Classification rule hierarchical tuning with linguistic modification based on solving fuzzy relational equations

Abstract

The common problem with the hierarchical tuning methods is the lack of conditions for modification of the primary rules. The incremental approach accelerates the generation of candidate rules, but complicates the ion of the primary and modified rules.

In the paper, the approach that combines semantic training, granular partition and solution of fuzzy relational equations for constructing accurate and interpretable rules is developed. The composite fuzzy model of direct logic inference based on the primary rules with granular parameters is proposed. The method of hierarchical tuning with the linguistic modification based on solving fuzzy relational equations is developed, which allows reducing the training time.

It is shown that the weights of the primary rules, which are subject to modification, as well as the hedging threshold of the primary terms, are solutions of the primary system of fuzzy logic equations with the hierarchical max-min/min-max composition, which solves the problem of the hierarchical ion of the primary and modified rules for the given output classes. The genetic-neural approach was used for tuning the primary rules and solving the system of equations, as well as tuning the composite rules.

The effectiveness of the approach is illustrated by the example of tuning and interpreting the solutions to the technological process quality control problem for the specified productivity classes. The primary model with granular parameters allows reducing the tuning error by 25 % compared to the primary relational model. The solution of the hierarchical ion problem allows reducing the tuning time by half