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The analysis of Markovs model of productive and economic system with the incomplete information about intensity streams


Yu. G. Bojarinov

In article it is considered Markovsky model of the productive and economic system, different by incompleteness of the information about intensity streams of events. A research objective – an estimation of probability of stay of system in one of conditions. Incompleteness of the information is offered for considering in the form of indistinct triangular numbers. The numerical decision of a problem is offered. Illustrating examples are resulted. It is known that Markovsky (Semi-Markovsky) models [1] are convenient tool means for research difficult, including, productive and economic, systems [2,3]. The specified models of similar systems usually are represented in the form of the focused count which tops correspond to possible conditions of system, and weight of arches connecting them – to such numerical parametres, as intensity of transitions from one condition to another (intensity streams of events). At modelling as an efficiency indicator value of probability is applied to find system in a desirable condition, thus the basic difficulty of use of the given models is incompleteness of the statistical information on values intensity [3]. In article the possible approach to use Markovsky models in the conditions of such incompleteness, the using device of indistinct numbers is considered. In article it is offered incompleteness of the information in Markovsky to model of productive and economic system to reflect by means of the device of indistinct logic, particularly, it is inexact known sizes intensity streams of events to describe triangular indistinct numbers. It is shown that use of the device of arithmetic operations with such numbers and Kolmogorov's equations, allows to receive the redefined system of the equations concerning unknown limiting probabilities. The decision of the given system is offered and is shown on an example, is noticed that this decision will be only the confidant, thus the error is caused basically by incompleteness of the initial information on model parametres.

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