パターンの変換構造と類似性認知に関する群論的研究
1989 年 60 巻 5 号 p. 297-303
詳細
1989 年 60 巻 5 号 p. 297-303
Transformational structures of linear binary patterns and their similarity judgment, which have been extensively studied from the viewpoint of Imai's transformational structure theory, were analysed mathematically with the aid of the theory of groups in order to clarify the mathematical basis of the transformational structure theory. Main findings are as follows. 1. Each of the basic cognitive transformations should be considered as a transformation (or permutation) group rather than a single transformation. The mirror image M, phase P and value-reversal R. transformations are such examples. 2. The transformation group classifies configurations, and has the following properties which are convenient for similarity cognition of patterns: symmetry of transformability, non-divergency of configurations produced and availability of stepwise transformation by heuristic strategies. 3. We can define the inter-configurational transformation structure of configuration pairs by the transformation group and predict their similarity order, in parallel with the existing transformational structure theory.
