INCREASING THE REDUNDANCY OF INFORMATION FIELDS OF ADAPTIVE CLASSIFIERS OF THE INFORMATION SECURITY SYSTEM.

INCREASING THE REDUNDANCY OF INFORMATION FIELDS OF ADAPTIVE CLASSIFIERS OF THE INFORMATION SECURITY SYSTEM..

NESTERUK Gennady Filippovich, Candidate of Technical Sciences
MOLDOVYAN Alexander Andreevich, Candidate of Technical Sciences
NESTERUK Filipp Gennadievich
VOSKRESENSKY Stanislav Igorevich
KOSTIN Andrey Aleksandrovich

INCREASING THE REDUNDANCY OF INFORMATION FIELDS OF ADAPTIVE CLASSIFIERS OF THE INFORMATION SECURITY SYSTEM

The article considers the issues of increasing the redundancy of information fields of neuro-fuzzy networks, necessary for the implementation of the main advantages of the neural network element base, such as adaptability, functional stability, distributed redundant storage of information. The need to use information on the state of the information security system (ISS) as one of the sources of input data for neuro-fuzzy classifiers of hierarchical levels of the adaptive ISS model is discussed.

In the adaptive protection model, the classifier of the hierarchical level of the information security system (ISS) contains a clear self-learning neural network (NN) for solving the problem of clustering input vectors, a fuzzy NN, the structure of which reflects the system of fuzzy rules of logical inference, a system of fuzzy rules describing the work of the classifier taking into account expert assessments [1].

At the same time, the initial system of fuzzy inference rules is formulated by an expert and may be incomplete or contradictory, and the type and parameters of the membership functions describing the input and output variables of the system are selected subjectively and may not adequately reflect reality. To eliminate these shortcomings, the adaptability property of fuzzy systems is used, which is most fully implemented in fuzzy NNs.

A fuzzy neural network is identical in structure to a multilayer neural network trained, for example, using the backpropagation algorithm, but the hidden layers in it correspond to the stages of fuzzy inference [2]:

• the input layer of neurons performs the function of introducing fuzzification based on the specified input membership functions;
• the hidden layers display a set of fuzzy inference rules;
• the output layer performs the function of defuzzification.

The main advantage of fuzzy neural networks implementing a given system of fuzzy inference rules is called the structural transparency of the NN information field (for subsequent analysis) after completion of the neural network training stage. To illustrate the correspondence between the stages of bottom-up fuzzy logical inference and the specialization of fuzzy NN layers, let us refer to Fig. 1 [3]:

Fig. 1. Specialization of fuzzy NN layers

1. the layer of input membership functions A1 – A3, B1 – B3 transforms each of the crisp input values ​​х1 and х2 into the degree of truth of the corresponding premise for each rule mАi, mBi, i = 1, 2, 3 (introduction of fuzziness);
2. the layer of fuzzy rules R1 – R6 according to the degree of truth of premise mАi, mBi, i = 1, 2, 3

generates fuzzy subsets of conclusions for each of the rules mRi, i = 1,…6 (fuzzy logical inference)

3. the layer of output membership functions С1, С2 combines fuzzy subsets mRi, i = 1,…6 into fuzzy subsets mСi, i = 1, 2 (composition);
4. the output layer generates a crisp output value y from fuzzy subsets mСi, i = 1, 2

If we use a pair of complementary functions of the type L (large) and S (small) as membership functions, which add up to 1 (complementary functions), then for classification purposes it is convenient to use fuzzy NNs similar to the one shown in Fig. 2.

Fig. 2. Application of fuzzy NN for classification purposes

The fuzzy classifier under consideration identifies input vectors with the same coordinates (the logical function equivalence). In the input layer, a pair of complementary functions L and S for each crisp variable forms a pair of mutually opposite fuzzy statements (FP). FPs in accordance with the logical function equivalence are combined into terms by the operation min of logical inference on formal neurons (FN) of the hidden layer of the NN. The final operation maxcomposition is performed on the FN, at the outputs of which a pair of complementary functions L and S are implemented.

The downside of the specialization of the layers of a fuzzy NN, which ensures the structural transparency of the information field, is the practical absence of information redundancy, which negatively affects the functional stability and protection of the NN information fields from destructive influences.

While maintaining the specialization of individual layers of neuro-fuzzy networks in accordance with the rules of fuzzy logical inference, convenient for subsequent analysis, it is necessary to introduce redundancy into the information field of the neuro-fuzzy classifier [4]. Redundancy of the information field creates prerequisites for distributed storage of information in structured fields of fuzzy NN in the form of a system of complementary fuzzy connections [1], and the structural specialization of NF layers in fuzzy NNs allows us to analyze the results of training the information fields of the NN.

The system of fuzzy rules of logical inference can be identified with a formal description of logical transformations of fuzzy statements. As an apparatus for formalizing transformations over NF, one can use an analog of normal forms for crisp statements in the form of disjunctive (DNF) and conjunctive (CNF) normal forms. Moreover, NF at the output of the function S corresponds to the inverse value of some fuzzy variable, and L to the direct value of the same variable (Fig. 3).

Fig. 3. Input node of the neuro-fuzzy classifier

If we apply a similar approach of complementary duplication to the hidden layers of the neuro-fuzzy network, we can achieve the formation of mutually opposite results for both the logical inference stage and the composition stage, which allows us to double the redundancy of the information fields of the neuro-fuzzy classifier (Fig. 4).

Fig. 4. Structure of the redundant neuro-fuzzy classifier

Further introduction of redundancy of the information field of the neuro-fuzzy classifier can be ensured if the formal record of the system of fuzzy predicate rules is presented in a form similar to the perfect DNF and CNF, i.e. terms implementing the operation minlogical inference at the outputs , represent min-terms (respectively, at the outputs – max-terms).

The following form of introducing redundancy into the information field of the neuro-fuzzy classifier seems appropriate – increasing the dimensionality of the input data by adding the vector Х to the input vector Z the current state of the NIS (Fig. 5).