Impact of Carbon Emission Factors on Economic Agents Based on the Decision Modeling in Complex Systems

Abstract

This article presents a methodology for modeling the impact of both internal and external environmental carbon emission factors on the resulting indicators of an international company. This research uses picture fuzzy rough sets to model the impact of factors on the resulting indicators as a research method. The proposed model is based on a dataset that includes the company’s profit, revenue, valuation, share price, and market share from 2012 through 2022. This empirical period is optimal for such a type of modeling. An approach of picture fuzzy rough sets based on the time series of endogenous and exogenous variables can provide an opportunity to analyze and consider the consequences of feedback changes in the systems of which they are a part. The article proposes a valuable framework for understanding the complex relationship between carbon emissions, economic factors, and the performance of international companies. The researchers of this study recommend a discussion that attempts to gain a deeper understanding of the challenges and opportunities that lie ahead for international companies in the context of climate change and technological innovation.

1. Introduction

This article uses the approach of complex systems theory [1]. The authors used these ideas and detection algorithms, which are based on the rules of interacting with participants and were identified using fuzzy methods, in this study [2]. International companies exist in many different types of environments in the modern context, which differ in their economic, social, technological, and environmental conditions [3]. Global markets, with their forces of supply and demand, changing technologies, a growing global population with increasing demands, and economic crises and inflation consequences, influence international companies and form the conditions for their development [4]. Economic, social, technological, and environmental factors affect all of the indicators of an international company, as well as all the processes that occur within a company or any other type of organization [5]. It is necessary to remember the mutual influence of the resulting indicators of an international company. The net profit of a company depends on the company’s total revenue and total assets. Management should consider the influence of the external environment and the interdependence of a company’s performance indicators. The picture fuzzy rough sets of the relationship between an international company and the external environment are a significant and exciting topic for research today. The development of a company is the result of many factors, both within the activities of an international company and due to the impact of economic, social, technological, and environmental factors [6]. The economic, social, technological, and environmental factors depend on each other [7,8]. In this study, the parameters of the constructed picture fuzzy rough sets are based on complex systems theory [9]. Furthermore, analyses of the information that characterizes the external environment and the analysis of data that represents the indicators of an international company have been conducted [10,11].

The indicators of both external environments and an international company’s indicators are constantly changing [12]. Some of them change slowly, but some change dramatically and unpredictably. A corporation’s activities should be evaluated from the point of view of maximizing its consumer value and minimizing the consumption of resources for its activities [13]. With the development of information technologies and computerized data management tools, IT solutions have become a means of implementing new organizational forms and picture fuzzy rough sets for the cooperation within and between companies [14]. Technologies such as the Internet of things (IoT), big data (BD), artificial intelligence (AI), and blockchains (BCs) have become possible solutions that allow one to collect instrumental data and share information in real time and globally. Under these conditions, new management models are emerging that are designed to maintain competitiveness [15]. The results confirm the need for a strategic approach for determining estimated performance indicators, which must take into account customer orientation [16].

In today’s world, it is essential to apply the concepts of Lean, Agile, Resilient, and Green, collectively known as LARG Manufacturing, to achieve business excellence. LARG’s abandonment practices can be combined with various aspects of Industry 4.0 to deliver operational, economic, and environmental benefits. Enhanced process transparency, the high level of failure response, and clean production are the main features of the LARG Manufacturing and Industry 4.0 synergy, which is fueled by automation and big data. A comprehensive, technologically integrated implementation framework may be developed by involving LARG participants with Industry 4.0 or artificial intelligence to achieve sustainability [17]. Although sustainability is a significant challenge for most international companies, tangible progress in this area is still not noticeable, and this is mainly due to the lack of reliable methodological foundations and reliable empirical data [18]. A higher sustained organizational effectiveness (SOE) means that a company has a sustained competitive advantage over its competitors and a higher level of customer satisfaction [19].

The external environment is characterized by increased instability, unpredictability, and changes in the behavior of companies in their activities, which are aimed at changing the indicators of economic processes [20]. Companies strive to shorten product life cycle stages, divide products into separate parts, formulate requirements for the operation of each part, and assign thoughtful design to firms with competencies in the blockchain field [21]. Tough competition has shown that prices in such conditions are not essential for cooperation. Environmental conditions, such as the division of the product into separate parts, prices, and other conditions related to the turbulence of ecological indicators and the indicators of international companies, have become requirements [22].

