Prototype-based Categorization of Structural Complexity Estimates of Simplicial Complexes

P. 27–37.

Degtyarev K. Y.

The material of the present paper is grounded on the holist algebraic method (Q-analysis) proposed by English mathematician and physicist R.H.Atkin. At its core, the approach is aimed at both analysis of systems structures (in the form of simplicial complexes K, which is formed by a set of properly adjoined objects called simplexes) and calculation of numeric estimates of structural complexity of systems based on the results of such analysis.

Turning complexity estimate of system’s structure into a real number creates additional difficulties in the comparison of two different complexes because there is no real verbal scale, which would have been accustomed to human beings and would allow a group of experts to express opinions and draw easily conclusions about degree of complexity of K at each particular dimensional level of its analysis. Therefore, the present paper deals with consideration of the approach that is more focused on human perception of characteristics obtained, mental comprehension and formation (comparison) of personal constructs in psychological space (or, P-space) – modified structural complexity estimate is based right on notions of distance and similarity within psychological space.

Keywords: категоризация, simplex, simplicial complex, structural complexity (connectivity), Q-analysis, proximity, concepts (categories), prototype of category, extended point (F-point), extended line, categorization, симплекс, симплициальный комплекс, структурная сложность (связность), Q-анализ, понятие близости, концепции (категории), прототип категории, расширенная точка (F-точка), расширенная линия

In book

Proceedings of the 10th International Conference on Application of Fuzzy Systems and Soft Computing (ICAFS-2012)

Kaufering: b-Quadrat Verlag, 2012.