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With the use of the grey incidence analysis (GIA), indicators such as the absolute degree of grey incidence (ε_ij), relative degree of grey incidence (r_ij) or synthetic degree of grey incidence (ρ_ij) are calculated. However, it seems that some assumptions made to calculate them are arguable, which may also have a material impact on the reliability of test results. In this paper, the authors analyse one of the indicators of the GIA, namely the relative degree of grey incidence. The aim of the article was to verify the hypothesis: in determining the relative degree of grey incidence, the method of standardisation of elements in a series significantly affects the test results.

To achieve the purpose of the article, the authors used the numerical simulation method and the logical analysis method (in order to draw conclusions from our tests).

It turned out that the applied method of standardising elements in series when calculating the relative degree of grey incidence significantly affects the test results. Moreover, the manner of standardisation used in the original method (which involves dividing all elements by the first element) is not the best. Much more reliable results are obtained by a standardisation that involves dividing all elements by their arithmetic mean.

Limitations of the conducted evaluation involve in particular the limited scope of inference. This is since the obtained results referred to only one of the indicators classified into the GIA.

In this article, the authors have evaluated the model of GIA in which the relative degree of grey incidence is determined. As a result of the research, the authors have proposed a recommendation regarding a change in the method of standardising variables, which will contribute to obtaining more reliable results in relational tests using the grey system theory.

The purpose of this paper is the application of the computational fluid dynamics model simulating the blood flow within the aorta of an eight-year-old patient with Coarctation of Aorta.

The numerical model, based on commercial code ANSYS Fluent, was built using the multifluid Euler–Euler approach with the interaction between the phases described by the kinetic theory of granular flow (KTGF).

A model of the blood flow in the arches of the main aorta branches has been presented. The model was built using the multifluid Euler–Euler approach with the interaction between the phases described by the KTGF. The flow and pressure patterns, as well as the volumetric concentration of the blood components, were calculated. The lumped parameter model was implemented to couple the interaction of the computational domain with the remaining portion of the vascular bed.

The multiphase model based on the Euler–Euler approach describing blood flow in the branched large vessel with a three-element Windkessel model in the coarcted geometry was not previously described in the literature.

Considering current development of Grey Systems Theory (GST), we can come up with the following thesis: practical applications are a dominant subject of research. Thus, what seems to be symptomatic for relatively young knowledge disciplines, the authors observe the presence of imbalance between the development of GST application tools and theory’s epistemological and methodological background. As for GST, epistemological and methodological problems are becoming visible especially in the issues of determining a clear criterion of demarcation of this kind of a theory from others. In other words, this problem can be reduced to the issue of a precise determination of what the category of a grey system and grey information is. This problem is of great importance for further development and popularisation of GST in the world of science. Realising its significance, the purpose of this paper is to create a general overview of Grey Systems epistemology and afterwards create axiomatic and formal frames for a category of greyness.

In order to achieve set goals, two research approaches were accepted. In the area of inference about epistemology of GST an approach characteristic of an analytical philosophy was used, whereas in the case of axiomatic and formal frames for a category of greyness the authors referred to terms of a set theory and the principles of a pragmatic logic.

The result of research is to formulate a concept of a grey system and a concept of grey information in the context of a process of cognition. Moreover, a function of greyness and other fundamental categories of GST will be defined in an axiomatic way.

The paper presents a new consistent frame for the issues of methodological and epistemological backgrounds of GST. An original concept is to refer in considerations to a newly proposed grey space. This space was used for a formal justification of such elementary categories as grey numbers, a weight function of whitenization or grey sequences. The value of achievements shown in the paper is underlined by the fact that proposed theoretical constructions require further development and they can potentially open up new research trends in the GST.

The degree of greyness may be regarded as a measure of cognitive uncertainty. Therefore, it is a part of the epistemological core of the grey systems theory. The theoretical importance of the degree of greyness concept is also due to its application in a range of uncertainty modelling methods: predictive, relational and decision-making methods. Greyness, being a result of cognitive uncertainty, was recently subjected to axiomatization in the form of grey space with the use of the classical sets theory. The purpose of this article is to develop a new approach to the degree of greyness, being consistent with the grey space concept.

In order to realise the article’s goals, the research is divided into three stages described in particular sections. The first section of the article presents a theoretical framework of the degree of greyness and the grey space. The second part includes the assumptions of the new degree of greyness concept, along with the mathematical models for the first, the second and the third degree of greyness. The third section contains numerical examples for each degree of greyness.

As a result of the research, a concept of a degree of greyness was created and it was linked with a concept of grey space. This new approach to the issue of the degree of greyness has allowed the analysing of this category in three dimensions dependent on an accepted reference base. As a result, a concept of concrete and abstractive grey numbers was introduced and relationships between these categories of numbers and the degree of greyness were determined.

The proposed approach to the issue of the degree of greyness is a theoretical unification of the previous considerations in this area. The proposed three dimensions of greyness degree will be derived from the grey space, so they will also be a function of quantity. Thus, the degree of greyness was linked with a classical set theory. An original input in this article is also a differentiation of concrete and abstractive grey numbers, which give a basis for deliberations connected with interpretation of grey numbers in the context of real applications.

This paper is a part of the application trend of the development of the grey systems theory. The purpose of this paper is to present the use of the GDM model in the diagnosis of the occurrence of crises in family businesses. The issue of the occurrence of conflicts and crises in family businesses is one of the most important and common in management science in Poland.

In the paper using the GDM model (in which the weights of the criteria were determined using the modified Thurstone method), the authors presented a way to diagnose the occurrence of crises in family businesses for a sample of Polish family businesses using, among others, a questionnaire-based survey.