The research purpose of this study is to develop a methodology for modeling the impact of internal and external environmental factors on the resulting indicators of an international company.

This research uses picture fuzzy rough sets to model the impact of factors on the resulting indicators as a research method. The proposed model is based on a dataset that includes the company’s profit, revenue, valuation, share price, and market share from 2012 through 2022.

2. Literature Review

In the scientific literature, a great deal of attention has been paid to the problems of constructing mathematical picture fuzzy rough sets and expanding the scope of their practical application [23,24]. Procedures for forming a system of mathematical and statistical models for the production processes of enterprises are proposed. An essential part of this research is the development of methods for determining model parameters and software tools. A literature review was conducted to research the problems of constructing mathematical picture fuzzy rough sets for modeling the activities of various corporate structures [25].

This research is devoted to forming picture fuzzy rough sets (econometric methods of enterprise management and scenario directions of development) and developing strategies for determining model parameters and software tools based on complex systems theory [1,26].

Table 1. Categories of methods and company performance indicators.

Description of Methods	Modeling the Impact on the Company’s Performance Indicators
Picture fuzzy rough sets	Models the axiomatics of building an econometric model
Modeling the impact of the external environment on the company’s performance indicators that depend on each other	Models the normalization of the values of exogenous and endogenous variables
System-related one equations	Models checking the time series of variables for stationarity
ADL model	Models the identifiability of a system of equations
ADL model system	Models the axiomatics of building an econometric model
Using the ADL model system for forecasting	Models the normalization of the values of exogenous and endogenous variables

shows how the use of picture fuzzy rough sets can be used for the research problem of this paper.

In addition, it can be noted that of all the articles included in the final review, some concerned specific models, while others covered modeling concepts [27,28].

In the second stage, the methodology for determining picture fuzzy rough sets and software tools for determining model parameters were analyzed [29]. An essential part of this study was to determine the inclusion and exclusion criteria. This section of the research considers the stages of the methodology for determining the model parameters [30].

3. Materials and Methods

This paper used picture fuzzy rough sets as they have been used in highly cited studies that are based on complex systems theory [19,20].

Within the methodology framework for modeling the influence of internal and external environmental factors on the resulting interdependent indicators of a company’s activity, a model of picture fuzzy rough sets was chosen. The task was to build a model that allows for estimating the values of interdependent and dependent variables based on the values of independent indicators, which are then expressed as a time series. Time series analysis is performed on datasets in which the dependent variables have some degree of a relationship. Such datasets are standard in all areas of science [31,32]. The basis of the proposed model is an equation in which the values of the dependent variable x are combined with the values of the past period variables, independent indicators (factors), and dependent variables, which is expressed as follows:

$$A=\left\{〈x,{\mu }_A\left(x\right)〉\left|x\right.\in X\right\},$$

(1)

$$A=\left\{〈x,{\mu }_A\left(x\right),v_A\left(x\right)〉\left|x\right.\in X\right\},$$

(2)

$$A=\left\{〈x,{\mu }_A\left(x\right),n_A\left(x\right),v_A\left(x\right),{\pi }_A\left(x\right)〉\left|x\right.\in X\right\},$$

(3)

$$A\subseteq B\mathrm{if}{\mu }_A\left(x\right)\le {\mu }_B\left(x\right)\mathrm{and}{n}_A\left(x\right)\le n_B\left(x\right)\mathrm{and}{v}_A\left(x\right)\ge v_B\left(x\right),\forall x\in X,$$

(4)

$$A=B\mathrm{if}A\subseteq B\mathrm{and}B\subseteq A,$$

(5)

$$A\cup B=\left\{\left(x,max\left({\mu }_A\left(x\right),{\mu }_B\left(x\right)\right),min\left(n_A\left(x\right),n_B\left(x\right)\right),min\left(v_A\left(x\right),v_B\left(x\right)\right)\right)\left|x\right.\in X\right\},$$

(6)

$$A\cap B=\left\{\left(x,min\left({\mu }_A\left(x\right),{\mu }_B\left(x\right)\right),min\left(n_A\left(x\right),n_B\left(x\right)\right),max\left(v_A\left(x\right),v_B\left(x\right)\right)\right)\left|x\right.\in X\right\},$$

(7)

$$coA=\overline{A}=\left\{\left(x,v_A\left(x\right),n_A\left(x\right),{\mu }_A\left(x\right)\right)\left|x\right.\in X\right\},$$

