Šárka Hošková-Mayerová

Improvement of digital geographic data quality

The article focuses on the study of characteristics of digital geographical data and the influence of these characteristics on the quality of the basis being ready for the decision-making processes. Characteristics of digital geographical data are mainly described from the point of view of their technical parameters and keeping the technological indicators while obtaining them. Our system brings a users view into the assessment of characteristics. We define users requirements on data and suggest the system of their evaluation. The assessment of data characteristics comes out of the standard ISO 19113 and the theory of value analysis. Both systems are joined into a complex system for data evaluation. Technical characteristics of data are evaluated mainly by the level of accomplishment of qualitative indicators, e.g. meeting all requirements of horizontal and vertical mean square error, or by completeness of filling of all expected information. Meeting all users’ requirements is usually expressed by the level of users satisfaction with the particular product. This level is set based on the survey among users. Simultaneously, the weight of the individual evaluating criteria is set according to specific types of solved tasks. The system of data evaluation is supplemented with a system of calculation of costs that are needed for obtaining the data. It is possible, however, to work either with the complete database, or to count also the influences of particular groups of data (e.g. communications, residential buildings, etc.) on the complete quality of the final product. The system of costs calculation and evaluation of data quality then enables the optimisation of the use of funds or disposable time for obtaining quality data. The use of the complete system is presented in a pilot project in which a model of terrain passability by a military heavy vehicle is solved.

Fuzzy Regression Models and Alternative Operations for Economic and Social Sciences

The economic and social research is often based on assumptions that have little to do with reality, because all scientific knowledge of the Western world is based on the Aristotelian binary logic. Often researchers use rigid conventions and treat things as if they were black or white, but the world around us is nuanced, in other words, is fuzzy. In particular, problems inherent the inaccuracy of measurements and the vagueness of linguistic attributes has led many scholars to consider the fuzzy theory during the recent decades. In this paper we face a particular aspect of fuzzy logic, that is, fuzzy regression. After a brief review of the recent studies about this topic, we focus on some limitations of the previous approaches and suggest some possible solutions. Specifically, we propose the use of alternatives operations to solve some problems of addition and multiplication between fuzzy numbers in fuzzy regression models.

On Certain Proximities and Preorderings on the Transposition Hypergroups of Linear First-Order Partial Differential Operators

Abstract The contribution aims to create hypergroups of linear first-order partial differential operators with proximities, one of which creates a tolerance semigroup on the power set of the mentioned differential operators. Constructions of investigated hypergroups are based on the so called “Ends-Lemma” applied on ordered groups of differnetial operators. Moreover, there is also obtained a regularly preordered transpositions hypergroup of considered partial differntial operators.

General actions of hyperstructures and some applications

Abstract The aim of this paper is to investigate useful generalizations of the classical concept of a quasi-automaton without outputs or a discrete dynamical system, which are also called actions of semigroups or groups on given phase sets. The paper contains also certain applications of presented concepts and examples from various areas of mathematics.

Usage of fuzzy spatial theory for modelling of terrain passability

Geographic support of decision-making processes is based on various geographic products, usually in digital form, which come from various foundations and sources. Each product can be characterized by its quality or by its utility value for the given type of task or group of tasks, for which the product is used. They also usually have different characteristics and thus can very significantly influence the resulting analytical material. The aim of the paper is to contribute to the solution of the question of how it is possible to work with diverse spatial geographic information so that the user has an idea about the resulting product. The concept of fuzzy sets is used for representation of classes, whose boundaries are not clearly (not sharply) set, namely, the fuzzy approach in overlaying operations realized in ESRI ArcGIS environment. The paper is based on a research project which is being solved at the Faculty of Military Technologies of the University of Defence. The research deals with the influence of geographic and climatic factors on the activity of armed forces and the Integrated Rescue System.

Decision-Making Process with Respect to the Reliability of Geo-Database

The aim of this paper is to propose a method that would focus on data and spatial information precision and reliability evaluation. The resulting characteristics of data reliability can be applied in various command and control systems. The method to contribute to increase the quality of decision-making process is proposed. Finally, the case scenario is focused on an intervention of a fire rescue unit and presents the proposal for the use of the system in practice.

Fuzzy Sets and Algebraic Hyperoperations to Model Interpersonal Relations

In Social Sciences propositions and descriptions of interpersonal relationships are given by means of linguistic expressions, which cannot be formalized with the classic binary logic. Then a necessary tool are fuzzy sets that give the possibility to measure the degree of belonging of an element to a set described by a linguistic property or the degree of a relation between individuals. Moreover many times there is uncertainty on the result of an aggregation operation and we can have the necessity to consider together many possible results of the interaction of any ordered pair of elements, e.g. individuals. We propose the algebraic hyperoperations as very useful instruments to manage these types of uncertainty. We show as fuzzy relations and hypergroupoids permit to have an efficient representations of many aspects of social phenomena.

Prime filters of hyperlattices

Abstract The purpose of this paper is the study of prime ideals and prime filters in hyperlattices. I-filter and the filter generated by a ∈ L are introduced. Moreover, we introduce dual distributive hyperlattices, and I-filter in dual distributive hyperlattices. Some properties of hyperlat- tices are studied and the relationship between prime ideals and prime filters in hyperlattices is discussed.

Mathematical Model Used in Decision-Making Process with Respect to the Reliability of Geodatabase

The first aim of the article is to show how it is possible - thanks to the use of sophisticated analytical tools for evaluation of data quality - to better understand geospatial data. Another aim is to assess the impact of data quality on the results of space analyses that are made of them and that are the basis for such decision-making processes, in which it is necessary to take into account the impact of geographical environment.

Decision-making Process Using Hyperstructures and Fuzzy Structures in Social Sciences

Algebraic hyperstructures represent an interesting field of algebra, important both from the theoretical point of view and also for their applications. A hypergroupoid structure can be associated with any social relationship. These hypergroupoids become hypergroups in some particular conditions, among them a condition concerning outer individuals. By analyzing it we can establish in a natural way when social relationships become optimal. The relations among persons are one of the bases of Social Sciences that usually are described by linguistic propositions. If U is a set of individuals (the universe set to consider), usually it is not possible to affirm that for an ordered pair (x, y) of persons belonging to U a relation R given in a linguistic form holds or not, as happens in a binary context. A correct and overall complete modeling of each of these relations is obtained only if we assign to every pair (x, y) ∈ U × U a real number R(x, y) = xRy belonging to interval [0, 1] that is the measure to which the decision maker believes the relation holds.