Визначення характеристик потенціальних кодів за моделями рангових конфігурацій

Abstract

В статті описані геометрична, комбінаторна, алгебрична та топологічна моделі рангових конфігурацій об’єктів системи в просторі ознак, розроблені з метою визначення характеристик двійкових кодів вказаних конфігурацій, що містять інформацію як про самі об’єкти, так і про ранги відстаней між ними. Такі коди названі потенціальними за аналогією з електричним полем, в якому величини зарядів визначають напруженість поля між ними. Проведена оцінка адекватності представлених моделей.The aim of the article is representation of models which were developed for determining of the characteristics of potential codes (DRP-codes - codes that preserves rank distances between objects encoded in the parametric space). The paper presents a unified method for describing and processing of knowledge about the state of the control systems using rank transform of their descriptions made in different parametric spaces: deterministic, probabilistic, fuzzy and others. This problem is solved on the basis of such fundamental concepts as the degree (rank)of the distance between the classes of objects in parametric space. The definition of rank configuration is presented, the efficient low computational cost binary encoding method is described, which determines both the objects (states), and ranks about the distances between them. This code is called potential or DRP-code (code that saves the distances ranks). The method for constructing such a code was defined and its characteristics obtained from the presented models ranked configurations - geometric, algebraic, combinatorial and topological. Adequacy of the proposed models was proved. The results can be used to unify the algorithms of information description and processing in the control systems of different purposes, and as a result to improve the efficiency of decision-making in such systems.