Application of a Methodology for Modeling the Influence of Environmental Factors on the Work of the Public Sector in the Context of Sustainable Development

2.1 Interaction between environmental factors and the public sector

The intersection of environmental factors and the public sector in the context of sustainable development has garnered significant attention within academic and professional circles, as evidenced by a diverse range of studies focusing on the institutional pressures, environmental strategies, environmental governance, and the role of knowledge and policy in shaping sustainable outcomes. This chapter reviews pertinent literature that informs the methodology for modelling the influence of environmental factors on the work of the public sector, drawing on recent empirical and theoretical research. Li and Ji [1] provide a foundational understanding of how institutional pressures and environmental strategies correlate with corporate environmental performance. Their empirical analysis highlights the direct and mediated effects these factors have on improving sustainability within organizations, offering insights into the broader implications for public sector entities seeking to enhance their environmental governance. In a similar vein, Fuzi et al. [2] delve into the relationship between environmental costs, organizational performance, and the implementation of environmental management systems. Through structural equation modelling, their study elucidates the positive impacts that proactive environmental management can have on organizational efficacy, suggesting a pathway for public sector organizations to integrate environmental considerations into their operational frameworks.

2.2 The development of modern environmental governance in the context sustainable development

The question of whether environmental governance is substantive or symbolic is critically examined by Rodrigue et al. [3]. Their empirical investigation into corporate practices reveals a complex landscape where governance mechanisms can vary widely in their effectiveness and sincerity, offering a cautionary perspective that is relevant to public sector efforts in environmental governance. O’byrne et al. [4] and Alinski's [5] researches highlight the importance of the public sector in driving sustainable development, particularly through the integration of sustainability principles into strategic planning and operations. The authors identify how government agencies can promote environmental sustainability, economic development, and social justice, making this study relevant to my analysis of the impact of environmental factors on public sector performance. These findings provide a basis for assessing and developing effective public sector management strategies to meet the challenges of sustainable development and help formulate specific recommendations for improving environmental responsibility and sustainable management. Kryshtanovych et al. [6] addressed the socio-ecological effects of public management in green development, presenting a philosophical and practical framework for understanding the ecological impacts of public sector actions. Their analysis points to the significance of adopting a holistic approach to environmental management, aligning with the principles of modern ecology to enhance sustainable development outcomes.

Khaled et al. [7] examined the relationship between sustainability goals and corporate sustainability, exploring how companies integrate sustainability goals into their operations and how this impacts sustainability performance. This analysis is important to my research because it provides insights into the mechanisms for implementing sustainability at the corporate level and helps identify how the public sector can facilitate or regulate this process to achieve broader environmental goals.

Further contributions by Singh et al. [8], Vagiona [9] and Paiders [10], they expand the discourse on sustainable development, environmental sustainability indices, and the financial implications of environmental protection for regional economic development. These studies collectively highlight the multifaceted relationships between environmental performance, sustainable development goals, and economic and social indices, providing a comprehensive backdrop for understanding the environmental dimensions of public sector work [8-10]. Muafi [11], Singh et al. [12], and Ovchynnykova et al. [13] offer insights into the roles of green culture, strategy, and the impact of environmental regulation implementation. By examining the moderating effects of green intellectual capital and the outcomes of environmental regulation, these studies contribute to a nuanced understanding of how green initiatives and regulations influence public sector operations and sustainability efforts [11-13].

In summary, the reviewed literature presents a diverse and complex picture of how environmental factors influence the public sector. From institutional pressures and environmental strategies to governance, knowledge, policy, and legal frameworks, these studies provide a rich tapestry of insights and empirical evidence that inform the development of methodologies for modelling environmental influences on public sector work. This body of work not only highlights the challenges faced but also points to the opportunities for integrating environmental considerations into the fabric of public sector operations, ultimately contributing to more sustainable and effective governance.

The scientific task is to evaluate the environmental factors in such a way as to reveal the most significant in the action of the sustainable development of the public sector.

Based on the data analysis, we will compile into two tables (Table 1) the environmental factors that influence the work of the public sector in Ukraine in the context of sustainable development. Essentially, this involves defining a set of factors (feasible alternatives) that, from the perspective of their emergence, require changes in the public administration system – x_і, і = 1, n.

