Abstract: The choice of the optimal cartographic projection, especially for large-scale maps, is an actual problem affected by the precision of positioning geodetic points using the new GNSS technologies in the coordinate systems. In this contribution we describe the map projections designed by minimax type criteria, Airy-Kavraiskii's variational criterion and map projections with a minimal RMS distortion in the category of conic, azimuthal and cylindrical projections. The aim of this paper is to compare the mentioned criteria based on the achieved values of scale distortion in the selected European countries.

Keywords: cartographic projection; conformal projection; scale distortion

Abstract: Inventory optimization in the supply chain is one of the most important goals in logistical business operations given the fact that optimized inventories directly impact the efficiency and profitability of the business. In the contemporary conditions of business processes, the goal of an enterprise’s business operations reflects in the maximal reduction in the level of inventories, simultaneously retaining a certain level of services provided, in order for them to become and remain competitive in the market. Understanding the significance of inventories enables optimal uninterrupted business doing, for which reason exactly the ABC-XYZ method, as one of the ways to efficiently manage inventories, is used in this paper. Given the fact that there are limitations to the ABC classification, the limitation to one single criterion and the non-existence of a demand analysis at determining the needed inventories, the problem is overcome by the introduction of the XYZ classification. The merging of the mentioned classifications results in the integrated ABC-XYZ classification model, which can be used, on the basis of a multi-criteria and multi-dimensional approach, to classify inventories and make a proposal for their optimization.

Keywords: inventory management; management; ABC-XYZ analysis; analytic hierarchical process

Abstract: This article describes the design of a new model IKMART, for classification of documents and their incorporation into categories based on the KMART architecture. The architecture consists of two networks that mutually cooperate through the interconnection of weights and the output matrix of the coded documents. The architecture retains required network features such as incremental learning without the need of descriptive and input/output fuzzy data, learning acceleration and classification of documents and a minimal number of user-defined parameters. The conducted experiments with real documents showed a more precise categorization of documents and higher classification performance in comparison to the classic KMART algorithm.

Keywords: Improved KMART; Category Proliferation Problem; Fuzzy Clustering; Fuzzy Categorization

Abstract: The paper presents numerical algorithms, post processing and validation steps for an automated cell tracking and cell lineage tree reconstruction from large-scale 3D+time two-photon laser scanning microscopy images of early stages of Zebrafish (Danio rerio) embryo development. The cell trajectories are extracted as centered paths inside segmented spatio-temporal tree structures representing cell movements and divisions. Such paths are found by using a suitably designed and computed constrained distance functions and by a backtracking in the steepest descent direction of a potential field based on a combination of these distance functions combination. Since the calculations are performed on big data, parallelization is required to speed up the processing. By careful choice and tuning of algorithm parameters we can adapt the calculations to the microscope images of vertebrae species. Then we can compare the results with ground truth data obtained by manual checking of cell links by biologists and measure the accuracy of our algorithm. Using an automatic validation process and visualization tool that can display ground truth data and our result simultaneously, along with the original 3D data, we can easily verify the correctness of the tracking.

Keywords: cell tracking; validation; big data; parallel computation

Abstract: Decision matrices represent a common tool for modeling decision-making problems under risk. They describe how the decision-maker's evaluations of the considered alternatives depend on the fact which of the possible and mutually disjoint states of the world will occur. The probabilities of the states of the world are assumed to be known. The alternatives are usually compared on the basis of the expected values and the variances of their evaluations. However, the states of the world as well as the alternatives evaluations are often described only vaguely. Therefore, we consider the following problem: the states of the world are modeled by fuzzy sets defined on the universal set on which the probability distribution is given, and the evaluations of the alternatives are expressed by fuzzy numbers. We show that the common approach to this problem, based on employing crisp probabilities of the fuzzy states of the world computed by the formula proposed by Zadeh, is not appropriate. Therefore, we introduce a new approach in which a fuzzy decision matrix does not describe discrete random variables but fuzzy rule bases. The problem is illustrated by an example.

Keywords: decision matrices; fuzzy decision matrices; decision making under risk; fuzzy states of the world; fuzzy rule bases system

Abstract: In this paper we consider special fuzzy implications as directional increasing functions and we introduce the notion of inversely special fuzzy implications as directional decreasing functions. We recall some results connected with special R-implications shown by Sainio et al. [A characterization of fuzzy implications generated by generalized quantifiers, Fuzzy Sets and Systems 159, 2008, pp. 491-499] and we present several new results connected with inversely special R-implications. Also, we discuss this new property for other families of fuzzy implications like (S,N)-implications, f-implications and g-implications.

