Optimization of knowledge bases on the basis of fuzzy relations by the criteria “accuracy – complexity”

Abstract

The method of optimization of fuzzy classification knowledge bases by the criteria “inference accuracy – complexity” was proposed. A relational fuzzy model, which corresponds to the fuzzy classification knowledge base, was developed. The matrix of fuzzy relations in the form of one-dimensional projection “input terms – output classes” is a simplified representation of the system of classification rules. A problem on the optimization of a knowledge base is reduced to the problem on the min-max clustering and comes down to ing such partition matrices “inputs – output” that provide for the required or extreme levels of inference accuracy and the number of rules.

In the relational models, a question about optimal choice of the number of output terms remains open. A ion of output classes, input terms and rules is reduced to the problem on discrete optimization of the algorithm reliability indicators, in order to solve which, we employed the gradient method. The number and location of hyperboxes are determined by the relations matrix, and the sizes of hyperboxes are defined as a result of tuning of the triangular membership functions. A ion of the number of input and output terms in the partition matrices may be performed both under the offline mode and by adaptive adding/removing of terms.

Known methods of the min-max clustering apply heuristic procedures for the ion of the number of rules (classes). The proposed method generates variants of fuzzy knowledge bases in accordance with the formalized procedures of reliability analysis and synthesis of algorithmic processes. This resolves a general problem on the methods of min-max clustering related to the minimization of the number of input terms without losing inference accuracy.

A transition to the relational fuzzy model provides simplification of the process of the knowledge bases tuning both for the assigned and unknown output classes

Запропоновано метод оптимізації класифікаційних нечітких баз знань за критеріями «точність – складність», який дозволяє спростити процес налаштування шляхом переходу до реляційної моделі. Задачу оптимізації бази знань зведено до задачі minmax кластеризації. Суть методу у виборі таких матриць розбиття «входи – вихід», які забезпечують необхідні або екстремальні рівні точності виведення та кількості правил

Предложен метод оптимизации классификационных нечетких баз знаний по критериям «точность – сложность», который позволяет упростить процесс настройки путем перехода к реляционной модели. Задача оптимизации базы знаний сведена к задаче min-max кластеризации. Суть метода в выборе таких матриц разбиения «входы – выход», которые обеспечивают необходимые или экстремальные уровни точности вывода и количества правил