Concept Formation Model of the Shape of Two-Dimensional Multimodal Functions and Its Application to Optimization

This paper describes a method of concept formation of human beings and its application to optimization. Human beings are able to grasp general shapes with only a small amount of information by using heuristics and fuzziness. We use the words “TOP,” “SIDE,” and “BOTTOM” of the mountain as basic concepts for representing a two-dimensional multimodal shape. The basic concepts for each point on a surface are defined by “IF-THEN” rules. First, a maximal point search experiment is carried out and the concept formation proceeding is observed. Secondly, the heuristical algorithm of human subjects is extracted. Next, the algorithm is represented using some simple rules. Finally, the human subjects’ shape-grasping process is simulated on a computer. The results are comparable to concepts of shape formed by human subjects, so the similarity between them can be confirmed. The proposed method is useful in making a machine-oriented concept formation of shape such as a topographic map.