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.

PROBABILISTIC INFERENCE FOR INTERVAL PROBABILITIES IN DECISION-MAKING PROCESSES

The present paper considers one approach to Bayes’ formula based probabilistic inference under interval values of relevant probabilities; the necessity of it is caused by the impossibility to obtain reliable deterministic values of the required probabilistic evaluations. The paper shows that the approach proves to be the best from the viewpoint of the required amount of calculations and visual representation of the results. The execution of the algorithm of probabilistic inference is illustrated using a classical task of decision making related to oil mining. For visualisation purposes, the state of initial and target information is modelled using probability trees.

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

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

Синдром Крузона: клинический случай

Relevance. Crouzon syndrome is a craniostenosis due to combination of cranial bones hypoplasia and premature ectocranial sutures fusion resulting in deformation of cerebral and facial cranium. Deformations of facial cranium are responsible for exophthalmos and corneoconjunctival xerosis and can lead to spontaneous eyeball dislocation. Clinical case description. The clinical case of bilateral eyeball dislocation in a patient (right eye at the age of 1 year 2 months, left — at 1 year 4 months) due to untimely original reconstructive surgery is presented. The blepharorrhaphy and osteotomy of cranio-orbital-zygomaxillary complex with installation of two distraction correction instruments on maxillary bone and two on frontal bone, distance osteogenesis, fronto-temporal region remodelling were performed at the age of 3 years 2 months. Conclusion. Crouzon syndrome is incurable illness that demands timely functional and cosmetic correction. Prognosis for this disease is unfavourable. These days the child is 8 years old: physical development delay and mental retardation progression as well as psychoneurological disorders are recorded.Обоснование. Синдром Крузона — краниостеноз, обусловленный сочетанием недоразвития костей черепа и преждевременным зарастанием черепных швов, что проявляется изменением формы мозгового и лицевого черепа. Развитие деформаций лицевого скелета при данном заболевании обусловливает развитие экзофтальма, роговично-конъюнктивального ксероза и может привести к спонтанному вывиху глазных яблок из орбит. Описание клинического случая. Представлен клинический пример двустороннего вывиха обоих глазных яблок у пациентки (правого — в возрасте 1 года 2 мес, левого — в 1 год 4 мес) в связи с несвоевременной первоначальной реконструктивной операцией. В 3 года 2 мес выполнены блефарорафия, остеотомия лобно-орбито-скуло-верхнечелюстного комплекса с установкой двух коррекционно-дистракционных аппаратов на верхнюю челюсть и двух — на лобную кость, дистракционный остеогенез, ремоделирование лобно-височных областей. Заключение. Синдром Крузона — неизлечимое заболевание, требующее своевременной функциональной и косметической коррекции. Прогноз заболевания неблагоприятный. В настоящее время ребенку 8 лет: отмечаются выраженная задержка физического развития и дальнейшее прогрессирование умственной отсталости, а также психоневрологических нарушений

Religious groups and religious organizations in the Russian Federation: Legal aspects of activity

The article provides a legal analysis of the activities of religious groups and religious organizations. Activities of religious organizations are regulated by the Federal Law of 1997 which defines religious organizations as associations of citizens of the Russian Federation, other persons permanently and legally residing in the territory of the Russian Federation, formed for joint confession and dissemination of faith and registered as a legal entity recognized in the Russian Federation. Religious groups are voluntary associations of citizens carrying out activities without state legal registration and acquisition of a legal capacity as a legal entity. The authorʼs work is largely based on regional material

A Fuzzy Version of the TOPSIS Method in Multi-Criteria Decision-Making Tasks

Choice and decision making are an integral part of the purposeful activities of people in all areas of public and private life. Tasks of multi-criteria decision making are characterised by the fact that alternative decisions are evaluated by a set of criteria and the concept of a decision and its outcome coincide. The defining concept in such problems is the concept of a set of Pareto optimal decisions (Pareto set). This set forms alternative decisions that are not comparable in terms of the set of evaluation criteria. The choice of the optimal decision in the Pareto set can be performed only on the basis of the subjective preferences of the decision maker. In recent decades, extensions of traditional methods of multi-criteria decision making to a fuzzy environment have been proposed. One of the well-known approaches to multi-criteria decision making is the TOPSIS method. In the paper, a fuzzy version of this method is considered in situations where the values of evaluation criteria are set in the form of fuzzy numbers

Operating with Fuzzy Probability Estimates in Decision Making Processes with Risk

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

Alternative Methods for Combining Probability Boxes

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