These environmental factors have a complex impact on sustainable development, requiring in-depth analysis and adaptive measures from the public sector. Changing climate conditions with extreme weather events and fluctuating temperatures threaten infrastructure, health care and the effectiveness of emergency services, highlighting the need to strengthen resilience to climate challenges. Deteriorating air quality requires immediate action to reduce emissions from industrial and vehicular sources, as it has a direct impact on public health and quality of life. Limited access to clean water affects health, agriculture and industry, requiring the development and implementation of comprehensive programs for the management and storage of water resources.

The loss of biodiversity and ecosystems leads to a decline in natural resources and services such as pollination and water purification, requiring government conservation measures. Finally, urban sprawl and land degradation require the public sector to undertake careful spatial planning and conservation measures to ensure environmental sustainability and promote sustainable development initiatives.

Table 1. Environmental factors affecting the work of the public sector

The next step was to define the criteria by which the selection among the identified factors (feasible alternatives) gj, j = 1, m (Table 2).

Table 2. The criteria by which the selection among the identified factors

In the process of implementing the task, it is important to identify key factors according to the selected criteria. This means that it is necessary to effectively solve the problem of choosing the optimal option from a set X, while taking into account the established fuzzy ratio of advantages g1, g2,... gm with given membership functions μ_gj: X × X → [0, 1].

Therefore, further, for each of the criteria gj, we evenly compare environmental factors that can have a significant impact on public administration. The results were assessed as follows (1):

$\mu_{g 1}\left(x_i, x_j\right)=\left\{\begin{array}{l}1, \text { if } x \mathrm{i} \succ x \mathrm{j} \\ 0, \text { if } x \mathrm{i} \prec x \mathrm{j}\end{array}\right.$     (1)

For g1 we have the following (2):

$\begin{gathered}x_1 \succ x_2, x_1 \succ x_3, x_1 \succ x_4, x_1 \prec x_5, x_1 \prec x_6, x_1 \succ x_7, x_1 \prec x_8, \\ x_2 \approx x_3, x_2 \succ x_4, x_2 \prec x_5, x_2 \prec x_6, x_2 \approx x_7, x_2 \prec x_8, \\ x_3 \approx x_4, x_3 \prec x_5, x_3 \prec x_6, x_3 \approx x_7, x_3 \prec x_8, \\ x_4 \prec x_5, x_4 \prec x_6, x_4 \approx x_7, x_4 \prec x_8, \\ x_5 \approx x_6, x_5 \succ x_7, x_5 \approx x_8, \\ x_6 \succ x_7, x_6 \approx x_8, \\ x_7 \prec x_8 .\end{gathered}$     (2)

For g2 we have the following (3):

$\begin{gathered}x_1 \approx x_2, x_1 \succ x_3, x_1 \succ x_4, x_1 \approx x_5, x_1 \prec x_6, x_1 \approx x_7, x_1 \prec x_8, \\ x_2 \succ x_3, x_2 \succ x_4, x_2 \prec x_5, x_2 \prec x_6, x_2 \approx x_7, x_2 \prec x_8, \\ x_3 \succ x_4, x_3 \prec x_5, x_3 \prec x_6, x_3 \approx x_7, x_3 \prec x_8, \\ x_4 \approx x_5, x_4 \prec x_6, x_4 \prec x_7, x_4 \prec x_8, \\ x_5 \succ x_6, x_5 \succ x_7, x_5 \prec x_8, \\ x_6 \succ x_7, x_6 \approx x_8, \\ x_7 \prec x_8 .\end{gathered}$      (3)

For g3 we have the following (4):

$\begin{gathered}x_1 \prec x_2, x_1 \approx x_3, x_1 \succ x_4, x_1 \prec x_5, x_1 \prec x_6, x_1 \approx x_7, x_1 \prec x_8, \\ x_2 \approx x_3, x_2 \approx x_4, x_2 \prec x_5, x_2 \prec x_6, x_2 \approx x_7, x_2 \prec x_8, \\ x_3 \approx x_4, x_3 \prec x_5, x_3 \prec x_6, x_3 \approx x_7, x_3 \prec x_8, \\ x_4 \prec x_5, x_4 \prec x_6, x_4 \prec x_7, x_4 \prec x_8, \\ x_5 \prec x_6, x_5 \succ x_7, x_5 \prec x_8, \\ x_6 \succ x_7, x_6 \prec x_8, \\ x_7 \prec x_8 .\end{gathered}$     (4)

The process of generating a matrix of fuzzy relations in the context of the multicriteria selection of alternatives method using fuzzy logic consists of turning qualitative assessments and expert judgments into quantitative membership values measured on a scale from 0 to 1. This scale represents the degree to which an element (for example, an alternative criterion) corresponds to a specific property or category. The process is based on turning subjective judgments about the importance, priority, or influence of various factors into precise numerical values, allowing mathematical analysis to be performed.

