Sequential Application of the Hierarchy Analysis Method and Associative Training of a Neural Network in Examination Problems

Abstract

We propose development of examination methodology based on a sequential application of the MAI method (i.e., the hierarchy analysis method) and associative training of neural networks. The proposed method is an alternative to the usual methods to solve a direct examination problem.We present a methodological approach to the examination problem. The approach allows to save information about all objects and consider their indicators in total. Therefore, there is the soft maximum principle (softmax), based on the model of expert evaluations mixing. This approach allows dierent interpretations of the examination results, which save quality unchanged overall picture of the examination object indicators ratio, and to get more reliable examination results, especially in cases where the objects characteristics are very dierent.Keywords: hierarchy analysis method; self-organizing neural networks; expert evaluations mixing.In order to examine technical objects, it is customary to use for each object (device) a generalized quality indicator in the form of the following linear functional:where k is a number of one of the K compared objects, x kj are variables (features) having dierent nature (quantitative, qualitative, cost, etc.), which are evaluated by the experts; m is a number of features considered when examination. In general, this model is natural and does not cause diculties. Exclusions are the cases when expert conditions are such that features area is expanded by addition of a feature of the general engineering evaluation x eng . The last feature can take negative values x eng ∈ [−1, 1] and therefore for the successful solution of the examination problem it is necessary to apply the hierarchy analysis method (MAI) proposed by T. Saati [1]. In order to solve a direct examination problem, the values of generalized indicators J k for all objects are determined, and then the object for which J k takes the maximum value is selected. In the neural networks application, the built-in function compet of nntool package of the MATLAB language corresponds to the method. The function implements 142

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“…Neural network methods are widely used in problems of recognition and machine vision [1][2][3][4][5]. Various deep neural network architectures have been developed for solving problems of current interest.…”