SAMPLE RATING IN WATER- ALCOHOL TECHNOLOGY BY PROFILE NON-LINEAR QUALITY CRITERIA

Topicality. Today, the restaurant technology product evaluation samples occurs organoleptic characteristics, in determining the average score calculation and subsequent tasting sheet. Important aspects of such evaluation are the collection, validation and comparison of the test specimens by organoleptic parameters. Purpose and methods. The purpose of the article is to create a mathematical model for the determination of rational recipe compositions based on water-alcohol infusions of vegetable raw materials for the technology of restaurant products. The task of the research was to substantiate the method of ranks with the use of sensory evaluation of samples of water-alcohol infusions in the restaurant products technology. Results. One aspect of the research is to compare samples with controls and with each other. For the effective evaluation of organoleptic indicators for the quality of infusions used the method of determining the quality criterion by profile, which covers a large number of indicators and is sensitive to changes in each of the descriptors used. The results were checked by the method of calculation of the complex quality criterion. Conclusions and discussions. When calculating the priority of samples, it is possible to use both the calculation of the complex quality criterion and the calculation of the quality criterion according to profiles that give identical results. The scientific novelty of the results obtained is to improve the use of the results of organoleptic evaluation of samples based on descriptors. The practical significance of the obtained results is manifested in the implementation of them in the work of competition commissions in the evaluation of the developed products relative to the possibility of determining the priority of samples.

oleptic characteristics (Kanter et al., 2003a), which allows institutions to focus their efforts on shaping the quality of restaurant products . This is possible due to innovative technologies, using modern methodologies, the latest mathematical apparatus (Dorokhovych et al., 2016).
One of the problems with the technology of restaurant products is the reliability of numerical values obtained from the organoleptic evaluation of quality indicators (Varakuta, 2004;Domanova & Shubina, 2014), especially in the expert evaluation of tasting sheets (Kanter et al., 2003b). Existing mathematical and statistical methods for processing expert assessments (Dorokhovych, 2016) (ranking method; direct estimation method; consistent advantages method; pairwise comparisons) allow to increase the reliability of organoleptic evaluation results (Kovalenko, 2012;Dietrich et al., 2017). Despite the considerable theoretical study of the problem, issues related to the processing of the information obtained to conduct a comprehensive independent evaluation need further research.

Purpose and research methods
The purpose of the article is to find a mathematical model of the organoleptic properties dependence on water-alcohol infusions of vegetable raw materials (Kuzmin et al., 2018) for the determination of rational recipe compositions in the technology of restaurant products (Kuzmin et al., 2016).
Research methods. To achieve this goal, we used the method of determining the quality criterion «quality polygon» (Koretska & Zinchenko, 2018).
Research methodology. A 10-point Quality Score was used to determine the descriptors. The total number of descriptors are 39 (5 is to characterize color and transparency; 17 is taste; 17 is aroma), taking into account the nature, intensity, order of manifestation and completeness of descriptors. Critical rating limit for Quality Score is 4 points (agreed by experts). Samples characterized by unsatisfactory taste were characterized as substandard, even by their corresponding appearance and aroma. In the first stage, experts (11 people) formed a list of organoleptic indicators and their components descriptors. In the second stage, the values of the organoleptic indicators in the scores were evaluated, as well as the values of a specific indicator is on the average of all descriptors of the group. By the average values of the selected quality criterion, all samples were evaluated and the most rated.

Research results
Analyzing the meanings of individual indicators, we evaluated (in points) descriptors by groups of individual indicators (Table 1). The final evaluation of a particular sample indicator was determined by obtaining the average of the individual descriptors used to calculate the average value of the main indicator («Color and Transparency», «Taste», «Flavor»).
During the analysis of the results obtained, it was found that the infusions samples were arranged (by the average score) as follows: the highest score was an infusion of "Vanilla", the second place was an infusion of "Strawberry", the third place was an infusion of "Rosemary", and in the fourth place there were at the same time three samples of infusions: "Carnation", "Honey" and "Lemon" (table. 2).  The most striking method is the visualization of the organoleptic properties of products in the form of profile grams, which can be used to assess the intensity, severity, difference of descriptors. The obtained values of the organoleptic parameters were used to determine the profile quality criterion (by profiles).
An important feature of this criterion is that samples are rejected (because of the established critical limit), in which at least one of the quality indicators has a false representation (characterized by a small value undesirable for the sample). The quality criterion in geometric interpretation determines the optimal variant of the product with the largest area of the polygon of quality, constructed using normalized dimensionless quality indicators.
The evaluation of the impact of vegetable raw materials on the quality of water-alcohol infusions was performed using the criterion in the form of the sum of the products of the component indicators fj. Comparison of different samples is possible if the quality criterion is used and the «quality polygon» (as the area of the polygon), which is calculated as the sum of the areas of the individual triangles formed by the rays of the individual quality indicators, with the central angle where f j . -the meaning of a specific Quality Score, points; N -number of samples.
Steel factors that do not depend on the current index of the sum j can be deduced from each application, after which the criterion formula takes the form: And for the comparison of several diverse specimens, the criterion S has the form: , point 2 Determining factors of importance (Boiko & Hrynevych, 2011) of selected indicators and their descriptors was performed by Delphi, expert method for each group as compared to the average values of the group descriptors provided that the sum of the team is 10 points.