(8)

$$\underset{\_}{Apr}\left(C_i\right)=\cup \left\{Y\in X/R\left(Y\right)\le C_i\right\},$$

(9)

$$\overline{Apr}\left(C_i\right)=\cup \left\{Y\in X/R\left(Y\right)\ge C_i\right\},$$

(10)

$$Bnd\left(C_i\right)=\cup \left\{Y\in X/R\left(Y\right)\ne C_i\right\},$$

(11)

$$\underset{\_}{Lim}\left(C_i\right)=\sqrt[N_L]{{\prod }_{i=1}^{N_L}Y\in }\underset{\_}{Apr}\left(C_i\right),$$

(12)

$$\overline{Lim}\left(C_i\right)=\sqrt[N_U]{{\prod }_{i=1}^{N_U}Y\in }\overline{Apr}\left(C_i\right),$$

(13)

$$RN\left(C_i\right)=⎡\underset{\_}{Lim}\left(C_i\right),\overline{Lim}\left(C_i\right)⎦,$$

(14)

$$\underset{\_}{Apr}\left(C_{i{\mu }_A}\right)=\cup \left\{Y\in X/\tilde{R}\left(Y\right)\le C_{i{\mu }_A}\right\},$$

(15)

$$\underset{\_}{Apr}\left(C_{i{n}_A}\right)=\cup \left\{Y\in X/\tilde{R}\left(Y\right)\le C_{i{n}_A}\right\},$$

(16)

$$\underset{\_}{Apr}\left(C_{i{v}_A}\right)=\cup \left\{Y\in X/\tilde{R}\left(Y\right)\le C_{i{v}_A}\right\},$$

(17)

$$\underset{\_}{Apr}\left(C_{i{\pi }_A}\right)=\cup \left\{Y\in X/\tilde{R}\left(Y\right)\le C_{i{\pi }_A}\right\},$$

(18)

$$\overline{Apr}\left(C_{i{\mu }_A}\right)=\cup \left\{Y\in X/\tilde{R}\left(Y\right)\le C_{i{\mu }_A}\right\},$$

(19)

$$\overline{Apr}\left(C_{i{n}_A}\right)=\cup \left\{Y\in X/\tilde{R}\left(Y\right)\le C_{i{n}_A}\right\},$$

(20)

$$\overline{Apr}\left(C_{i{v}_A}\right)=\cup \left\{Y\in X/\tilde{R}\left(Y\right)\le C_{i{v}_A}\right\},$$

(21)

$$\overline{Apr}\left(C_{i{\pi }_A}\right)=\cup \left\{Y\in X/\tilde{R}\left(Y\right)\le C_{i{\pi }_A}\right\},$$

(22)

$$\underset{\_}{Lim}\left(C_{i{\mu }_A}\right)=\frac{1}{N_{L{\mu }_A}}{\sum }_{i=1}^{N_{L{\mu }_A}}Y\in \underset{\_}{Apr}\left(C_{i{\mu }_A}\right),$$

(23)

$$\underset{\_}{Lim}\left(C_{i{n}_A}\right)=\frac{1}{N_{L{n}_A}}{\sum }_{i=1}^{N_{L{n}_A}}Y\in \underset{\_}{Apr}\left(C_{i{n}_A}\right),$$

(24)

$$\underset{\_}{Lim}\left(C_{i{v}_A}\right)=\frac{1}{N_{L{v}_A}}{\sum }_{i=1}^{N_{L{v}_A}}Y\in \underset{\_}{Apr}\left(C_{i{v}_A}\right),$$

(25)

$$\underset{\_}{Lim}\left(C_{i{\pi }_A}\right)=\frac{1}{N_{L{\pi }_A}}{\sum }_{i=1}^{N_{L{\pi }_A}}Y\in \underset{\_}{Apr}\left(C_{i{\pi }_A}\right),$$

(26)

$$\overline{Lim}\left(C_{i{\mu }_A}\right)=\frac{1}{N_{U{\mu }_A}}{\sum }_{i=1}^{N_{U{\mu }_A}}Y\in \overline{Apr}\left(C_{i{\mu }_A}\right),$$

(27)

$$\overline{Lim}\left(C_{i{n}_A}\right)=\frac{1}{N_{U{n}_A}}{\sum }_{i=1}^{N_{U{n}_A}}Y\in \overline{Apr}\left(C_{i{n}_A}\right),$$

