Ймовірнісно-статистичні невизначеності в системах підтримки прийняття рішень

Abstract

Ринок систем підтримки прийняття рішень (СППР) пропонує численні системи різного функціонального призначення і їх кількість постійно збільшується. Для подальшого поліпшення якості рішень, що приймаються за допомогою СППР, необхідно впроваджувати нові методи побудови математичних моделей, прогнозування та генерування альтернатив з використанням сучасних інформаційних технологій. Розроблено узагальнену процедуру побудови математичних моделей та оцінювання прогнозів на їх основі, сформовано послідовність дій стосовно обробки можливих невизначеностей під час моделювання і запропоновано методи врахування невизначеностей ймовірнісно-статистичного характеру у процесі побудови моделей, а також розглянуто ілюстративний приклад зменшення рівня невизначеності. Available on the market decision support systems (DSS) provide a possibility for solving of a wide range of problems in various directions of human activities. To further enhance quality of decision making it is necessary to develop new methods and approaches to model constructing and decision making in the frames of modern concepts of DSS development using available information technologies. The main objective of this study is in solving of the following problems: development of the general procedure for model constructing and decision alternatives generation using statistical or experimental data and expert judgments in the frames of DSS; development of procedure for processing possible probabilistic and statistical uncertainties in the model constructing process and forecasts estimating; to review some approaches to taking into consideration possible probabilistic and statistical uncertainties and to give an illustrative example for uncertainty reducing. To develop DSS for modeling dynamic processes in various areas of human activities and forecasts estimation on the basis of these models we propose to use the following system analysis principles: hierarchical architecture, identification and taking into consideration of possible uncertainties, tracking of all the stages of model constructing and forecasts estimating with separate sets of statistical quality criteria etc. An analysis is provided for selecting possible methods and techniques for taking into consideration statistical and probabilistic types of uncertainties identified in the process of data processing. The set of methods proposed for decreasing the negative influence of uncertainties are as follows: Kalman filters of various modifications, nonparametric regression, static and dynamic Bayesian networks, Bayesian regression, and hierarchical Bayesian modeling. The set of modern Kalman filtering techniques provides a possibility for taking into consideration an influence of external stochastic disturbances, measurement errors (noise), and estimation of non-measurable variables in the frames of linear and non-linear models. Estimation of non-measurable variables is possible when appropriate elements of covariance matrix for estimation errors have nonzero values. Nonparametric and Bayesian regressions have the features of modeling various probability distributions besides normal that are characteristic for specific cases. Such approach provides a possibility for reducing uncertainties that appear due to the use of incorrect probability distributions for model variables and its parameters. Static and dynamic Bayesian networks are a powerful probabilistic and statistical tool for modeling high dimensional processes and systems that are characterized by quantitative and qualitative variables, parametric uncertainty, expert judgments, hidden variables and unknown (unidentified) cause-and-effect relations. Their field of applications is very wide and continues to grow. The hierarchical Bayesian modeling reflects availability of parametric dependences at different levels of a complex system model. Such models provide more correct insight into hierarchical links and dependences in the frames of a system under investigation and consequently such models are more adequate to real world. Generally the set of Bayesian models provides many mentioned above possibilities for handling the uncertainties related to model constructing, forecasts estimating, and generating decision alternatives that could be rather easily implemented in the frames of intellectual DSS. The main result of the study is in development of system analysis based theory for building modern DSS helping to construct mathematical models, estimate forecasts and compute decision alternatives using statistical data and expert judgments. High quality of the final result is achieved thanks to identification and taking into consideration of possible probabilistic and statistical uncertainties, and tracking of all computational stages within DSS using several sets of statistical quality criteria. The main attention is paid to application of Bayesian approaches to uncertainties handling. An example is given for reducing parametric model uncertainty with the use of Markov chain Monte Carlo computational procedure for parameter estimation. Thus, we developed a systemic approach to constructing DSS aiming to forecasting model development and decision alternatives generation in conditions of influence of probabilistic, statistical and parametric uncertainties. The future studies will be directed towards further extension of the number of uncertainty processing techniques and their application to investigation of real life systems and processes.