Linear Ordering Methods Research Articles

Determinant of educational infrastructure development in conditions of regional economy transformation and digitalization

Motivation: In the context of sustainable development, it is objectively conditioned to base the social infrastructure development on the transformations and digitalization of the regional economic space. The transformation of the potential of social infrastructure involves changing not only the quantitative parameters of its components, but also transforming the objects of the infrastructure complex of the region, restructuring the connections between them and moving to a qualitatively new level of development. The determinant of social infrastructure that provides quality human development is education. High-quality educational infrastructure provides comprehensive human development through the formation of a complex of services necessary for the qualitative development of human potential.
 Aim: The purpose of the research is to analyse the structural and dynamic features of the educational component of social infrastructure at the meso level in Ukraine and Poland, to work out practical recommendations for its transformation and digitalization.
 Results: An author’s methodology for assessing the educational infrastructure development is developed. The methodology includes, in particular, the calculation of the synthetic index for the educational infrastructure development using the method of linear ordering by Julian Perkal. The negative trend of decreasing in the number of Ukrainian educational institutions between 2010 and 2020 is detected. It is established that the dynamics of the number of students in vocational schools and higher education institutions in Ukraine reflects, first, the demographic trends that have taken place and are taking place in the country, as well as society’s attitude to vocational and higher education. In addition, the rating of Ukrainian and Polish regions according to the level of the educational infrastructure development is created.

Analysis of the Relationship of the Degree of Aviation Sector Development with Greenhouse Gas Emissions and Measures of Economic Development in the European Union Countries

The rapid growth of aviation over the past fifty years has resulted in numerous negative environmental impacts due to the combustion of fossil fuels in aircraft engines. This paper presents the relationship between air transport and GHG emissions. Based on data on the development of aviation, the level of GHG emissions from transport, environmental tax revenues and the amount of GDP per capita in the countries of the European Union, an attempt was made to create a typification that would illustrate the interaction of GHG emissions with air transport, environmental taxes and GDP in the years 2009–2018. The next step to confirm the obtained results was the application of statistical methods: the TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) method of linear ordering and the Perkal index. Based on the study findings, the analyzed countries were divided into three groups: the group of innovators, the stable group and the group of students. The analysis revealed the relationship of all three analyzed variables with air transport. The development of the aviation sector leads to a significant increase in GHG emissions from transport, increased revenues from environmental taxes and acceleration of the rate of economic growth of a country.

Evaluation of the level of social development of poviats in Małopolskie Voivodship with the use of a dynamic synthetic measure

The level of social development of territorial units in Poland is an important topic in the context of the pursued policy to equalise the differences in regional development. Nowadays, spatial disproportions in development are considered one of the main social problems also in Małopolskie Voivodship. The purpose of the study described in the article involves the comparison of changes in the level of social development in the poviats of Małopolskie Voivodship in the period of 2010–2019 by means of a dynamic synthetic measure. The situation of these poviats was evaluated based on data provided by the Local Data Bank of Statistics Poland, describing 10 selected diagnostic features relating to the following areas: the demographic situation, the labour market, education, standard of living and health protection of the inhabitants. The method of linear ordering of multidimensional objects in a dynamic approach was applied. The volume of changes in the level of development of the poviats was determined on the basis of a dynamic synthetic measure. The results of the study indicate that in all of the poviats, a significant decline was observed in the value of the synthetic measure describing the demographic situation and education. On the other hand, the positive aspect is that in all of the poviats the value of the synthetic measure relating to the labour market, living conditions and health protection of the population increased significantly. Consequently, the disproportions between the poviats in the analysed period deepened in terms of the demographic situation and education, whereas the differences in the level of development decreased in the case of the labour market, living conditions and health protection of the population.

A new class of strong stability preserving general linear methods

We systematically investigate strong stability preserving general linear methods of order p, stage order q=p or q=p−1, with r=p+1 external approximations, and s=p−1 internal approximations, for numerical solution of differential systems. Examples of methods of order p and stage order q=p or q=p−1, with large strong stability preserving coefficients and large regions of absolute stability, are provided for p=2, p=3, and p=4. The results of numerical experiments confirm that the methods constructed in this paper achieve the expected order of accuracy, do not produce spurious oscillations, and they are suitable to preserve the monotonicity of the numerical solution, when applied to discretization of hyperbolic conservation laws with discontinuous initial conditions.

