変換と写像の概念に基づくパターン認知論

概要

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We have investigated how a simplified cognitive system perceives a simplified world which consists of a set of n dimensional binary patterns. We can find a clear mathematical structure in the underlying cognitive mechanism. In this paper, we consider two different types of cognitive judgments of patterns, i. e., goodness and similarity judgments of patterns, from the viewpoint of the Transformational Structure Theory. The theory can explain how cognitive judgments of patterns are performed and can predict ordinal relations between rated goodness and between rated similarities, respectively. The prediction has been supported by many experimental results. Moreover, the Transformational Structure Theory has the following distinctive characteristics: it can be formulated in a dual way for the two qualitatively different types of cognitive judgments of patterns, and it can give a multiple and cognitive definition of "pattern". We expect that mathematical method is applicable and will produce interesting results in the study of fundamental human cognitive phenomena.
日本応用数理学会の論文
1998-03-16