Entropy of expert quality assessments according to multiple criteria
Abstract
Importance: the concept of entropy (according to Shannon) is extended to expert assessments of complex quality indicators of objects used for optimization or ranking. The entropy of expert assessments serves as a measure of their uncertainty, which allows measuring and monitoring its reduction as a result of applying certain methods of reducing uncertainty and, accordingly, increasing the objectivity of fuzzy parameters. Purpose: to introduce the concept of entropy of expert assessments of complex quality and to apply it in the problem of marketing analysis solved using the method of interactive approximation of expert assessments. Research design: based on a comprehensive rating of 10 smartphones by 7 consumer properties: smartphone price in dollar, size of permanent and operational memory in GB, battery capacity in MAH, screen size in CM, quality of the front camera in MP, processor clock frequency in GHZ, a polynomial of degree 2 was constructed and the entropy reduction was calculated when using the interactive approximation method. Results: a practical example related to the task of obtaining a comprehensive rating, i.e., ranking smartphones by several consumer properties, is considered. It is shown that as a result of applying the method of interactive approximation of expert assessments, entropy decreased by 60%.
Downloads
References
2. Брызгалин Г.И. Теория качеств и системные приложения // Справочник. Инженерный журнал, 2009, no. 5 (146), c. 57-63.
3. Зотьев Д.Б. Нормализованные средние функции и проблема свертывания показателей качества // Справочник. Инженерный журнал, 2009, no. 5 (146), с. 43-48.
4. Зотьев Д.Б. О многокритериальной оптимизации качества с помощью взвешенных средних показателей // Справочник. Инженерный журнал, 2010, no. 5 (158), c. 38-42. 5. Зотьев Д.Б. О нормализованных средних критериях, интерполирующих экспертные оценки // Справочник. Инженерный журнал, 2012, no. 7 (184), c. 50-56.
6. Кондрашова Н.В., Данилов И.С. Совершенствование алгоритма расчета интегрального показателя устойчивого развития экономического субъекта // Современная экономика: проблемы и решения, 2002, no. 5, c. 54-66.
7. Махин А.А. Уменьшение энтропии экспертных оценок при использовании комплексного показателя качества в виде нормализованного среднего многочлена // Бизнес. Образование. Право, 2024, no. 2 (67), с. 158-165.
8. Орлов А.И. Экспертные оценки // Заводская лаборатория. Диагностика материалов, 1996, no. 1 (62), c. 54-60.
9. Goswami S.S., Behera D. K. Evaluation of the best smartphone model in the market by integrating fuzzy-AHP and PROMETHEE decision-making approach // Decision, 2021, no. 1 (48), рр. 71-96.
10. Zotev D.B. and Makhin A.A., Polynomial Regression of Expert Estimates of Complex Quality // Control Sciences, 2025, no. 1, pp. 13-24.
11. Marler R., Arora J. The weighted sum method for multi-objective optimization: New insights // Structural and Multidisciplinary Optimization, 2010, no. 41, pp. 853-862.
12. Saaty T.L. Decision making with the analytic hierarchy process // Int. J. Services Sciences, 2008, no. 1 (1).