(28)

$$\overline{Lim}\left(C_{i{v}_A}\right)=\frac{1}{N_{U{v}_A}}{\sum }_{i=1}^{N_{U{v}_A}}Y\in \overline{Apr}\left(C_{i{v}_A}\right),$$

(29)

$$\overline{Lim}\left(C_{i{\pi }_A}\right)=\frac{1}{N_{U{\pi }_A}}{\sum }_{i=1}^{N_{U{\pi }_A}}Y\in \overline{Apr}\left(C_{i{\pi }_A}\right),$$

(30)

$$\begin{array}{c}PFRN\left(\widetilde{C_i}\right)=\\ \left(⎡\underset{\_}{Lim}\left(C_{i{\mu }_A}\right),\overline{Lim}\left(C_{i{\mu }_A}\right)⎦,⎡\underset{\_}{Lim}\left(C_{i{n}_A}\right),\overline{Lim}\left(C_{i{n}_A}\right)⎦,⎡\underset{\_}{Lim}\left(C_{i{v}_A}\right),\overline{Lim}\left(C_{i{v}_A}\right)⎦,⎡\underset{\_}{Lim}\left(C_{i{\pi }_A}\right),\overline{Lim}\left(C_{i{\pi }_A}\right)⎦\right)\end{array}$$

(31)

The normalization of data is a necessary initial stage of data transformation since variables are measured on scales that differ significantly in values [33]. In this study, the critical value of the pair correlation coefficient so that it could be excluded from further analysis of the variable or such that the variable could be left in the analysis was assumed to be a pair correlation coefficient value equal to |0.7|. The analysis excluded agents of the right-hand side of the equation, whose correlation coefficient with the endogenous variable was lower than |0.7|, as well as the agents of the right-hand side that had a close relationship with each other above |0.7|.

$${\tilde{\mathrm{Z}}}_{\mathrm{k}}=\left[\begin{array}{cccccc}0& {\tilde{z}}_{12}& \cdots & & \cdots & {\tilde{z}}_{1n}\\ {\tilde{z}}_{21}& 0& \cdots & & \cdots & {\tilde{z}}_{2n}\\ ⋮& ⋮& \ddots & & \cdots & \cdots \\ ⋮& ⋮& ⋮& & \ddots & ⋮\\ {\tilde{z}}_{n1}& {\tilde{z}}_{n2}& \cdots & & \cdots & 0\end{array}\right],$$

(32)

$$\mathrm{P}\mathrm{F}\mathrm{R}\mathrm{N}\left(\widetilde{{\mathrm{C}}_{\mathrm{i}\mathrm{j}}}\right)=\left(\begin{array}{c}⎡\underset{\_}{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\mathrm{C}}_{\mathrm{i}\mathrm{j}{\mathsf{\mu }}_{{\tilde{\mathrm{z}}}_{\mathrm{i}\mathrm{j}}}}\right),\overline{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\mathrm{C}}_{\mathrm{i}{\mathrm{j}\mathsf{\mu }}_{{\tilde{\mathrm{z}}}_{\mathrm{i}\mathrm{j}}}}\right)⎦,⎡\underset{\_}{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\mathrm{C}}_{\mathrm{i}\mathrm{j}{\mathrm{n}}_{{\tilde{\mathrm{z}}}_{\mathrm{i}\mathrm{j}}}}\right),\overline{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\mathrm{C}}_{\mathrm{i}\mathrm{j}{\mathrm{n}}_{{\tilde{\mathrm{z}}}_{\mathrm{i}\mathrm{j}}}}\right)⎦,\\ ⎡\underset{\_}{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\mathrm{C}}_{\mathrm{i}\mathrm{j}{\mathrm{v}}_{{\tilde{\mathrm{z}}}_{\mathrm{i}\mathrm{j}}}}\right),\overline{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\mathrm{C}}_{\mathrm{i}{\mathrm{j}\mathrm{v}}_{{\tilde{\mathrm{z}}}_{\mathrm{i}\mathrm{j}}}}\right)⎦,⎡\underset{\_}{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\mathrm{C}}_{\mathrm{i}\mathrm{j}{\mathsf{\pi }}_{{\tilde{\mathrm{z}}}_{\mathrm{i}\mathrm{j}}}}\right),\overline{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\mathrm{C}}_{\mathrm{i}\mathrm{j}{\mathsf{\pi }}_{{\tilde{\mathrm{z}}}_{\mathrm{i}\mathrm{j}}}}\right)⎦\end{array}\right),$$

