Distances between Predicates in By-Analogy Reasoning Systems

The purpose is to develop expert systems where by-analogy reasoning is used. Knowledge “closeness” problems are known to frequently emerge in such systems if knowledge is represented by different production rules. To determine a degree of closeness for production rules a distance between predicates is introduced. Different types of distances between two predicate value distribution functions are considered when predicates are “true”. Asymptotic features and interrelations of distances are studied. Predicate value distribution functions are found by empirical distribution functions, and a procedure is proposed for this purpose. An adequacy of obtained distribution functions is tested on the basis of the statistical 2 χ –criterion and a testing mechanism is discussed. A theorem, by which a simple procedure of measurement of Euclidean distances between distribution function parameters is substituted for a predicate closeness determination one, is proved for parametric distribution function families. The proposed distance measurement apparatus may be applied in expert systems when reasoning is created by analogy.

Обобщенные Интервальные Оценки в Сценарном Анализе

Показано, что метод обобщенных интервальных оценок (ОИО), первоначально предназначавшийся для выявления и формализованного представления экспертных знаний об известных с неопределенностью количественных исходных данных моделей интеллектуальных систем поддержки экспертных решений (СПЭР), можно рассматривать как развитие сценарного подхода в теории принятия решений. Предложены процедуры исследования методом ОИО задач с зависимыми параметрами, таких как задача прогнозирования объемов извлекаемых запасов месторождений в зависимости от уровней цены на углеводороды. Установлены аналитические соотношения для функций распределения вероятностей обобщенных равномерных распределений, используемых в сценарном анализе и анализе результирующих показателей моделей включенных в базу моделей СПЭР.

A Recession Notion for a Class of Monotone Bivariate Functions

Using monotone bifunctions, we introduce a recession concept for general equilibrium problems relying on a variational convergence notion. The interesting purpose is to extend some results of P. L. Lions on variational problems. In the process we generalize some results by H. Brezis and H. Attouch relative to the convergence of the resolvents associated with maximal monotone operators.

Extreme Situations Prediction by MultidimenSional Heterogeneous Time Series Using Logical Decision Functions

* The work is supported by RFBR, grant 04-01-00858-a

Fuzzy Membership Functions in a Fuzzy Decision Making Problem

Authors analyses questions of the subjective uncertainty and inexactness situations in the moment of using expert information and another questions which are connected with expert information uncertainty by fuzzy sets with rough membership functions in this article. You can find information about integral problems of individual expert marks and about connection among total marks “degree of inexactness” with sensibility of measurement scale. A lot of different situation which are connected with distribution of the function accessory significance and orientation of the concrete take to task decision making are analyses here.

Hermite Polynomials and the Zero-Distribution of Riemann's Zeta Function

AMS Subject Classification 2010: 11M26, 33C45, 42A38.

Some Properties of Mittag-Leffler Functions and Matrix-Variate Analogues: A Statistical Perspective

Mathematical Subject Classification 2010:26A33, 33E99, 15A52, 62E15.

Special Functions and Pathways for Problems in Astrophysics: An Essay in Honor of A.M. Mathai

The paper provides a review of A.M. Mathai's applications of the theory of special functions, particularly generalized hypergeometric functions, to problems in stellar physics and formation of structure in the Universe and to questions related to reaction, diffusion, and reaction-diffusion models. The essay also highlights Mathai's recent work on entropic, distributional, and differential pathways to basic concepts in statistical mechanics, making use of his earlier research results in information and statistical distribution theory. The results presented in the essay cover a period of time in Mathai's research from 1982 to 2008 and are all related to the thematic area of the gravitationally stabilized solar fusion reactor and fractional reaction-diffusion, taking into account concepts of non-extensive statistical mechanics. The time period referred to above coincides also with Mathai's exceptional contributions to the establishment and operation of the Centre for Mathematical Sciences, India, as well as the holding of the United Nations (UN)/European Space Agency (ESA)/National Aeronautics and Space Administration (NASA) of the United States/ Japanese Aerospace Exploration Agency (JAXA) Workshops on basic space science and the International Heliophysical Year 2007, around the world. Professor Mathai's contributions to the latter, since 1991, are a testimony for his social con-science applied to international scientific activity.

Dependence Structure of some Bivariate Distributions

Dependence in the world of uncertainty is a complex concept. However, it exists, is asymmetric, has magnitude and direction, and can be measured. We use some measures of dependence between random events to illustrate how to apply it in the study of dependence between non-numeric bivariate variables and numeric random variables. Graphics show what is the inner dependence structure in the Clayton Archimedean copula and the Bivariate Poisson distribution. We know this approach is valid for studying the local dependence structure for any pair of random variables determined by its empirical or theoretical distribution. And it can be used also to simulate dependent events and dependent r/v/’s, but some restrictions apply. ACM Computing Classification System (1998): G.3, J.2.

Bayesian Prediction of Weibull Distribution Based on Fixed and Random Sample Size

2000 Mathematics Subject Classification: 62E16, 65C05, 65C20.