In some economic or social division problems, we may encounter uncertainty of claims, that is, a certain amount of estate has to be divided among some claimants who have individual claims on the estate, and the corresponding claim of each claimant can vary within a closed interval or fuzzy interval. In this paper, we classify the division problems under uncertainty of claims into three subclasses and present several division schemes from the perspective of axiomatizations, which are consistent with the classical bankruptcy rules in particular cases. When claims of claimants have fuzzy interval uncertainty, we settle such type of division problems by turning them into division problems under interval uncertainty.
Electrocardiography (ECG) in rats is a widely applied experimental method in basic cardiovascular research. The technique of ECG recordings is simple; however, the interpretation of electrocardiographic parameters is challenging. This is because the analysis may be biased by experimental
settings, such as the type of anesthesia, the strain or age of animals. Here, we aimed to review electrocardiographic parameters in rats, their normal range, as well as the effect of experimental settings on the parameters variation. Furthermore, differences and similarities between rat and human ECG are discussed in the context of translational cardiovascular research.
The article presents an evaluation and quantification of the reliability interval of measurement parameters based on the theory expressing an uncertainty in measurement as was recommended by the CIPM (Comité International des Poids et Measures) in 1993. Numerical values of the reliability interval are quantified by statistical methods. the quantification technique for reliability interval has three components. the reliability interval ue is obtained as a statistical calculation of measurement parameters xi using the reliability coefficient e = 2.72. the combined reliability interval uce is obtained as a statistical (square) sum of reliability interval ue and uncertainty of parameters measuring device ub. the reliability interval of measurement parameters Ue is obtained as a multiplication of combined reliability interval uce with coverage factor k relevant to the probability P. the reliability interval of measurement parameters is used for evaluation and managing technology processes with aim to secure the quality of products and the efficiency of production. and Článok predstavuje postup hodnotenia a kvalifikácie intervalu spoľahlivosti meraných parametrov založenom na teórii vyjadrenia neistoty merania doporučeného CIPM (Comité International des Poids et Measures) (Medzinárodný výbor pre váhy a meranie) v roku 1993. Číselné hodnoty intervalu spoľahlivosti získame štatistickými metódami. Technika kvantifikácie má tri zložky. Interval spoľahlivosti označený symbolom ue získame štatistickým výpočtom meraných parametrov xi použitím koeficientu spoľahlivosti e = 2,72. Kombinovaný interval spoľahlivosti označený symbolom uce získame štatistickým sčítaním intervalu spoľahlivosti ue s neistotou merania meracieho prístroja uB (merací prístroj na meranie parametrov). Interval spoľahlivosti meraných parametrov označený symbolom Ue získame násobením kombinovaného intervalu spoľahlivosti faktorom pokrytia k pri zodpovedajúcej pravdepodobnosti P. Interval spoľahlivosti meraných parametrov pokrýva rozptyl meraných parametrov so stanovenou pravdepodobnosťou. Interval spoľahlivosti meraných parametrov použijeme pri hodnotení a riadení technologických procesov s cieľom zabezpečenia kvality produktov a efektívnosti výroby.
Let Int $\mathcal A$ be the lattice of all intervals of an $MV$-algebra $\mathcal A$. In the present paper we investigate the relations between direct product decompositions of $\mathcal A$ and (i) the lattice Int $\mathcal A$, or (ii) 2-periodic isometries on $\mathcal A$, respectively.
The main subject of our study are spherical (weakly spherical) graphs, i.e. connected graphs fulfilling the condition that in each interval to each vertex there is exactly one (at least one, respectively) antipodal vertex. Our analysis concerns properties of these graphs especially in connection with convexity and also with hypercube graphs. We deal e.g. with the problem under what conditions all intervals of a spherical graph induce hypercubes and find a new characterization of hypercubes: $G$ is a hypercube if and only if $G$ is spherical and bipartite.
The article describes use of fuzzy logic in the evaluation of nonlimited values at measurement of lightning arresters in telecommunication networks. It describes the application of Γa-cut method and evaluates their electrical parametres and functional features based on the measurement of a selected sample of lightning arresters. and Článek popisuje využití fuzzy logiky v oblasti mimolimitních hodnot při měření bleskojistek nasazených v telekomunikačních sítích. Popisuje aplikaci metody αa-řezů, hodnotí elektrické parametry a funkční vlastnosti bleskojistek založené na měření vybraného vzorku.
A matrix A is said to have \mbox{\boldmathX}-simple image eigenspace if any eigenvector x belonging to the interval \boldmathX={x:x−−≤x≤x¯¯¯} containing a constant vector is the unique solution of the system A⊗y=x in \mbox{\boldmathX}. The main result of this paper is an extension of \mbox{\boldmathX}-simplicity to interval max-min matrix \boldmathA={A:A−−≤A≤A¯¯¯¯} distinguishing two possibilities, that at least one matrix or all matrices from a given interval have \mbox{\boldmathX}-simple image eigenspace. \mbox{\boldmathX}-simplicity of interval matrices in max-min algebra are studied and equivalent conditions for interval matrices which have \mbox{\boldmathX}-simple image eigenspace are presented. The characterized property is related to and motivated by the general development of tropical linear algebra and interval analysis, as well as the notions of simple image set and weak robustness (or weak stability) that have been studied in max-min and max-plus algebras.