As a result of the conducted research, it turned out that in eight surveyed businesses no symptoms of conflicts were diagnosed. In three businesses, the symptoms of conflicts were diagnosed, but they did not threaten their existence. In the case of four businesses, the symptoms of crisis that threaten their existence were diagnosed and immediate remedial action was recommended to them.

The authors are of the opinion that the presented research results may be a reason for the validity of using the GDM model in the diagnosis of crises in family businesses. At the same time, it is recommended to undertake further research on, inter alia, conflict fields in family businesses, or on the use of the modified Thurstone method as a part of determining the validity of decision-making criteria in GDM models.

The article proposes a new method of strategic analysis. The method was called the grey portfolio analysis method. The presented method is complementary to the popular BCG matrix. The use of the grey portfolio analysis method enables to make a dynamic portfolio analysis for data with a high level of uncertainty.

First, the article presents current problems related to the application of portfolio methods in strategic management, in particular with reference to the BCG matrix. Second, the basics of grey numbers, operations with them and the way of acting in the grey portfolio analysis method are presented. Finally, the developed method is presented in a case study concerning an IT enterprise, whose portfolio includes cloud computing services.

In the article, a new method of a strategic analysis based on the BCG matrix was presented. It combines grey methodologies of decision making with a grey prognostic model in the context of a strategic analysis. Due to this fact, a dynamic approach to the issues of portfolio methods is possible.

The article fits the current need related to the development of new expert systems supporting strategic management in enterprises.

An introduced method is new and innovative in the area of portfolio methods. Its originality results from the fact that it eliminates a static nature of the BCG matrix through the use of grey prognostic models. What is more, when grey numbers are used, a problem of uncertainty of information, which appears, is solved at a methodological level.

The purpose of this paper is to present an accurate and efficient hybrid method for the calculation of the inductance of a coil and its inductance change due to deformed turns using numerical methods.

The paper opted for finite element method coupled with analytical method (FCA) to accurately calculate the inductance of a coil, which is used as reference value. An algorithm with a power function is presented to approximate the partial inductance matrix with the purpose of obtaining the percentage change of the inductance due to deformed turns by using the partial element equivalent circuit (PEEC) with an approximated model and an optimization process. The presented method is successfully validated by the numerical results.

The paper provides a systematic investigation of the inductance of an arbitrary shaped coil and shows how to accurately and efficiently evaluate the inductance change of a coil due to its deformed turns. It suggests that the inductance of a coil can be accurately calculated by using FCA and its percentage change due to deformed turns can be efficiently calculated by using the PEEC_Approximation.

As this research is for the magnetostatics, the skin- and proximity-effects have not been taken into account.

The paper includes implication for the worst-case analysis of the coil’s inductance due to mechanical damage or manufacturing tolerance.

This paper fulfills an identified need to study how the inductance change of a coil can be obtained accurately and efficiently.

One of the sources for the increase in the carbon footprint on the earth is the manufacturing of cement, which causes a severer environmental impact. Abundant research is going on to diminish CO₂ content in the atmosphere by appropriate utilization of waste by-products of industries. Alkali-activated slag concrete (AASC) is an innovative green new concrete made by complete replacement of cement various supplementary cementitious raw materials. Concrete is a versatile material used in different fields of structures, so it is very important to study the durability in different exposures along with the strength. The purpose of this paper is to study the performance of AASC by incorporating quartz sand as fine aggregate under different exposure conditions.

The materials for this innovative AASC are selected based on preliminary studies and literature surveys. Based on numerous trials a better performance mix proportion of AASC with quartz sand is developed with 1:2:4 mix proportion, 0.8 alkali Binder ratio, 19 M of NaOH and 50% concentration of Na₂SiO₃. Subsequently, AASC cubes are prepared and exposed for 3, 7, 14, 28, 56, 90, 112, 180, 252 and 365 days in ambient, acid, alkaline, sulfate, chloride and seawater and tested for compressive strength. In addition, to study the microstructural characteristics, scanning electron microscope (SEM), energy dispersive X-ray analysis and X-ray diffraction analysis was also performed.

Long-term performance of AASC developed with quartz sand is very good in the ambient, alkaline environment of 5% NaOH and seawater with the highest compressive strength values of 51.8, 50.83 and 64.46, respectively. A decrease in compressive strengths was observed after the age of 14, 56 and 112 days for acid, chloride and sulfate exposure conditions, respectively. SEM image shows a denser microstructure of AASC matrix for ambient, alkaline of 5% NaOH and seawater.

The proposed AASC is prepared with a mix proportion of 1:2:4, so the other proportions of AASC need to verify. In general plain, AASC is not used in practice except in few applications, in this work the effect of reinforced AASC is not checked. The real environmental exposure in fields may not create for AASC, as it was tested in different exposure conditions in the laboratory.

The developed AASC is recommended in practical applications where early strength is required, where the climate is hot, where water is scarce for curing, offshore and onshore constructions exposed to the marine environment and alkaline environment industries like breweries, distilleries and sewage treatment plants. As AASC is recommended for ambient air and in other exposures, its implementation as a construction material will reduce the carbon footprint.

The developed AASC mix proportion 1:2:4 is an economical mix, because of low binder content, but it exhibits a higher early age compressive strength value of 45.6 MPa at the age of 3 days. The compressive strength increases linearly with age from 3 to 365 days when exposed to seawater and ambient air. The performance of AASC is very good in the ambient, alkaline environment and seawater compared to other exposure conditions.