Impact of the COVID-19 crisis on the Portuguese banking system. Linear ordering method

The goal of this paper is to assess the resilience of Portuguese banks to the potential impact of the COVID-19 pandemic. For this purpose, diagnostic variables of 19 banks were selected and prioritized using linear ordering methods. This methodology allowed us to perform rankings of banks using six linear ordering methods and taking into account two weighting procedures and two variants of the diagnostic feature. The study was also supplemented by a sensitivity analysis and an optimization procedure aimed at identifying the optimal linear ordering method. The main results obtained show that the resilience of Portuguese banks is not evenly distributed among individual banks. These findings could be used by regulators to plan support measures for the most fragile banks.

Normalizacja zmiennych a porządkowanie krajów Unii Europejskiej pod względem stopnia wykorzystania technologii ICT w przedsiębiorstwach

The main issue of multivariate comparative analysis is the normalization of variables. The literature offers various procedures for data normalization, and therefore the researcher has to choose between them. The article presents and discusses the most commonly used normalizing formulas. The article assesses the impact of data normalization procedures on the results of the linear ordering of European Union countries in terms of the level of ICT usage in enterprises. A hypothesis was formulated that the method of data normalization influenced the position of the objects in the ranking. The study is based on statistical data from Eurostat for the year 2018. Based on the selected diagnostic variables, values for a synthetic measure have been determined for individual countries. The synthetic measure was calculated according to the model-less method of linear ordering using four types of normalization. The method used in the research allowed the creation of rankings for the countries. The compliance of the orders thus obtained was compared using the Spearman’s coefficient of range correlation and the measure of similarity of rankings. As the study shows, the choice of normalization formula influences the result of linear ordering, which is not due to any change in the data structure. It was proven that the quotient transformation with the normalization base equal to the maximum value allowed the most similar ranking to be obtained of the examined objects in relation to the Rother rankings. The results of the study show that Denmark, Sweden and Finland had the highest positions in each ranking while Bulgaria, Romania and Latvia had the lowest positions.

Analysis of Iterative Process for Nauru Voting System

Game theory is a popular area of artificial intelligence in which the voter acknowledges his own desires and favors the person he wants to be his representative. In multi-agent systems, social choice functions help aggregate agents’ different preferences over alternatives into a single choice. Since all voting rules are susceptible to manipulation, the analysis of elections is complicated by the possibility of voter manipulation attempts. One approach to understanding elections is to treat them as an iterative process and see if we can reach an equilibrium point. Meir et al. proposed an iterative process to reach a stable outcome, i.e., Nash Equilibrium. This technique, explored in previous work, converges to a Nash equilibrium for plurality voting, along with a tie-breaking rule that chooses a winner according to a linear order of preferences over candidates. Almost all the scoring rules have been studied in previous work, we identified the iterative processes of the Nauru voting system. We analyzed the Nauru voting system with Copelands and lexicographic rule for tiebreaking. Nauru is the modified version of Borda counting. Like Borda counting, Nauru voting system scores each candidate with different points. In the iterative behavior analysis of the Nauru voting system, when two or more winning candidates have the same score, a tie occurs. To break the tie, we use the Copeland method, which is a pairwise comparison to rank the candidates. If there is still a tie, we break it using the traditional linear ordering method, the lexicographic rule. We have observed cycles for different manipulative moves.

Selection of the Multiple-Criteria Decision-Making Method for Evaluation of Sustainable Energy Development: A Case Study of Poland

One of the basic objectives of the European Union’s energy policy is to obtain and use energy in a sustainable way. Multiple-criteria decision making (MCDM) methods, in particular linear ordering based on the synthetic variable procedure, are used for comparative analyses of the level of energy sustainability. Despite many studies, the problem of choosing the optimal ordering method is still not fully resolved. This paper presents an original procedure that facilitates the selection of an effective method of the linear ordering of multi-feature objects for the evaluation of sustainable energy development of regions. What is understood as the effective ordering of regions is not only the effective ranking of objects but also their effective clustering. In order to obtain the best results of linear ordering, the authors put forward a multi-stage optimization of the selection of the method of ordering and normalization of diagnostic variables. Analysis of variance was used for the assessment of the object ranking quality, while for the assessment of the object clustering quality, an innovative approach was presented based on the analysis of the empirical distribution of the frequency of occurrence of the distance between objects. The linear ordering method, selected on the basis of the procedure proposed in the paper, was used to assess the energy sustainability of Polish regions. The calculations and analyses were carried out using the set of indicators developed by the authors. They characterize the sustainable energy development of regions in the social, economic, and environmental dimensions.

