Calculation of harrington function (desirability function) values under interval determination of its arguments
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Purpose of work. Development of proposals for desirability function calculation by interval arithmetic method. Obtained results. A connection was shown between multiple-criterial (vector) optimization problem and calculation of Harrington function (desirability function) values. Generalized desirability function was shown to be treated as a multiplicative convolution of partial desirabilities. Using golden section properties, a connection was discerned between hierarchy analysis methods and calculation of desirability function values. In this case the distribution of probable desirability function values among intervals determined in accordance with golden mean rule does coincide with values obtained by expert method. Application of golden proportion enables increasing the number of intervals; thus, it may prove convenient in improvement of Harrington function sensitivity. Conclusions. For partial desirability function in its explicit form such geometric characteristics were determined as values of tangent, curvature of curve and center of curvature coordinates. For a necessary averaged desirability system obtaining process control, such characteristics were determined in general and explicit form as partial desirability elasticity, generalized desirability elasticity relative to partial desirability, generalized desirability elasticity relative to a variable that has physical sense and respective dimension depending on particular subject area and affects partial desirability value. To determine the boundary value of one partial desirability being substituted for another partial desirability, the rate of substitution function and boundary rate of substitution elasticity function were established. Due to errors emerging in determination of desirability function values application of interval analysis methods was proposed. Application of interval numbers as presented in hyperbolic form was shown for calcutaion of partial and generalized desirability, A partial power series sum was determined relative to a variable presented in hyperbolic form. Suggestions. The method of calculation of Harrington function (desirability function) values at interval determination of arguments was shown to be eventually used in development of specifications and preliminary design of complicated engineering аnd organizational systems.
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Zaburanna, L. V. (2014), Optimization methods and models, Agrar Media Group, Kyiv, 373 p.
Shtojer, R. (1992), Multicriteria optimization. Theory, calculations and applications, Radio i svjaz', Moscow, 504 p.
Melamed, I. I. (1997), “Linear convolution of criteria in multicriteria optimization”, Avtomatika i telemehanika, Issue I,
pp. 119-125.
Kovalenko, Y. Y. and Pavlenko, A. Ju. (2017), “Reducing the number of criteria in multi-criteria decision-making problems by pairwise comparison”, Computer technologies: Science , Mykolaiv, Issue 295, vol. 307, pp. 47-53.
Chernetska, Yu. A. (2012), “Methods of multi-criteria optimization of the capital structure of the enterprise”, Scientific Bulletin. Odesa National University of Economics. All-Ukrainian Association of Young Scientists. – Sciences: economics, political science, history, No. 10 (162), pp. 100-110.
Harrington, E. C. (1965), “The desirable function”, Industrial Quality Control, Vol. 21, No. 10, pp. 494-498.
Adler, Yu. P., Markova, E. V. and Granovsky, Yu. V. (1976), Planning of experiment in search of optimal conditions, NAUKA, Moscow, 279 p.
Akhnazarova, S. L. and Gordeev, L. S. (2003), Using the Harrington desirability function in solving optimization problems of chemical technology: Educational and methodological manual, RCTU, Moscow, 76 p.
Malyarets, L., Martynova, O. and Chudaieva, L. (21018), “Multi-criteria optimization of the balanced scorecard for the enterprise’s activity evaluation: management tool for business-innovations”, Marketing and Management of Innova-tions, No. 3, pp. 48-58.
Zahozhai, B.V. (2006), Statistics: basic outline of lectures, MAUP, Kyiv, 160 p,
Honcharov, I. V. (2003), Risk and managerial decision-making: Study guide, NTU KhPI, 150 p.
Saaty, Thomas L. (2008), “Relative Measurement and its Generalization in Decision Making: Why Pairwise Compari-sons are Central in Mathematics for the Measurement of Intangible Factors The Analytic Hierarchy/Network Process”, Review of the Royal Academy of Exact, Physical and Natural, Vol. 102 (2), pp. 251-318.
Demidovich, B. P. and Maron, I. A, (1966), “Fundamentals of Computational Mathematics, Nauka, Moscow, 658 p.
Novitsky, P. V. and Zograf, I. A. (1991), “Estimation of Measurement Errors,, Energotomizdat, Leningrad, 302 p.
Kuz, M. V. and Andreiko, V. M. (2016), “Qualimetric scales of software products”, Methods for adjusting the quality control, No. 1 (36), pp. 54-62.
Muzychenko, M. V. (2017), “Verhulst’s Logistics Function as a Baggage Function for Normalization of Indicators for the Safety of Natural Gas Supply”, Economics and Suspіlstvo, No 9, pp. 83-88.
Stakhov, A. P. (1978), Codes of the golden ratio, Radio i svyaz, Moscow, 144 p.
Vorobyov, N. N. (1978), Chisla Fibonachch, NAUKA, Moscow, 144 p.
Dubnytskyi, V. Yu. and Samorodov, V. B. (2009), “The model of pardon vindication in the process of choosing the best alternative in the method of analysis of hierarchy”, Biznes-inform, No. 2(2), pp. 171-174.
Petrov, Yu. P. (2012), Ensuring the reliability and reliability of computer calculations, BHV-Peterburg, St. P., 160 p.
Dubnitsky, V., Kobilin, A., Kobilin, O. and Kushneruk, Yu. (2021), “EXCEL-oriented procedure for calculating the values of special functions with an interval argument, set in hyperbolic form”, Advanced information systems, Vol. 5, No,4,
pp, 116-123. DOI: https://doi.org/10.20998/2522-9052.2021.4.16.
Dubnitsky, V. Yu., Kobylin, A. M. and Kobylin, O. A. (2017), “Calculation of the values of elementary and special functions with an interval specified argument defined in the CENTER-RADIUS system”, Applied radio electronics, Vol. 16, No. 3-4, pp. 147-154.
Zhukovska, O. A. (2009), “Fundamentals of interval analysis: a study guid”, Education of Ukraine, Kyiv, Ukraine, 136 p.
Molodtsov, D. A. and Kovkov, D. V. (2011) ,“ Introduction to the theory of approximate numbers”, Bulletin of the Tver State University. Series: Applied Mathematics, 23, pp. 111-128.
Ljusternik, L. A., Chervonenkis, O. A. and Janpolskij, A. R. (1963), “Mathematical Analysis: Calculation of Elementary Function], NAUKA, Moscow, 248 p.
Gadecka, S. V., Dubnitsky, V. Yu., Kushneruk, Yu. I., Filatova, L. D. and Khodirev, O. I. (2021), “Geometrical characteristics of S-like (logistic) curves, which are to be observed when modeling the phenomenon of hysteresis”, Advanced information systems, No. 2(165), pp. 14-27, doi: https://doi.org/10.30748/soi.2021.165.02.
Beskorovayny, V. V., and Soboleva, E. V. (2010), “Identification of private utility of multifactorial alternatives using
S-shaped utility functions”, Bionics of intelligen, No. 1 (72), pp. 50-54.
Abramowitz, M. and Stigan, I. (1979), Handbook of Special Functions with Formulas, Graphs and Mathematical Tables, Nauka, Moscow, 832 p.
Bessonov L. A. (1996), Theoretical foundations of electrical engineering, Vysshaya shkola, Moscow,638 p.
Hackevich, G. A., Pronevich, A. F., and Chajkovskij, M. V. (2018) “Economic-mathematical analysis of production functions with constant production elasticity”, Business. Innovation. Economy, Issue 2, pp. 171-180.