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ANALYSIS OF BEHAVIOUR OF INACCURATELY GIVEN FUNCTIONS WITH THE HELP OF THEIR BOUNDARY FUNCTIONS

Annotation

The existing approaches to the calculation, analysis, synthesis and optimization of systems under conditions of uncertainty are considered. The problem of calculating and analyzing the behavior of not fully determined function specified up to a range of possible values is formulated and described in detail. To solve this problem, an algorithm of determination is proposed, which reduces the problem to two similar problems - the upper and lower boundary functions of the original incompletely defined function. This algorithm uses means of interval mathematics and interval-differential calculus. We highlighted the different types of possible behaviour of interval functions (consistency, increase, decrease, expansion, contraction) and various types of extreme points of these functions (the maximum point, minimum point, the point of maximum expansion, the point of minimum expansion). The theorems admitting to allocate areas in the different behavior of interval functions and points of their various extreme are proved. The execution of the proposed determination algorithm that allows analyze behavior of interval functions is described. This operation is illustrated by the example.

Keywords

problem of system optimization; uncertainty; deterministic function; interval function; analysis of functions’ behaviour

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UDC

62-50:519.7/8

Pages

1762-1770

References

1. Fikhtengol'ts G.M. Kurs differentsial'nogo i integral'nogo ischisleniya: v 3 t. M.: Fizmatlit, 2001. T. 1. 616 s. 2. Levin V.I. Interval'naya proizvodnaya i nachala nedeterminist-skogo differentsial'nogo ischisleniya // Ontologiya proektirova-niya. 2013. № 4. S. 72-84. 3. Miln V.E. Chislennyy analiz. M.: Izd-vo inostr. lit-ry, 1980. 350 s. 4. Alefel'd G., Khertsberger Yu. Vvedenie v interval'nye vychisleniya. M.: Mir, 1987. 360 s. 5. Levin V.I. Interval'nye metody optimizatsii sistem v usloviyakh neopredelennosti. Penza: Izd-vo Penz. tekhnol. in-ta, 1999. 101 s. 6. Levin V.I. Optimizatsiya v usloviyakh interval'noy neopredelen-nosti. Metod determinizatsii // Avtomatika i vychislitel'naya tekhnika. 2012. № 4. S. 157-163. 7. Tsoukias A., Vincke P. A Characterization of PQI Interval Orders // Discrete Applied Mathematics. 2003. № 127 (2). P. 387; 397. 8. Ozturk M., Tsoukias A. Positive Negative Reasons in the Interval Comparisons: Valued PQI Interval Orders. LAMSADE-CNRS: Uni- versite Paris Dauphine, 2004. 7 p. 9. Davidov D.V. Identification of Parameters of Linear Interval Controllable Systems with the Interval Observation // Journal of Computer and Systems Sciences International. 2008. V. 47. № 6. P. 861-865. 10. Piyavskiy S.A. Prostoy i universal'nyy metod prinyatiya resheniy v prostranstve kriteriev «stoimost'–effektivnost'» // Ontolo-giya proektirovaniya. 2014. № 3. S. 89-102. 11. Borgest N.M. Klyuchevye terminy ontologii proektirovaniya // Ontologiya proektirovaniya. 2013. № 3 (9). S. 9-31.

Received

2015-09-04

Section of issue

Mathematics

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