Abstract

The paper deals with the theory of fuzzy sets as applied to food industry products. The fuzzy indicator function is shown as a criterion for determining the properties of the product. We compared the approach of fuzzy and probabilistic classifiers, their fundamental differences and areas of applicability. As an example, a linear fuzzy classifier of the product according to one-dimensional criterion was given and an algorithm for its origination as well as approximation is considered, the latter being sufficient for the food industry for the most common case with one truth interval where the indicator function takes the form of a trapezoid. The results section contains exhaustive, reproducible, sequentially stated examples of fuzzy logic methods application for properties authentication and group affiliation of food products. Exemplified by measurements of the criterion with an error, we gave recommendations for determining the boundaries of interval identification for foods of mixed composition. Harrington’s desirability function is considered as a suitable indicator function of determining deterioration rate of a food product over time. Applying the fuzzy logic framework, identification areas of a product for the safety index by the time interval in which the counterparty selling this product should send it for processing, hedging their possible risks connected with the expiry date expand. In the example of multi-criteria evaluation of a food product consumer attractiveness, Harrington’s desirability function, acting as a quality function, was combined with Weibull probability density function, accounting for the product’s taste properties. The convex combination of these two criteria was assumed to be the decision-making function of the seller, by which identification areas of the food product are established.

Keywords

Fuzzy logic, Harrington’s desirability function, identification criteria of food products, identification areas