(33)

$${\tilde{\mathrm{k}}}_{\mathrm{j}}=\left\{\begin{array}{c}1\mathrm{j}=1\\ {\tilde{\mathrm{s}}}_{\mathrm{j}}+1\mathrm{j}>1\end{array}\right.,$$

(34)

$${\tilde{\mathrm{q}}}_{\mathrm{j}}=\left\{\begin{array}{c}1\mathrm{j}=1\\ \frac{{\tilde{\mathrm{k}}}_{\mathrm{j}-1}}{{\tilde{\mathrm{k}}}_{\mathrm{j}}}\mathrm{j}>1\end{array}\right.,$$

(35)

$${\tilde{\mathrm{w}}}_{\mathrm{j}}=\frac{{\mathrm{q}}_{\mathrm{j}}}{\sum _{\mathrm{k}=1}^{\mathrm{n}}{\mathrm{q}}_{\mathrm{k}}},$$

(36)

$$\begin{array}{c}{\mathrm{w}}_{\mathrm{j}\mathrm{m}\mathrm{i}\mathrm{n}}=\underset{\_}{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\mathrm{C}}_{\mathrm{i}\mathrm{j}{\mathsf{\mu }}_{{\tilde{\mathrm{z}}}_{\mathrm{i}\mathrm{j}}}}\right)+\frac{\underset{\_}{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\mathrm{C}}_{\mathrm{i}\mathrm{j}{\mathrm{n}}_{{\tilde{\mathrm{z}}}_{\mathrm{i}\mathrm{j}}}}\right)}{2}+\\ \frac{\left(1+\underset{\_}{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\mathrm{C}}_{\mathrm{i}\mathrm{j}{\mathsf{\mu }}_{{\tilde{\mathrm{z}}}_{\mathrm{i}\mathrm{j}}}}\right)+\frac{\underset{\_}{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\mathrm{C}}_{\mathrm{i}\mathrm{j}{\mathrm{n}}_{{\tilde{\mathrm{z}}}_{\mathrm{i}\mathrm{j}}}}\right)}{2}-\underset{\_}{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\mathrm{C}}_{\mathrm{i}\mathrm{j}{\mathrm{v}}_{{\tilde{\mathrm{z}}}_{\mathrm{i}\mathrm{j}}}}\right)+\frac{\underset{\_}{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\mathrm{C}}_{\mathrm{i}\mathrm{j}{\mathrm{n}}_{{\tilde{\mathrm{z}}}_{\mathrm{i}\mathrm{j}}}}\right)}{2}\right)}{2}\times \underset{\_}{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\mathrm{C}}_{\mathrm{i}\mathrm{j}{\mathsf{\pi }}_{{\tilde{\mathrm{z}}}_{\mathrm{i}\mathrm{j}}}}\right),\end{array}$$

(37)

$$\begin{array}{cc}\hfill {\mathrm{w}}_{\mathrm{j}\mathrm{m}\mathrm{a}\mathrm{x}}=\overline{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\mathrm{C}}_{\mathrm{i}\mathrm{j}{\mathsf{\mu }}_{{\tilde{\mathrm{z}}}_{\mathrm{i}\mathrm{j}}}}\right)& +\frac{\overline{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\mathrm{C}}_{\mathrm{i}\mathrm{j}{\mathrm{n}}_{{\tilde{\mathrm{z}}}_{\mathrm{i}\mathrm{j}}}}\right)}{2}\hfill \\ & +\frac{\left(1+\overline{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\mathrm{C}}_{\mathrm{i}\mathrm{j}{\mathsf{\mu }}_{{\tilde{\mathrm{z}}}_{\mathrm{i}\mathrm{j}}}}\right)+\frac{\overline{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\mathrm{C}}_{\mathrm{i}\mathrm{j}{\mathrm{n}}_{{\tilde{\mathrm{z}}}_{\mathrm{i}\mathrm{j}}}}\right)}{2}-\overline{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\mathrm{C}}_{\mathrm{i}\mathrm{j}{\mathrm{v}}_{{\tilde{\mathrm{z}}}_{\mathrm{i}\mathrm{j}}}}\right)+\frac{\overline{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\mathrm{C}}_{\mathrm{i}\mathrm{j}{\mathrm{n}}_{{\tilde{\mathrm{z}}}_{\mathrm{i}\mathrm{j}}}}\right)}{2}\right)}{2}\hfill \\ & \times \overline{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\mathrm{C}}_{\mathrm{i}\mathrm{j}{\mathsf{\pi }}_{{\tilde{\mathrm{z}}}_{\mathrm{i}\mathrm{j}}}}\right)\hfill \end{array}$$

