which are more or less similar to median chromosomes and very very similar to a given chromosome A ” are presented and illustrated by examples. For shape-oriented storage of triangles, it is proposed to store the angles of each triangle in decreasing order of the magnitude and logically order all the triangles according to the magnitude of the angles. For shape-oriented storage of chromosomes, it is proposed to logically order all the chromosomes individually and independently according to the angular sums of its exterior biangles and interior biangles. The results may have useful applications in information storage and retrieval, artificial intelligence and pattern recognition.