After all qualitative assessments are converted into numerical membership values, a matrix of fuzzy relations is formed, where each element of the matrix represents the degree of membership between pairs of criteria or alternatives. Such a matrix allows further analysis to determine optimal decisions or rank alternatives taking into account all criteria, which contributes to an objective and comprehensive approach to decision making in complex conditions of unclear information.

Next, based on a relation (2-4), membership functions of the given preference relations μgj(xi, xj) were constructed (Table 3).

The data were presented in the form of matrices μg1(xi, xj), μg2(xi, xj), μg3(xi, xj), meeting the criteria gj.

Now we construct the convolution of the relations g1, g2, g3 in the form of a section Q1 = g1 ∩ g2 ∩ g3 with a membership function (5):

$\mu_{Q 1}\left(x_i, x_j\right)=\min \left\{\mu_{g 1}\left(x_i, x_j\right), \mu_{g 2}\left(x_i, x_j\right), \mu_{g 3}\left(x_i, x_j\right)\right\}$     (5)

The result of the calculation using the formula for the environmental factors we identified is presented in Table 4.

Table 3. The relation matrix for g1-g3

Table 4. Matrix μQ1(xi, xj) of minimal elements xi, xj among matrices μgj(xi, xj)

After identifying the precise advantage ratio through the initial convolution, we proceed to establish the membership function as indicated in Eq. (6):

$\mu_{Q_1}^s\left(x_i, x_j\right)=\max \left\{0 ; \mu_{Q_1}\left(x_i, x_j\right)-\mu_{Q_1}\left(x_j, x_i\right)\right\}$      (6)

Subsequently, we specify the collection of non-dominated options Q1nd within the set (X, Q1) and develop a corresponding membership function. In this instance, it is presented as follows in Eq. (7):

$\begin{gathered}\mu_{Q 1}(X)=[0 ; 0 ; 0 ; 0 ; 1 ; 1 ; 0 ; 1] \\ \mu_{Q 2}(X)=[0,51 ; 0 ; 0 ; 0,21 ; 0,21 ; 73 ; 1]\end{gathered}$     (7)

Thus, we determine the non-dominated environmental factor (alternatives) from both convolutions (Table 5).

The results obtained demonstrate that for the public sector of Ukraine, the most important external factor is x8 – Urban sprawl and land degradation affect environmental sustainability, requiring careful planning, green space preservation, and sustainable development initiatives. The degree of non-dominance of this factor is equal to one, that is, this is a true non-dominated alternative.

In Ukraine, a country with diverse geographic and climatic conditions ranging from rainforests in the north to steppes and semi-deserts in the south, the problem of land degradation and urban sprawl is particularly pressing. This is due to intensive agricultural use of land, which leads to soil erosion, a decrease in soil fertility and loss of natural biodiversity. In addition, urbanization and urban expansion lead to overuse of land resources, pollution and reduction of green spaces, which are critical to ensure ecological balance and sustainability of ecosystems. Given these conditions, the importance of careful planning, conservation and sustainable development initiatives is clear to help conserve natural resources, maintain biodiversity and adapt to climate change.

Table 5. The non-dominated environmental factor (alternatives) from both convolutions

The significance of urban sprawl and land degradation as the most critical external factor for Ukraine's public sector, particularly identified as factor x8, stems from its profound impact on sustainability. Urban sprawl refers to the uncontrolled expansion of urban areas into rural lands and natural habitats, leading to a multitude of environmental issues. This expansion often results in land degradation, where the quality and productivity of the land diminish, affecting ecosystems, biodiversity, and the ability to provide for future generations. The reason this factor is paramount, especially for a country like Ukraine, lies in its direct challenge to sustainable development. Sustainable development aims to meet the needs of the present without compromising the ability of future generations to meet their own needs. However, urban sprawl and land degradation counteract these goals by causing irreversible harm to the environment, which includes loss of green spaces, increased pollution, and disruption of natural processes. These changes not only affect the ecological balance but also have social and economic repercussions, such as health issues due to pollution and increased costs for sustainable development in sprawled areas.