(38)

$${\mathrm{w}}_{\mathrm{j}}=\frac{\left({\mathrm{w}}_{\mathrm{j} \mathrm{m}\mathrm{i}\mathrm{n}}+{\mathrm{w}}_{\mathrm{j} \mathrm{m}\mathrm{a}\mathrm{x}}\right)}{2},$$

(39)

$${\tilde{\mathrm{X}}}_{\mathrm{i}\mathrm{j}}=\begin{array}{c}{\mathrm{A}}_1\\ {\mathrm{A}}_2\\ {\mathrm{A}}_3\\ ⋮\\ {\mathrm{A}}_{\mathrm{m}}\end{array}\left[\begin{array}{ccccc}{\mathrm{x}}_{11}& {\mathrm{x}}_{12}& {\mathrm{x}}_{13}& \dots & {\mathrm{x}}_{1\mathrm{n}}\\ {\mathrm{x}}_{21}& {\mathrm{x}}_{22}& {\mathrm{x}}_{23}& \dots & {\mathrm{x}}_{2\mathrm{n}}\\ {\mathrm{x}}_{31}& {\mathrm{x}}_{32}& {\mathrm{x}}_{33}& \dots & {\mathrm{x}}_{3\mathrm{n}}\\ ⋮& ⋮& \ddots & \dots & ⋮\\ {\mathrm{x}}_{\mathrm{m}1}& {\mathrm{x}}_{\mathrm{m}2}& {\mathrm{x}}_{\mathrm{m}3}& \dots & {\mathrm{x}}_{\mathrm{m}\mathrm{n}}\end{array}\right],$$

(40)

$$\mathrm{P}\mathrm{F}\mathrm{R}\mathrm{N}\left({\tilde{\mathrm{X}}}_{\mathrm{i}\mathrm{j}}\right)=\left(\begin{array}{c}⎡\underset{\_}{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\tilde{\mathrm{X}}}_{\mathrm{i}\mathrm{j}{\mathsf{\mu }}_{{\tilde{\mathrm{x}}}_{\mathrm{i}\mathrm{j}}}}\right),\overline{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\tilde{\mathrm{X}}}_{\mathrm{i}\mathrm{j}{\mathsf{\mu }}_{{\tilde{\mathrm{x}}}_{\mathrm{i}\mathrm{j}}}}\right)⎦,⎡\underset{\_}{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\tilde{\mathrm{X}}}_{\mathrm{i}\mathrm{j}{\mathrm{n}}_{{\tilde{\mathrm{x}}}_{\mathrm{i}\mathrm{j}}}}\right),\overline{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\tilde{\mathrm{X}}}_{\mathrm{i}\mathrm{j}{\mathrm{n}}_{{\tilde{\mathrm{x}}}_{\mathrm{i}\mathrm{j}}}}\right)⎦,\\ ⎡\underset{\_}{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\tilde{\mathrm{X}}}_{\mathrm{i}\mathrm{j}{\mathrm{v}}_{{\tilde{\mathrm{x}}}_{\mathrm{i}\mathrm{j}}}}\right),\overline{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\tilde{\mathrm{X}}}_{\mathrm{i}\mathrm{j}{\mathrm{v}}_{{\tilde{\mathrm{x}}}_{\mathrm{i}\mathrm{j}}}}\right)⎦,⎡\underset{\_}{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\tilde{\mathrm{X}}}_{\mathrm{i}\mathrm{j}{\mathsf{\pi }}_{{\tilde{\mathrm{x}}}_{\mathrm{i}\mathrm{j}}}}\right),\overline{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\tilde{\mathrm{X}}}_{\mathrm{i}\mathrm{j}{\mathsf{\pi }}_{{\tilde{\mathrm{x}}}_{\mathrm{i}\mathrm{j}}}}\right)⎦\end{array}\right).$$

(41)

Reducing the structural form of the picture fuzzy rough sets of the model consisted of obtaining equations in which the endogenous variables on the left side of the equations were expressed in terms of all the exogenous variables and lagged endogenous variables, i.e., the transition from the structural form of the model to the reduced form consisted of transforming it such that no endogenous variables remained on the right side [34].

