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# Grabusts, Pēteris

## Research Output

#### Decision Making Based on Possibility Theory

2022, Oleg Uzhga-Rebrov, Grabusts, Pēteris

In decision-making problems under risk, one of the main tasks is to evaluate the probabilities of the occurrence of such random events that affect the outcomes of alternative decisions. In some specific situations, due to the lack of initial information, it is difficult or even impossible to perform such evaluation. In this article we present an alternative approach to choosing decisions under uncertainty. This approach is based on the possibility theory, which is at the intersection of various developed theories of uncertainty: the theory of fuzzy sets, the theory of evidence and the theory of probabilities. Evaluating the possibilities of relevant events is a simpler task than evaluating the probabilities of these events. The article presents the conceptual foundations of the possibility theory. The use of this theory for decision making is demonstrated with a simple illustrative example.

#### SIMULATED ANNEALING METHOD IN THE CLASSIC BOLTZMANN MACHINES

2023, Grabusts, Pēteris, Oleg Uzhga-Rebrov

The classical Boltzmann machine is understood as a neural network proposed by Hinton and his colleagues in 1985. They added noise interferences to the Hopfield model and called this network a Boltzmann machine drawing an analogy between its behaviour and physical systems with the presence of interferences. This study explains the definition of “simulated annealing” and “thermal equilibrium” using the example of a partial network. A technique for calculating the probabilities of transition states at different temperatures using Markov chains is described, an example of the application of the SA - travelling salesman problem is given. Boltzmann machine is used for pattern recognition and in classification problems. As a disadvantage, a slow learning algorithm is mentioned, but it makes it possible to get out of local minima. The main purpose of this article is to show the capabilities of the simulated annealing algorithm in solving practical tasks.

#### Comparative Evaluation of Four Methods for Exploratory Data Analysis

2021, Oleg Uzhga-Rebrov, Grabusts, Pēteris

Research activities in many areas are associated with the use of various types of data. This data may contain important information, but this information is hidden in the data. In order to extract relevant information, this data must be subjected to appropriate processing and analysis. Data analysis allows to clarify the data structure and, if necessary, transform the data into a form that allows to extract the required information. In recent years powerful data analysis techniques have been developed. Typically, these methods are computationally complex and require the use of suitable software to implement. This paper summarizes and analyses four widely used methods of exploratory data analysis: principal component analysis, singular value decomposition, factor analysis, and linear discriminant analysis.

#### Analysis of Fuzzy Time Series Forecasting for Migration Flows

2022, Oleg Uzhga-Rebrov, Grabusts, Pēteris

The goal of this article is to forecast migration flows in Latvia. In comparison with many other countries with sufficiently symmetric emigration and immigration flows, in Latvia, migration flows are very asymmetric: the number of emigrants considerably exceed the number of immigrants. Since statistical data about migration are usually inaccurate, we employ fuzzy time series forecasting methods for prognosticating migration flows in Latvia forecasting. The use of this type of method is often useful not only for forecasting purposes. Three different methods for fuzzy time series forecasting are used. A detailed comparative analysis of the obtained results is given. Generalized forecasts of the expected net migration flow in the future are presented.

#### Cumulative Prospect Theory Version with Fuzzy Values of Outcome Estimates

2021, Oleg Uzhga-Rebrov, Grabusts, Pēteris

Choosing solutions under risk and uncertainty requires the consideration of several factors. One of the main factors in choosing a solution is modeling the decision maker’s attitude to risk. The expected utility theory was the first approach that allowed to correctly model various nuances of the attitude to risk. Further research in this area has led to the emergence of even more effective approaches to solving this problem. Currently, the most developed theory of choice with respect to decisions under risk conditions is the cumulative prospect theory. This paper presents the development history of various extensions of the original expected utility theory, and the analysis of the main properties of the cumulative prospect theory. The main result of this work is a fuzzy version of the prospect theory, which allows handling fuzzy values of the decisions (prospects). The paper presents the theoretical foundations of the proposed version, an illustrative practical example, and conclusions based on the results obtained.

#### SUBJECTIVE PROBABILITIES ELICITATION AND COMBINATION IN RISK ASSESSMENTS PROBLEMS

2023, Oleg Uzhga-Rebrov, Grabusts, Pēteris

Very many areas of human activity are associated with greater or lesser risks. In order to make reasonable decisions, these risks must be properly assessed. The consequences of any risk can be characterized on the basis of two fundamental dimensions (metrics): (1) losses associated with the outcomes of implementation an unfavourable event; (2) probabilities that quantify the uncertainties in the occurrence of these outcomes. This article in a concise form presents and analyses approaches to subjective probabilities elicitation and combining the obtained individual estimates in group subjective probabilities estimation.

#### Methodology for Environmental Risk Analysis Based on Intuitionistic Fuzzy Values

2023, Oleg Uzhga-Rebrov, Grabusts, Pēteris

Ecological risks are characterized by a high degree of uncertainty about the chances of unfavorable event outcomes and the losses associated with those outcomes. Subjective expert judgment is widely used when baseline data are insufficient. This introduces additional uncertainties in the results of risk analyses. In order to successfully model the existing uncertainties, this paper presents a methodology for ecological risk analysis that is based on input evaluations in the form of intuitionistic fuzzy values (IFVs). The advantage of this approach is the ability to model a wide range of uncertainties in ecological risk analysis tasks.