Narrow Results

We look at the issue of obtaining a variance like measure associated with probability distributions over ordinal sets. We call these dissonance measures. We specify some general properties desired in these dissonance measures. The centrality of the cumulative distribution function in formulating the concept of dissonance is pointed out. We introduce some specific examples of measures of dissonance.

The paper considers the analytical solution methods of the maximizing entropy or minimizing variance with fixed orness level problems and the maximizing orness with fixed entropy or variance value problems together. It proves that both of these two kinds of problems have common necessary conditions for their optimal solutions. The optimal solutions have the same forms and can be seen as the same OWA (ordered weighted averaging) weighting vectors from different points of view. The problems of minimizing orness problems with fixed entropy or variance constraints and their analytical solutions are proposed. Then these conclusions are extended to the corresponding RIM (regular increasing monotone) quantifier problems, which can be seen as the continuous case of OWA problems with free dimension. The analytical optimal solutions are obtained with variational methods.

Interval multi-objective linear programming (IMOLP) ímodels are one of the methods to tackle uncertainties. In this paper, we propose two methods to determine the efficient solutions in the IMOLP models through the expected value, variance and entropy operators which have good properties. One of the most important properties of these methods is to obtain different efficient solutions set according to decision makers’ preferences as available information. We first develop the concept of the expected value, variance and entropy operators on the set of intervals and study some properties of the expected value, variance and entropy operators. Then, we present an IMOLP model with uncertain parameters in the objective functions. In the first method, we use the expected value and variance operators in the IMOLP models and then we apply the weighted sum method to convert an IMOLP model into a multi-objective non-linear programming (MONLP) model. In the second method, the IMOLP model using the expected value, variance and entropy operators can be converted into a multi-objective linear programming (MOLP) model. The proposed methods are applicable for large scale models. Finally, to illustrate the efficiency of the proposed methods, numerical examples and two real-world models are solved.

The basic paradigm for decision making under uncertainty is introduced. A methodology is suggested for the calculation of the variance associated with each of the alternatives in the case when the uncertainty is not necessarily of a probabilistic nature.

The questions of representation, processing, and analysis of continuous deterministic and random image contours and estimation of their parameters are considered. An approach is proposed to describe continuous complex-valued signals represented on the complex plane in the form of closed contours. A linear space of vector contours is defined and the main analytical relations are obtained.

A model of a random continuous contour is proposed, which is a complex random function. In this case, the complex random function is considered as a set of its possible realizations. The concepts of mathematical expectation and variance of a random contour are introduced. Geometrically, the mathematical expectation of a random contour is interpreted as an “average contour” around which other contours are located: realizations. The dispersion characterizes the degree of scattering of possible realizations (contours) around the mathematical expectation of a random contour (the “middle contour”). It is shown that an important condition for the formation of an adequate contour model with a random form is the equality of the values of the parameters of the linear transformations of the contours of its realizations. Alignment of these parameters should be performed during the formation of a contour model with a random form.

The problems of spectral and correlation analysis of continuous contours are considered and features of their spectra are revealed. The problems of discretization of continuous contours of images are investigated. The structure of the device for processing continuous contours of images and the results of its modeling are presented.