Given the completed procedure when normalizing the values of the exogenous and endogenous variables, it was necessary to return from the coefficients of each model equation that were calculated on the normalized data array to the coefficients corresponding to the actual data [35,36].

$${\tilde{\mathrm{r}}}_{\mathrm{i}\mathrm{j}}=\frac{\underset{\_}{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\tilde{\mathrm{X}}}_{\mathrm{i}\mathrm{j}{\mathsf{\mu }}_{{\tilde{\mathrm{x}}}_{\mathrm{i}\mathrm{j}}}}\right)}{\mathrm{m}\mathrm{a}\mathrm{x}{\tilde{\mathrm{X}}}_{\mathrm{i}}},\dots ,\frac{\overline{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\tilde{\mathrm{X}}}_{\mathrm{i}\mathrm{j}{\mathsf{\pi }}_{{\tilde{\mathrm{x}}}_{\mathrm{i}\mathrm{j}}}}\right)}{\mathrm{m}\mathrm{a}\mathrm{x}{\tilde{\mathrm{X}}}_{\mathrm{i}}},$$

(42)

$${\tilde{\mathrm{v}}}_{\mathrm{i}\mathrm{j}}={\mathrm{w}}_{\mathrm{j}}\times \underset{\_}{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\tilde{\mathrm{r}}}_{\mathrm{i}\mathrm{j}{\mathsf{\mu }}_{{\tilde{\mathrm{x}}}_{\mathrm{i}\mathrm{j}}}}\right),\dots ,{\mathrm{w}}_{\mathrm{j}}\times \overline{\mathrm{L}\mathrm{i}\mathrm{m}}\left({\tilde{\mathrm{r}}}_{\mathrm{i}\mathrm{j}{\mathsf{\pi }}_{{\tilde{\mathrm{x}}}_{\mathrm{i}\mathrm{j}}}}\right),$$

(43)

$${\mathrm{Q}}_{\mathrm{i}}={\sum }_{\mathrm{j}=1}^{\mathrm{t}}{\mathrm{v}}_{\mathrm{i}\mathrm{j}\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t}}+\frac{{\mathrm{R}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\sum _{\mathrm{i}=1}^{\mathrm{m}}\sum _{\mathrm{j}=\mathrm{t}+1}^{\mathrm{n}}{\mathrm{v}}_{\mathrm{i}\mathrm{j}\mathrm{n}\mathrm{o}\mathrm{n}-\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t}}}{\sum _{\mathrm{j}=\mathrm{t}+1}^{\mathrm{n}}{\mathrm{v}}_{\mathrm{i}\mathrm{j}\mathrm{n}\mathrm{o}\mathrm{n}-\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t}}\sum _{\mathrm{i}=1}^{\mathrm{m}}\frac{{\mathrm{R}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}{\sum _{\mathrm{j}=\mathrm{t}+1}^{\mathrm{n}}{\mathrm{v}}_{\mathrm{i}\mathrm{j}\mathrm{n}\mathrm{o}\mathrm{n}-\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t}}}},$$

(44)

$${\mathrm{U}}_{\mathrm{i}}=\frac{{\mathrm{Q}}_{\mathrm{i}}}{{\mathrm{Q}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}\times 100\mathrm{\%}.$$

(45)

The authors considered two additional approaches to extend the proposed explanation of the authors’ model.

 1.

Carbon Policy and International Companies.

The work of [37] analyzed carbon policies in the US, China, and Nigeria using a dynamic stochastic general equilibrium model. Their findings highlighted the following potential impacts of carbon policies on international companies:

–

Increased production costs: Carbon pricing mechanisms, such as carbon taxes or emissions trading schemes, can increase the cost of production for companies that rely heavily on fossil fuels. This can lead to higher prices for consumers and reduced competitiveness in international markets.

–

Investment in clean technologies: Carbon policies can incentivize companies to invest in clean technologies and renewable energy sources. This can lead to long-term cost savings and improved environmental performance.

