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Open access

Oleg Uzhga-Rebrov and Galina Kuleshova

Problems of Fuzzy Clustering of Microarray Data

Microarray technology has been the leading research direction in medicine, pharmacology, genome studies and other related areas over the past years. This technology enables researches to simultaneously study activity expression of tens of thousands of genes. After the experimental data have been processed, arrays of numerical values of gene expressions are obtained that are the basis for receiving relevant information and new knowledge. This paper briefly overviews the basics of microarray technology as well as task classes that could be solved using microarray data. The existing approaches to clustering gene expression sets are discussed. It is shown that the fuzzy c-means clustering method appears the most appropriate for that purpose. Due to that, the problem of choosing an optimal size of fuzziness parameter arises. Three widespread techniques for solving the problem are considered and their comparative analysis is provided.

Open access

Imants Zarembo and Oleg Uzhga-Rebrov

Abstract

Many pathfinding problems in real-world applications require real-time computation of the shortest path between two points in a grid-based environment. It is not a trivial task. While some shortest pathfinding algorithms may perform admissibly in one condition, they may prove inadmissible in other conditions. HPA* path finding algorithm is faster and more memory efficient than the A*algorithm in relatively large two dimensional grids, but this advantage may not apply to very small or very large grids. The paper deals with the efficiency of A* and HPA*in two-dimensional grids of different sizes. For the sake of completeness of the analysis, HPA* efficiency is measured taking into consideration the number of hierarchy levels and different cluster sizes. Both algorithms have been implemented and tests conducted. Experimental evidence is proposed to demonstrate the algorithm efficiency in various conditions.

Open access

Andrejs Radionovs and Oleg Uzhga-Rebrov

Abstract

Risk assessment is an important task in many areas of human activity: economic, technical, ecological etc. Preliminary data adequacy in risk assessments is carried out on the basis of statistical methods and experts’ evaluation on potential losses and probabilities of the event. But in many cases, risk assessment must be carried out under the conditions of lack of initial information or uncertainty of information. For that reason, special risk assessment approaches (methods) are necessary. One of them is the usage of fuzzy logic approach. In this paper, fuzzy logic approach is used to manage this uncertainty in information concerning accidental releases of toxic chemicals at chemical plants. This approach can be used by plant risk advisers in Latvia to make right decisions in the situations where chemical releases can harm not only the environment but also human health.

Open access

Oleg Uzhga-Rebrov and Galina Kuleshova

Abstract

Probability boxes (p-boxes) are used as a tool for modeling uncertainty regarding probability distributions in the sets of relevant elements (random events, values of the random variable etc.). To combine information produced by two or more p-boxes, Dempster’s rule for belief combination is commonly used. However, there are plenty of other rules for belief combination developed within the theory of evidence. The purpose of this paper is to present and analyze some widespread rules of that kind as well as examine their potentialities regarding combining the information provided by probability boxes.

Open access

Oleg Uzhga-Rebrov and Galina Kuleshova

Abstract

This paper considers different techniques of operating with fuzzy probability estimates of relevant random events in decision making tasks. The recalculation of posterior probabilities of states of nature based on the information provided by indicator events is performed using a fuzzy version of Bayes’ theorem. The choice of an optimal decision is made on the basis of fuzzy expected value maximisation.

Open access

Oleg Uzhga-Rebrov and Galina Kuleshova

Abstract

Different types of uncertainty are widely spread in all areas of human activity. Probabilistic uncertainties are related to the chances of occurrence of random events. To deal with this kind of uncertainty, statistics and probability theory are successfully employed. Another kind of uncertainty, fuzzy uncertainties refer to imprecision and fuzziness of different kinds of measurements. To cope with this kind of uncertainty, the fuzzy set theory is used. This paper addresses widespread approaches to combining probabilistic and fuzzy uncertainties. The theoretical fundamentals of the approaches are considered within the context of the generalized theory of uncertainty (GTU).

Open access

Oleg Uzhga-Rebrov and Galina Kuleshova,

Abstract

Probabilistic estimates are numerical representations of chances of random event occurrence. The classical theory of probability is based on the assumption that probabilistic estimates are deterministic. If available initial data are sufficient, this kind of estimates can be really obtained. However, when such data are not available, probabilistic estimates become uncertain. This paper analyses and compares three widespread approaches to modelling uncertain estimates and provides practical recommendations on their use.