Вестник Витебского
государственного
технологического
университета

Abstract

Classic assessment approaches based on the analysis of multiple individual indicators complicate the comprehensive assessment of the suitability of polymer-coated textile materials. In turn, the use of aggregation methods based on the calculation of weighted averages is associated with the risk of compensating for low values of some properties by high values of others, subjectivity in assigning weighting factors, and the impossibility of reverse decomposing the indicator. The aim of this study is to develop and validate a method for constructing a comprehensive quality indicator for polymer-coated textile materials using the prime number theory.

According to the proposed methodology, each individual quality indicator is assigned a prime number. The advantage of this method is the replacement of subjective weighting factors with a ranking of indicators by significance. Based on the specified order of significance, indicators are assigned prime numbers (the most significant is assigned the highest prime number in the selected series). Scales have been developed to convert absolute values of quality indicators to ordinal gradation numbers. The comprehensive indicator is calculated as the product of prime numbers raised to the power corresponding to the ordinal gradation number of each individual indicator. For ease of comparison and interpretation, a logarithmic transformation is proposed to avoid large numbers.

The proposed method provides a reverse decomposition of the complex indicator, allowing the original values of individual indicators to be retrieved. The method does not require weighting factors, which increases the objectivity of the assessment. The method's effectiveness is demonstrated using polyurethane-coated fabric samples. To quantitatively assess the degree of approximation of the ith sample to the standard, it is proposed to use the Ki indicator, calculated as the ratio of the logarithm of the ith sample to the logarithm of the standard sample.

This comprehensive quality assessment method based on prime number theory is objective, informative, and feasible. It eliminates the main shortcomings of traditional approaches and can be recommended for use.

Application of the theory of prime numbers in constructing a comprehensive quality indicator for textile materials with a polymer coating