Showing papers in "Kybernetika in 1989"

Addition of fuzzy quantities: Disjunction-conjunction approach

Abstract: This paper is subjected to the problem of algebraical operations over fuzzy quantities with rational values. The concept of the fuzzy quantity was introduced in [3] and [4] and applied e.g. in [5] and [6]. It represents one of possible models of uncertainty connected with rational numerical data. The elementary properties of the addition of fuzzy quantities were shown in [3] and further developed in [8]. It is also shown there that such conception of addition leads to some unconsistency with the usual notion of fuzzy sets. Another definition of the addition of fuzzy quantities, avoiding the mentioned discrepancies, is suggested and investigated below. It is shown there that the main properties of the addition of fuzzy quantities are analogous for both concepts of the operation. Namely, the fundamental group properties can be guaranteed only up to an equivalence relation.

Weak conditions for the existence of optimal stationary policies in average Markov decision chains with unbounded costs

Abstract: Average cost Markov decision chains with discrete time parameter are considered. The cost function is unbounded and satisfies an additional condition which frequently holds in applications. Also, we assume that there exists a single stationary policy for which the corresponding Markov chain is irreducible and ergodic with finite average cost. Within this framework, the existence of an average cost optimal stationary policy is proved.

Attempts at axiomatic description of conditional independence

Abstract: This paper concerns the problem of characterization of conditional-independence relations (the abbreviation CIR) which arises in connection with probabilistic expert systems. The first two sections contain some lately found properties (axioms) of CIRs; the rest of the paper is a proposal for a proper generalization of the concept of CIR. Since it is defined by means of the concept of multiinformation it is called the M-relation. Some advantages of the M-relations are discussed. Some questions are still open, we express our hypotheses through the paper. The paper is a survey only, the extended version with proofs will be published later.

Equivalence, invariance and dynamical system canonical modelling. I: Invariant properties of observable models and associated transformations

Abstract: Cette 2eme partie d'article considere 2 classes differentes de modeles pour les systemes MIMO, lineaires, atteignables: modeles «espace etat», et modeles polynomiaux entree-etat partiel-sortie

New models in durability tool-testing: pseudo-Weibull distribution.

Abstract: The problem of tool durability is considered to be a most important factor in mechanical engineering. In the last three decades various models for tool life have been proposed. Among these models the statistical ones play a major role, since almost all tool characteristics are regarded as random variables. Classical distribution functions — as for instance log-normal, exponential or Weibull ones — have proved their utility in this matter, but the large variety of tools themselves have imposed the need to find other distributions to describe the behaviour of tool life. Two Soviet engineers (Druzhinin [1] and Katzev [2]) have introduced the socalled \"Alpha\" distribution, initially to describe merely the time for performing a given operation. A detailed statistical analysis of the Alpha model has been perfor­ med by the present author in [3]. In the present paper we shall derive a new distribution function which has proved its utility in durability tool-testing.

A vanishing discount limit theorem for controlled Markov chains

Abstract: The definition and basic properties of multidimensional locally stationary and normal covariance functions are given. Necessary and sufficient conditions characterizing these covariance functions are presented and a close connection with normal operators is shown too

Estimating income inequality in the stratified sampling from complete data. I. The unbiased estimation and applications.

Abstract: In order to answer the problem of quantifying the degree of unequalness among the individual shares in the distribution of income, several authors proposed and characterized the well-known additively decomposable measures of relative income inequality. In a previous paper, Perez, Caso and Gil [12] verified that for a large uncensused population of income earners, the additively decomposable index of order — 1 may be readily and unbiasedly estimated from a sample drawn at random from it. The Part 1 of the present paper deals with the study of the precision of the unbiased estimators in the stratified samplings with and without replacement. Then, some applications are briefly discussed. The aim of the Second Part is to analyze the asymptotic distribution of the sample income inequality index and to select the suitable sample size to estimate the population index with a specified degree of precision.

Decentralized control of linear dynamical systems with partial aggregation

Abstract: La methode proposee est utilisee pour la synthese de commande decentralisee sous-optimale grâce a la resolution du probleme LQ avec retroaction de sortie pour un sous-systeme sous l'hypothese que la partie restante du systeme est stable

Multidimensional random processes with normal covariances.