Towards Green Growth: A Taxonomic Analysis Based on the Headline Indicators

Purpose: Based on headline indicators, green growth's aggregate indexes have been constructed for 28 EU countries (including the United Kingdom). This allowed creating a ranking of the countries and identifying the strengths and weaknesses of green growth both at the European and national levels. Design/Methodology/Approach: Research was carried out based on the taxonomic linear ordering method. The reference years 2013-2018 were chosen due to data availability for individual indicators on the OECD database. Findings: The analysis showed that Sweden features the highest level of green growth, while Estonia received the lowest rating. Generalizing the study results, it can be stated that the level of 'greening' growth in European Union countries is still low. Practical Implications: The research results fill in the existing information gap by providing an answer to the fundamental question: How can green growth be evaluated synthetically based on headline indicators? This also allows countries to identify areas where their performance is weak and prioritize their mitigation measures accordingly. Originality/Value: The proposed method advances the OECD approach by adding evaluation metrics to assess each country's performance relative to other jurisdictions by indicator and by a synthetic measure.

General relaxation methods for initial-value problems with application to multistep schemes

Recently, an approach known as relaxation has been developed for preserving the correct evolution of a functional in the numerical solution of initial-value problems, using Runge-Kutta methods. We generalize this approach to multistep methods, including all general linear methods of order two or higher, and many other classes of schemes. We prove the existence of a valid relaxation parameter and high-order accuracy of the resulting method, in the context of general equations, including but not limited to conservative or dissipative systems. The theory is illustrated with several numerical examples.

The Financing of Renewable Energy Sources and the Level of Sustainable Development of Poland’s Provinces in the Area of Environmental Order

The overall purpose of this study is to evaluate the impact of financing renewable energy sources on the assessment of sustainable development in Poland’s provinces. There are also two detailed objectives: (1) define how Polish policies are being passed on to local authorities; (2) realize a Poland’s provinces ranking, taking into account the indicators of sustainable development, thanks to the taxonomic measure of development in the area of environmental order. This study deals with the taxonomic assessment of local sustainable development in the local administration units of Poland. To this end, the methods of linear ordering were applied for the assessment of the level of objects differentiation with the use of a closed set of statistical features. The presented analysis proved that the taxonomic distances between synthetic measures for particular provinces are considerable. The highest values of the integrated measure in 2018 were obtained by the following provinces: Podlaskie, Subcarpathian and Lubusz. It is noteworthy to point to the big changes in the ranking between 2018 and 2016. The cluster analysis showed some progress in achieving the goals of sustainable development. The group of provinces with an average level of sustainable development in 2018 included six provinces compared to two provinces in 2016. Removing one indicator from the integrated measure (the financing of renewable energy sources (RES)) led to a moderate increase in the integrated measure across all the provinces. This implies that, on average, the financing of renewable energy sources exerts increasingly smaller impacts on the level of sustainable development in Poland.

How Circular Are the European Economies? A Taxonomic Analysis Based on the INEC (Index of National Economies’ Circularity)

In this paper, the aggregate index of national economies’ circularity (INEC) was proposed and empirically verified. For this purpose, the taxonomic linear ordering method was used, which is a multi-criteria decision-making procedure. This method replaces the analysis of the phenomenon described by a set of indicators with an analysis using one aggregate indicator: the so-called ‘synthetic metric’. Based on 14 circular economy indicators that are available in the Eurostat database, the circularity indexes were constructed for 24 EU countries (including the United Kingdom). This allowed the author, on the one hand, to create a ranking of the countries, and on the other, to assign them to four groups, which were characterized by a similar level of circularity. This paper attempts to answer the following questions: how circular are the European economies? What are the main challenges in achieving circularity in Europe? Taking into account the INEC range [0,1], it should be noted that the level of circularity in the analysed European countries is low (an average of 0.3021). Therefore, the paper indicates the areas requiring improvement in this respect.