Keywords: fuzzy implications; special implications; inversely special implications; directional monotonicity

Abstract: This paper presents a new linear optimization model which improves a nutritional adviser’s work and prevents mistakes when preparing a diet plan for a client manually. The model takes the client’s favourite or the adviser’s recommended recipes into account, prevents unbalanced nutrition, respects the client’s eating habits and habits of measuring when cooking, ensures recommendations for people from the Czech Republic and prevents wasting food items. The model also ensures that the client’s daily recommended intake of nutrients is met, that certain nutrients are balanced in proportion when applicable, and that the energy intake is distributed during the whole day. The model involves linear constraints to ensure that two incompatible recipes are not used in the same meal and that a recipe is not used in an incompatible meal. A corresponding balanced feeding plan is produced for the client for several days. The solution will yield particular recipes for particular days with the exact amounts of the food items used. The final dietary plan for the client is optimal.

Keywords: linear programming; diet problem; nutrient requirement; menu planning; nutrition adviser

Abstract: The main idea of the paper is an attempt to numerically simulate the data obtained by acoustic measurements. These measurements were performed in specialized acoustic laboratory. Their main idea was to study the reflection of different frequencies from boards with openings of various size and shape. The Finite volume method was used to make the simulations, where the Helmholtz equation is solved using the impedance boundary conditions. The results of the simulations are presented herein.

Keywords: measurement; Finite volume method; acoustic simulation; Fourier transform

In the paper a sufficient condition for the asymptotic stability with respect to total variation norm of semigroup generated by an abstract evolutionary non-linear Boltzmann-type equation in the space of signed measures with the right-hand side being a collision operator is presented. For this purpose a sufficient condition for the asymptotic stability of Markov semigroups acting on the space of signed measures for any distance ([4]), adapted to the total variation norm, joined with the maximum principle for this norm is used. The paper generalizes the result in [4] related to the same type of non-linear Boltzmann-type equation, where the asymptotic stability in the weaker norm, Kantorovich-Wasserstein, was investigated.

Keywords: Asymptotic stability, Markov operators, maximum principle for the total variation metric, nonlinear Boltzmann-type equation

A new approach for the mutation operation in the differential evolution (DE) algorithm is introduced. The aim of this technique is to enhance the mutation strategy to avoid the local minimum area. The proposed method is implemented to five state-of-the-art DE variants and the standard DE variant DE/rand/1/bin. Twelve DE variants are compared on CEC 2015 problems at four dimension levels. The results show that the proposed method is able to increase the performance of the original DE variants in the significant part of the test problems.

Keywords: Global optimization problem; differential evolution; auxiliary population; experimental comparison; CEC 2015 test suite

Abstract: Receiving an early diagnosis of schizophrenia is a crucial step towards its treatment. However, in current thinking, the diagnosis is based on time-consuming criteria, burdened with subjectivity. Hence, objective and more reliable therapeutic tests are desirable for the clinical practice of Psychiatry. Since schizophrenia is characterized by progressive brain volume changes during the course of the disease, many studies have recently turned attention to machine learning and brain morphometric techniques serving as tools for computer-aided diagnosis of schizophrenia based on neuroimaging data. In our study, the methodology is applied to distinguish between 52 first-episode schizophrenia patients and 52 healthy volunteers on the basis of T1-weighted magnetic resonance images of their brains preprocessed by the means of voxel-based and deformation-based morphometry. The proposed classification schemes vary in the feature extraction and selection steps. Namely, Mann-Whitney testing is implemented as a simple univariate approach playing the role of a comparator to multivariate methods such as inter-subject PCA, the K-SVD algorithm, and pattern-based morphometry. The highest classification accuracy, 70%, is reached with the pattern-based morphometry technique. The study points out the difference between univariate and multivariate approaches towards neuroimaging data. Additionally, the contrast between feature extraction capabilities of voxel-based and deformation-based morphometry is demonstrated.

Keywords: feature extraction; computer-aided diagnosis; schizophrenia; brain morphometry; voxel-based morphometry; deformation-based morphometry; magnetic resonance imaging; classification; machine learning