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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.

The airline industry has been significantly hit by the occurrence of the new coronavirus SARS-CoV-2, facing one of its worst crises in history. In this context, the present paper analyses one of the well-known boarding methods used in practice by the airlines before and during the coronavirus outbreak, namely back-to-front and suggests which variations of this method to use when three passenger boarding groups are considered and a jet bridge connects the airport terminal with the airplane.

Based on the importance accorded by the airlines to operational performance, health risks, and passengers' comfort, the variations in three passenger groups back-to-front boarding are divided into three clusters using the grey clustering approach offered by the grey systems theory.

Having the clusters based on the selected metrics and considering the social distance among the passengers, airlines can better understand how the variations in back-to-front perform in the new conditions imposed by the novel coronavirus and choose the boarding approach that better fits its policy and goals.

The paper combines the advantages offered by grey clustering and agent-based modelling for offering to determine which are the best configurations that offer a reduced boarding time, while accounting for reduced passengers' health risk, measured through three indicators: aisle risk, seat risk and type-3 seat interferences and for an increased comfort for the passengers manifested through a continuous walking flow while boarding.

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 the paper is to analyse the relationships between the competency structure of the successors of family enterprises in Poland and dimensions like gender, self-awareness of development, taking their ideas into consideration in shaping the strategy of the firm and the size of the firm.

Grey relational analysis was employed to analyse the empirical material in the paper. The results of the analysis served a more thorough qualitative analysis of the subject of the family enterprise successors’ competencies by comparing them to theoretical assumptions and other research within this scope.

In the paper, the relation was shown between the structure of family firm successors’ competencies and the variables such as gender, development self-awareness, taking their ideas into consideration in shaping the strategy of the firm and the size of the firm.

The research was conducted in Poland and therefore its generalisation has limited scope resulting from the cultural and historical conditioning.

The results of the research may serve the creation of tools and methods of succession process management in a family enterprise.

The paper presents the possibilities of employing grey system theory in the research remaining within the scope of the subject of succession in family enterprises, as a tool complementing qualitative analysis.