Taxonomic Analysis of the Diversity in the Level of Wind Energy Development in European Union Countries

In this paper, the development of the wind energy sector in 28 European Union countries in 2017 is described. By means of taxonomic methods—i.e., Ward’s method and the Wroclaw taxonomic methods—clusters of countries similar in terms of their potential and level of development of the wind energy sector in the EU are distinguished. The main purpose of the paper is to separate and cluster EU countries due to the current development potential of the wind energy sector and determinants stimulating the development of this sector. By means of the ranking methods of linear ordering (Technique for Order of Preference by Similarity to Ideal Solution—TOPSIS method), a ranking of EU countries that defines their position in the development of this very important wind energy sector was determined. The results show that the research hypothesis of a great diversity of EU countries considering the development potential of the wind energy sector is justified. The countries of the former European Union, which have focused for a long time on the development of wind energy in their energy policy and have had favorable climate and natural conditions, as well as a large social acceptance of programs supporting the acquisition of energy from renewable sources, have primacy in the development ranking of the energy sector. Additionally, new members of the union, in spite of some delays associated with the development of “green” energy, are trying to increase their energy potential in this area. The research may be extended to include further analyses regarding other renewable energy sources and take into account other European and world countries.

O pewnych dylematach związanych z budową rankingu obiektów ze względu na poziom zjawiska złożonego

W artykule podjęto dyskusję nad trzema kluczowymi zagadnieniami związanymi z budową rankingu obiektów w oparciu o ich wielokryterialne oceny. Pierwszym z problemów, z którym musi się zmierzyć prowadzący badania (analityk), to wybór zmiennych diagnostycznych. Wybór ten w decydujący sposób wpływa na kształt konstruowanego rankingu. Drugim zagadnieniem jest wybór metody porządkowania liniowego. Trzeci zaś dotyczy obiektów układu porządkowego, jakim jest ranking i sprowadza się do ich podziału na grupy mniejsze względem wartości zmiennej syntetycznej. Z uwagi na to, że w dotychczasowej literaturze związanej z budową rankingu obserwuje się pewną dowolność przy wyborze stosowanych procedur, podjęto się zadania przeprowadzenia dyskusji na ten temat.

Regional Development in Poland in Taxonomic Terms

Regional development is a complex economic category and a commonly used term today, yet it is vaguely defined and, therefore, interpreted implicitly and understood intuitively. From a statistical point of view, this concept, on account of its imprecision and ambiguity, is a kind of multidimensional characteristic which may be measured, though not conclusively. Due to the lack of a universal set of diagnostic variables adopted in taxonomic analyses, the quantitative approach to the examined research area, which is in most cases presented descriptively, poses the main problem. The objectives of the article are to rank the provinces of Poland in terms of regional development in the years 2006–2018 and to assess the similarity of results over time. The research study is based on linear ordering methods within the scope of multidimensional statistical analysis. The results of the conducted analyses allowed us to rank the provinces of Poland in terms of regional development in the years 2006–2018 and to assess the similarity of the results over time. The results of the analysis indicate a clear stabilization of high ranked positions during the examined period, last places are generally taken by the same regions. This situation may indicate an increase or at least strengthening of the disproportions between the most and least developed regions in Poland. Theoretical considerations presented in the article as well as the empirical results of our own research may provoke more detailed discussion on the subject.

The Assessment of the Local Security Policy Efficiency

Purpose: The purpose of this article is to assess the local security efficiency across the districts of the Kuyavian-Pomeranian province in northern Poland. The authors are looking for an answer to the following questions: does the local security policy live up to its expectations, i.e., do citizens feel safe at their place of their residence, and how do they assess the individual components of the local security system? How do residents perceive local security depending on their place of residence across the Kuyavian-Pomeranian province? Design/Methodology/Approach: In order to achieve the goal of the research, the authors conducted a survey employing a sample of 4500 residents of the Kuyavian-Pomeranian province. Based on the survey findings and using linear ordering methods, a ranking of districts of the Kuyavian-Pomeranian province was compiled. Findings: There are significant discrepancies between the subjective assessment of local security efficiency by the residents and its objective evaluation conducted with indicators. Generally, the residents of the districts of the Kuyavian-Pomeranian province are much more content with the local security system than implied by traditional indicators. Practical Implications: The findings of the research are of great significance to local authorities as they allow them to design the systems of local development management more effectively by taking account of the residents’ opinions on the individual components of the security system. Originality/Value: The research was conducted on a relatively extensive group of respondents. The presented findings proved the usefulness of the multidimensional analysis and linear ordering methods in the assessment of local security policy efficiency.