Abstract: On donne la definition et les proprietes elementaires de fonctions de covariance multidimensionnelles localement stationnaires et nornales. Des conditions necessaires et suffisantes sont presentees pour caracteriser ces fonctions, et on montre un lien etroit avec des operateurs normaux

Test for submodel in Gibbs-Markov binary random sequence.

Abstract: Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library The Gibbs-Markov random sequences (as studied in frame of statistical physics) are convenient as probability models for sequences of dependent binary data. Thus, the model is given by a system of interactions which may be understood and estimated as a vector parameter. Setting some of the interactions equal to zero, we obtain a submodel. A test for the submodel is derived in the present paper, and a numerical example with simulated data is included.

Generating dirichlet random vectors using a rejection property

Abstract: Let aj, 1 <. j <: n + 1, be n + 1 positive real numbers. The random vector (X1,X2,...,Xn) has a Dirichlet D(n; au a2,...,an, att+1) distribution if its probability density function (p.d.f.) is given by (cf. Wilks [14]): (i) f(xt,x2,...,xn) = Kx'rM ' ••• < \" _ 1 ( i x , x 2 . . . X T 1 for every (xx,x2,...,xn)e Sn, where Sn -= {(*,., x2,..., xn) | Xi > 0, 1 <: r g n; xt + x2 + ... + x„ < 1} K = T(at + a2 + ... + an + 0,+ i)/(r(fli) r (« i ) • • • T(an) T(an+1)) with . , T(a) = J ' J > t 0 ~ 1 exp( t )d ! ; a > 0 .

AR(1) processes with given moments of marginal distribution

Abstract: Let X t be an AR(1) process given by X t =bX t−1 + e t where b ∈(−1,1) and e t is a strict white noise. Sometimes X t must satisfy also some additional conditions, e.g. X t ≥O or C≤X t ≤D. The problem solved in the paper is how to find a distribution of e t such that the moments EX k t (k=1, ..., n) have given values

Estimating income inequality in the stratified sampling from complete data. II. The asymptotic behaviour and the choice of sample size

Abstract: The First Part of this paper deals with the study of the precision of an unbiased estimator of a population income inequality index in the stratified samplings with and without replacement. In this Second Part, we first analyze the asymptotic distribution of the sample income inequality index. Then, we establish different criteria to select the suitable sample size to estimate the population index with a desired degree of precision. One of these criteria is based on Chebyshev's approach and the other one follows from the preceding asymptotic study.

Evaluation of clarke's generalized gradient in optimization of variational inequalities

Abstract: Optimization of systems governed by variational inequalities with linear constraints in IR" yields nonsmooth cost functions to be minimized. After discussion about various numerical methods to solve such optimization problems, we propose usage of a bundle or a subgradient algorithm and deal with the only problem how to evaluate in such case the generalized gradient of Clarke, required by it. As the problem in general is very complicated, an effective procedure is proposed only for certain special data. However, using the transversality theory, it is shown that "almost all" (possibly in the generic sense) sufficiently smooth data fulfil the conditions that guarantee the validity of the procedure proposed. 1. FORMULATION OF THE PROBLEM AND CLASSICAL METHODS This paper contains a new approach to such optimization problems where the state is' governed by a variational inequality on a finite-dimensional space. For simplicity we confine ourselves to the elliptic case with control-independent linear constraints. Yet, our method could be extended to evolution variational inequalities (after a discretization both in space and in time) or to linear constraints depending on a control parameter as well. On the other hand, general convex constraints or nonlinear monotone operators in the variational inequality v/ould cause probably considerable complications. First we formulate our problem. Let bi e W, ct e U, i eIK, I K be a finite index set, denote the usual scalar product in IR", n ^ 1. We consider the convex poly­

Model-reference intelligent control system.

Abstract: Le systeme de commande intelligent adaptatif a un modele de reference peut etre utilise pour obtenir les dynamiques requises du systeme boucle qui peut etre choisi a l'interieur d'une gamme large de vitesse en respectant la dynamique du systeme