MODELING PARTIAL IGNORANCE IN ARTIFICAL INTELLIGENCE APPLICATIONS

This study aims to extend and deepen a survey of modern extensions of probability theory represented in [6, 7]. The classical probability theory possesses rather limited possibilities and cannot cope with situations of partial ignorance. Other approaches are required allowing one to solve tasks of that kind. The given paper considers the generalised approach to modelling partial ignorance and its interpretation in the terms of upper and lower probabilities, second order probabilities and belief functions

SIMULATED ANNEALING METHOD IN THE CLASSIC BOLTZMANN MACHINES

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.

FUZZY ROBUST ESTIMATES OF LOCATION AND SCALE PARAMETERS OF A FUZZY RANDOM VARIABLE

A random variable is a variable whose components are random values. To characterise a random variable, the arithmetic mean is widely used as an estimate of the location parameter, and variation as an estimate of the scale parameter. The disadvantage of the arithmetic mean is that it is sensitive to extreme values, outliers in the data. Due to that, to characterise random variables, robust estimates of the location and scale parameters are widely used: the median and median absolute deviation from the median. In real situations, the components of a random variable cannot always be estimated in a deterministic way. One way to model the initial data uncertainty is to use fuzzy estimates of the components of a random variable. Such variables are called fuzzy random variables. In this paper, we examine fuzzy robust estimates of location and scale parameters of a fuzzy random variable: fuzzy median and fuzzy median of the deviations of fuzzy component values from the fuzzy median.

COMPARISON OF DIFFERENT FUZZY AHP METHODOLOGIES IN RISK ASSESSMENT

Being able to evaluate risks is an important task in many areas of human activity: economics, ecology, etc. Usually, environmental risk assessment is carried out on the basis of multiple and sometimes conflicting factors. Using multiple criteria decision-making (MCDM) methodology is one of the possible ways to solve the problem. Methodologies of analytic hierarchy process (AHP) are the most commonly used MCDM methods, which combine subjective and personal preferences in risk assessment process. However, AHP involves human subjectivity, which introduces vagueness type of uncertainty and requires the usage of decision making under those uncertainties. In this paper it was considered to deal with uncertainty by using the fuzzy-based techniques. However, nowadays there exist multiple Fuzzy AHP methodologies developed by different authors. In this paper, these Fuzzy AHP methodologies will be compared, and the most appropriate Fuzzy AHP methodology for the application in case of environmental risks assessment will be offered on the basis of this comparison

Using the Concept of Fuzzy Random Events in the Assessment and Analysis of Ecological Risks

In many cases, the assessment and analysis of ecological risks is a complicated task, which is first of all related to obtaining reliable initial information. As a rule, ecological risks are due to unrepeated unique situations; from this it follows that sufficient statistical data on whose basis reliable evaluation of specific risks is made, are not available. On the other hand, unfavourable impacts on the external environment can affect the components of an ecosystem differently. The complexity of correlations among the components of an ecosystem significantly complicates an analysis of possible impacts on the components of a specific system.When statistical data are missing or insufficient, experts who perform the required assessment on the basis of their knowledge and experience but often also using their intuition, are the only source of initial data. Here, however, the problem of reliability of expert evaluations arises. If other sources of information are missing, we have to accept subjective evaluations of experts as a basis, without an opportunity to evaluate the degree of their confidence.In this kind of situation, it seems to be validated to introduce the extent of uncertainty into the evaluations of parameters of ecological risks. This can be accomplished by using fuzzy initial evaluations. This paper focuses on the concept of fuzzy random events and shows favourable chances of using that concept in the assessment and analysis of ecological risks.

The Prospects of Using Fuzzy Approaches to Ecological Risk Assessment

The issue of environmental quality improvement has been receiving much attention in the developed countries in recent years. Due to that, the role of assessment of ecological risks associated both with natural events and technogene activity of humans is increasing. Previous approaches to the assessment of ecological risks were fully based on statistical data and expert evaluation of potential losses and probabilities of unfavourable consequences. When this kind of assessment is carried out, it is assumed explicitly that experts are able to evaluate point probabilities. However, such assumptions are far from being true. As a result, fuzzy approaches to ecological risk assessment became popular lately. This paper focuses on two practical approaches of that kind. The paper is aimed at attracting practical attention to new up-to-date techniques that could be successfully applied to assess ecological risks in Latvia

Fuzzy multiple criteria decision making approach in environmental risk assessment

Being able to evaluate risks is an important task in many areas of human activity: economics, ecology, etc. In case of a sufficient amount of source information the risk is evaluated using statistical methods. However, in reality the sufficiency of statistical data in risk assessment is more exceptional than normal. In such cases experts’ assessment make the only source of data. Experts are able to provide the necessary for analysis data due to their professional knowledge and experience. Certain amount of factors, which is to be evaluated by an expert (experts), significantly affects the process of experts’ assessment. If a big number of relevant factors occur, an expert may face a problem of defining links between “factors” and “outcome”. Fuzzy multiple criteria decision making approach can be used to solve the problem. Ecological risk assessment towards human health in case of gaseous substances escape at a chemical factory using hierarchical method and fuzzy multiple criteria decision making approach has been analyzed in the article

SUBJECTIVE PROBABILITIES ELICITATION AND COMBINATION IN RISK ASSESSMENTS PROBLEMS

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.

PROPERTY INSURANCE DECISION-MAKING ON THE BASIS OF UTILITY FUNCTIONS

Property and other valuables insurance is widespread all over the world. An insurance company assumes the risk of damage or total destruction of the insured property. When this kind of damage or destruction is established, the company pays its client compensation (insurance premium) up to the amount specified in the insurance contract. For his part, the insured must pay a certain amount to the firm for the provision of insurance services. In any property insurance process, the question arises as to whether it is appropriate to insure the property for the price offered by the firm. The paper considers an approach to solving this problem based on expected utility theory

Cumulative Prospect Theory Version with Fuzzy Values of Outcome Estimates

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