Identification of Regional Smart Specialisations on the Basis of Aggregate Measures – A Case of the Dolnośląskie Voivodeship

Abstract Research background: Strengthening endogenous potentials, enhancing competitive advantage based on research and innovation remains an important component of regional development policy. Over the years this task has been carried out through e.g. the identification and support focused on smart specialisations. Purpose: The purpose of the assessment was to identify smart specialisations in the Dolnośląskie voivodeship and evaluate their competitiveness against the background of other voivodeships. Research methodology: The set of diagnostic indicators as well as the dynamics and location measures calculated on their basis, and also linear ordering methods using a weights system (Synthetic Measure of Smart Specialisations – SMSS) were used to identify regional smart specialisations. A statistical analysis was conducted on the basis of data at the level of PKD divisions (Polish Statistical Classification of Economic Activities; NACE is the EU equivalent). The identification was carried out taking into account the period 2012–2017 and focused primarily on 2017. Results: As a result, 4 RSSs were identified, of which the first two are the mining of non-ferrous metal ores and the production of motor vehicles. Novelty: The study proposes, based on the example of the Dolnośląskie voivodeship, the possibility of using linear ordering methods in determining the region’s smart specialisations (RSS), i.e. unique regional qualities and assets, which may constitute its competitive advantage, supported by appropriate research and development facilities and essential for the development of modern and innovative sectors of the economy.

An Analysis of Tourist Attractiveness of Poviats of the Lesser Poland Voivodeship

AbstractResearch background:Lesser Poland is one of the most visited regions in Poland. Among the reasons why it is so, there are a variety of attractions located in this voivodeship and also the activities taken by local government, for which the development of the tourism industry is one of the key goals.Purpose:Building a ranking of poviats of Lesser Poland in terms of tourist attractiveness.Research methodology:Selected multivariate analysis tools, i.e. three methods of linear ordering and cluster analysis.Results:Using the Ward algorithm, poviats are grouped into four clusters of areas with similar characteristics due to tourist values. In addition, using three linear ordering techniques, poviats of the Lesser Poland voivodeship are ordered according to tourist attractiveness. The results of ordering are rather consistent and indicate that the most attractive poviats are: nowotarski, oświęcimski, tatrzański and the city of Kraków. Interestingly, these areas belong to three different groups obtained as part of a cluster analysis. This means that Lesser Poland is a diversified region in terms of the attractions that draw tourists’ to the area.Novelty:The study of tourist attractiveness using linear ordering techniques is not an original topic. The thesis is of cognitive value and fills a gap in the literature, in which there are no studies based on data from Lesser Poland.

A New Business Design Tool for Digital Business Model Innovation: DEA Approach

The new economic structures characterized by the growing dynamics of the economic context and a greater influence of the market on entrepreneurial activities requires companies to generate and adopt more and more competitive innovations, to maintain and develop a high level of innovative activity. Innovations are perceived as a necessity, they are a factor, and they are the mobile strength of companies in the 21st century. Every modern manager should recognize the role of innovations for the existence of companies and aim for innovative development. The news in various sectors must be followed. In this sense, it is necessary to look for options and overcome the obstacles that stand in the way of innovations. This paper attempts to assess the level of innovativeness of 26 European economies in the years 2016–2018 by using the Data Envelopment Analysis (DEA). To perform this study, the evaluation used was carried out on the basis of a summary index constructed with the use of statistical methods of non linear ordering; in particular. In the analysis carried out, the statistics of the Global Innovation Index were used to describe the innovative capacity of economies in two areas: (a) science and technology; and (b) education and training. The evolved classification of innovativeness of these countries, built on the basis of a synthetic index, will allow to create a ranking that will lead to comparative analysis among these countries.

Selected Elements of Technical Infrastructure in Municipalities Territorially Connected with National Parks

The article addresses the problem of selected technical infrastructure elements (e.g., water supply, sewage, gas networks) in municipalities territorially connected with Polish national parks. Therefore, the research refers to the specific areas: both naturally valuable and attractive in terms of tourism. The time range of the research covers the years 2003–2018. The studied networks were characterized based on the statistical analysis using linear ordering methods; synthetic measures of development were applied. It allowed the ranking construction of the examined municipalities in terms of the development level of water supply, sewage, and gas networks. The results show that the period 2003–2018 was characterized by a development of the analyzed networks in the vast majority of municipalities. Thus, the level of anthropopressure caused by the presence of local community and tourists in municipalities showed a decline. It is worth emphasizing that the infrastructure investments are carried out comprehensively. Favoring investments in the development of any of the abovementioned networks was not observed.