Source: own development
As it can be seen from the presented graphical profiles of the criterion "quality polygon", not all the presented samples have the same number of indicators (descriptors). This can be explained by the fact that the presented samples, in our case, infusions of vegetable raw materials, made using different plant raw materials and therefore have specific individual indicators (descriptors) that are inherent in one or the other representatives of the flora, which do not have any descriptors at all.
The calculation of the profile quality criterion was performed by comparing the S parameters with the following linear approximation of the partial criteria dependencies (Fig. 2).
The analysis of the obtained results made it possible to rank the samples of infusions (by quality criterion). Vanilla was the highest, while Rosemary was second; third place was strawberry infusion, fourth place was Carnation infusion, fifth place was Honey infusion and sixth place was Lemon infusion.
During the evaluation of organoleptic quality indicators of samples of water-alcohol infusions, the values of individual descriptors (in points) were monitored. Scientific research has substantiated the means that provide reliable results in assessing the consistency of expert judgment. Such means, in particular, are the Spearman or Kendall rank correlation coefficients. We assume that such issues should have equal weight in a number of problems. Therefore, it is advisable to use an a priori ranking that gives equal rank to issues of equal importance. Using rankings, individual metrics are ranked in order of decreasing their impact on the final result (diminishing importance, priority or superiority). To confirm the expertise of each expert and a sufficient degree of consistency of experts, rank statistical methods were used to study the correlation between the benchmarks (or selected as the best) and the indicators of each expert. Spearman's rank correlation coefficient was used to evaluate the degree of correlation.
To calculate the rank correlation coefficients, the indicators were arranged in order of decreasing points, after which they were numbered from 1 to 36. If in the aggregate (accepted as «E») met values with the same values, their ranks were calculated as the arithmetic mean of their numbers in descending order. The obtained numbers (numbers) are indicators' ranks X i totality Е: X 1 , X 2 , ... X 36 . To assign rankings to Expert A's scores, items were arranged in order of decreasing their scores and numbered. The rank value is equal to the number of the element corresponding to the element of the set E.
The calculation of ranks for the selected (first) expert on the example of the sample "Vanilla" is presented in table. 3. Table 3. The values of the indicators ranks for the aggregates E (X i ) and А (Y i ) Spearman's rank correlation coefficient was determined by the formula (Kovalenko, 2012): If there are related rankings (for groups with the same metric values), Spearman's rank correlation coefficient was determined using the refined formula: where m x , m y -the number of expert groups that do not differ in rank in sets E and A; t x , t y -the number of ranks in a group of unclassified ranks; d i -the difference between the ranks of the two variables.
Further calculations were performed according to the table. 3 and obtained the results: , , , .
Analyzing the calculations, we can conclude that the obtained value of the Spearman correlation coefficient is close to 1. This means that the expert's estimates of the quality indicators and the benchmarks are fairly tight. Ranks for other tasting participants were also calculated. Since for all experts correlation coefficient values are close to 1:, the work of the expert group can be considered coherent. The product rating was calculated by organizing an appropriate expert survey to identify individual indicators and their descriptors, which were carried out in two stages.
Determining the priority (rating) of the obtained samples (Table 4) is possible provided that the coefficients of weight (on a 10-point scale) are used and the main indicators are converted into rating values. , m i -the meaning of weight factor, score; p i -the meaning of the main indicator, score.  When compiling a rating list of test samples (Table 5), different non-linear methods can be selected, such as the calculation of the «quality criterion» and the proposed calculation of the rating, which give identical results.
One of the important aspects of scientific research is the comparison of the obtained final indicators of the quality criterion of the samples using different methods of verification of the obtained results.
Using the method of determining the quality criterion by profiles (formula 3), we obtain the following rating series (the order of distribution of results by the best value): 1 is vanilla; 2 is rosemary; 3 is carnation; 4 is honey; 5 is lemon; 6 is strawberries. The meanings of this rating series were confirmed by the method of calculation of the complex quality criterion (formula 4). The calculations showed the identity of the results when using the proposed methods in determining the rating (the order priority) of prototypes of water-alcohol infusions, and this means that they are legitimate.

Conclusions and discussion of results
The results of the studies allow us to confirm the feasibility of using sensory analysis and to reach such conclusions: -when calculating the priority of prototypes, it is possible to use both the calculation of the definition of the complex quality criterion and the calculation of the quality criterion according to profiles that give identical results; -scientific novelty of the obtained results is to determine the regularity of the processes of organoleptic evaluation of samples based on descriptors; -the practical significance of the obtained results is manifested in their implementation in the work of competition commissions during the evaluation of the developed products for the possibility of determining the priority of samples; -prospects for further scientific work to create a system of integrated sample evaluation.