REFERENCES

1. Khurshudyan SA. Consumer and Food Quality. Food Industry. 2014;(5):16–18. (In Russ.)
2. Gupta RK, Minhas D, Minhas S. Food safety in the 21st century: Public health perspective. Academic Press; 2016. 624 p. DOI: https://doi.org/10.1016/C2014-0-01094-5.
3. Oganesyants LA, Khurshudyan SA, Galstyan AG, Semipyatnyi VK, Ryabova AE, Vafin RR, et al. Base matrices – invariant digital identifiers of food products. News of the Academy of Sciences of the Republic Kazakhstan. Series of Geology and Technical Sciences. 2018;6(432):6–15. DOI: https://doi.org/10.32014/2018.2518-170X.30.
4. Ehrl M, Ehrl R. Primery razrabotki pishchevykh produktov. Analiz keysov [Examples of food development. Case Analysis]. St. Petersburg: Professiya; 2010. 464 p. (In Russ.).
5. Filzmoser P, Todorov V. Review of robust multivariate statistical methods in high dimension. Analytica Chimica Acta. 2011;705(1–2):2–14. DOI: https://doi.org/10.1016/j.aca.2011.03.055.
6. Aung MM, Chang YS. Traceability in a food supply chain: Safety and quality perspectives. Food Control. 2014;39(1):172–184. DOI: https://doi.org/10.1016/j.foodcont.2013.11.007.
7. Oganesyants LA, Vafin RR, Galstyan AG, Semipyatniy VK, Khurshudyan SA, Ryabova AE. Prospects for DNA authentication in wine production monitoring. Foods and Raw Materials. 2018;6(2):438–448. DOI: https://doi.org/10.21603/2308-4057-2018-2-438-448.
8. Schiano AN, Harwood WS, Drake MA. A 100-year review: Sensory analysis of milk. Journal of Dairy Science. 2017;100(12):9966–9986. DOI: https://doi.org/10.3168/jds.2017-13031.
9. Zadeh LA. Fuzzy sets. Information and Control. 1965;8(3):338–353. DOI: https://doi.org/10.1016/s0019-9958(65)90241-x.
10. Alghannam ARO. Design of a simple fuzzy logic control for food processing. In: Eissa AHA, editor. Trends in vital food and control engineering. InTech; 2012. pp. 99–114. DOI: https://doi.org/10.5772/39086.
11. Eerikäinen T, Linko T, Linko S, Siimes T, Zhu Y-H. Fuzzy logic and neural network applications in food science and technology. Trends in Food Science and Technology. 1993;4(8):237–242. DOI: https://doi.org/10.1016/0924-2244(93)90137-Y.
12. Podrzaj P, Jenko M. A fuzzy logic-controlled thermal process for simultaneous pasteurization and cooking of softboiled eggs. Chemometrics and Intelligent Laboratory Systems. 2010;102(1):1–7. DOI: https://doi.org/10.1016/j.chemolab.2009.12.002.
13. Birle S, Hussein MA, Becker T. Fuzzy logic control and soft sensing applications in food and beverage processes. Food Control. 2013;29(1):254–269. DOI: https://doi.org/10.1016/j.foodcont.2012.06.011.
14. Perrot N, Baudrit C. Intelligent quality control systems in food processing based on fuzzy logic. In: Caldwell DG, editor. Robotics and automation in the food industry. Current and future technologies. Cambridge: Woodhead Publishing Ltd.; 2013. pp. 200–225. DOI: https://doi.org/10.1533/9780857095763.1.200.
15. Dórea JRR, Rosa GJM, Weld KA, Armentano LE. Mining data from milk infrared spectroscopy to improve feed intake predictions in lactating dairy cows. Journal of Dairy Science. 2018;101(7):5878–5889. DOI: https://doi.org/10.3168/jds.2017-13997.
16. Aryana KJ, Olson DW. A 100-year review: Yogurt and other cultured dairy products. Journal of Dairy Science. 2017;100(12):9987–10013. DOI: https://doi.org/10.3168/jds.2017-12981.
17. Kramer E, Cavero D, Stamer E, Krieter J. Mastitis and lameness detection in dairy cows by application of fuzzy logic. Livestock Science. 2009;125(1):92–96. DOI: https://doi.org/10.1016/j.livsci.2009.02.020.
18. Albelwi S, Mahmood AA. Framework for designing the architectures of deep convolutional neural networks. Entropy. 2017;19(6). DOI: https://doi.org/10.3390/e19060242.
19. Osman T, Mahjabeen M, Psyche SS, Urmi AI, Ferdous JMS, Rahman RM. Application of fuzzy logic for adaptive food recommendation. International Journal of Fuzzy System Applications. 2017;6(2):110–133. DOI: https://doi.org/10.4018/IJFSA.2017040106.
20. Montet D, Ray RC. Food traceability and authenticity: Analytical techniques. Boca Raton: CRC Press; 2017. 354 p. DOI: https://doi.org/10.1201/9781351228435.
21. Magomedov GO, Zhuravlev AA, Sheviakova TA, Sedykh DV. Use of function of Harrington for optimization of prescription structure bars like a praline. Proceedings of the Voronezh State University of Engineering Technologies. 2014;60(22):99–103. (In Russ.).
22. Abdul Kadir MK, Hines EL, Qaddoum K, Collier R, Dowler E, Grant W, et al. Food security risk level assessment: A fuzzy logic based approach. Applied Artificial Intelligence. 2013;27(1):50–61. DOI: http://doi.org/10.1080/08839514.2013.747372.
23. Jensen DB, Hogeveen H, De Vries A. Bayesian integration of sensor information and a multivariate dynamic linear model for prediction of dairy cow mastitis. Journal of Dairy Science. 2016;99(9):7344–7361. DOI: http://doi.org/10.3168/jds.2015-10060.
24. Yu P, Low MY, Zhou W. Design of experiments and regression modelling in food flavour and sensory analysis: A review. Trends in Food Science and Technology. 2018;71:202–215. DOI: https://doi.org/10.1016/j.tifs.2017.11.013.
25. Valero A, Carrasco E, Garcia-Gimeno RM. Principles and methodologies for the determination of shelf-life in foods. In: Eissa AHA, editor. Trends in vital food and control engineering. InTech; 2012. pp. 3–42. DOI: https://doi.org/10.5772/35353.