–

Changes in global trade patterns: Carbon policies can influence global trade patterns by making it more expensive to produce and export goods from countries with high carbon emissions. This can create opportunities for companies in countries with lower emissions.

 2.

Artificial Intelligence and International Companies.

The research of [38] provided a comprehensive review of the application of artificial intelligence (AI) in the shipping industry. Their findings suggest that AI can play a significant role in improving the efficiency and sustainability of international companies via the following avenues:

–

Optimizing logistics and transportation: AI can be used to optimize shipping routes, reduce fuel consumption, and improve delivery times. This can lead to significant cost savings and reduced carbon emissions.

–

Predictive maintenance: AI can be used to predict equipment failures and schedule maintenance accordingly. This can prevent costly breakdowns and improve the overall efficiency of operations.

–

Demand forecasting: AI can be used to forecast demand for goods and services, thereby allowing companies to adjust their production and inventory levels accordingly. This can reduce waste and improve resource utilization.

4. Results

An analysis of the tightness of the relationship of endogenous variables with each other and on the tightness of the relationship of endogenous and exogenous variables with each other, as well as on exogenous variables with each other at a critical level of tightness of the relationship of more than |0.7|, revealed the variables of the right-hand sides of the equations (

Table 2. Criteria table.

Endogenous Variables	Exogenous Variables
The company’s profit in t year (i.e., the money that remained in the company at the end of the reporting period after all expenses and taxes were paid and were distributed among the shareholders in the form of dividends), in RUB billion.	The number of integration solutions of the company in t year (i.e., the number of integrations of the company with other services/platforms made in a year, including those where the company developed the product or implemented its existing product), in pcs.
The company’s revenue in t year (i.e., the total amount of funds received from the sale of all or part of the products, services, and works produced for the year), in RUB billion.	The Central Bank of Russia interest rate in t year (i.e., the market value of shares directly depends on the interest rate of the Central Bank of Russia since the lower the rate, the higher the growth of consumption and investment, and vice versa), in % per annum.
The company’s estimated value in t year (i.e., the valuation of the company’s value was determined by taking into account all the sources of its financing, such as debt obligations, preferred shares, ordinary shares, etc.), in RUB billion.	The company expenses in t year (i.e., the company’s day-to-day costs for doing business and producing products and services), in RUB billion.
The price of the company’s shares in t year (i.e., the price per share from the number of sold shares of the company), in RUB/unit.	Inflation in t year (i.e., the percentage of inflation in Russia for the year), in % per year.
The total investments in the share capital in t year, in % of the total share capital of companies on the market.	The main part of investment project costs in t year (i.e., the capital expenditures intended for investing in companies, such as the cost of purchasing fixed assets, which can range from, for example, buildings, equipment, technologies, etc.), in RUB billion.
The search engine market share in t year owned by the company, in %.	The number of competitors in t year (i.e., other TNCs and major competitors of the company), in digits.
The share of employees in the company compared against all of the employees on the market, in %.	The number of employees of the company in t year, in digits.
The total company asset share compared against all of the companies on the market, in %.	The value of the company’s assets in t year (i.e., the value of the company’s property and cash, including property and other rights that have a monetary value), in RUB billion.

).

An approach to model development based on the use of the following endogenous and exogenous variables can provide an opportunity for analyzing and considering the consequences of changes in feedback in the systems of which they are a part: bulk storage (B), dynamic line (DL), phasor measurement unit (P), and flexible energy (F).

Table 3. Picture fuzzy numbers.

Scales for Criteria	Picture Fuzzy Numbers
	(${\mathit{y}}_{\mathit{t}}^1$)	(${\mathit{y}}_{\mathit{t}}^2$)	(${\mathit{y}}_{\mathit{t}}^3$)
Very low (VL)	0.1	0.1	0.5
Low (L)	0.2	0.2	0.4
Middle (M)	0.3	0.3	0.3
High (H)	0.6	0.2	0.2
Very High (VH)	0.8	0.1	0.1

presents the pairwise correlation coefficients of endogenous and exogenous variables, and it also includes the following: the search engine market share owned by the company in t year, which depends on the company’s profits in t year ($y_t^1$); the company’s pods in t year ($y_t^2$), and the prices of the company’s value in t year ($y_t^3$).

In general, based on the results of the constructed model, it can be concluded that the described modeling approach can assess the impact of factors of both internal and external environmental factors on the resulting indicators of an international company. The practical aspects of a company’s activities are consistent with the need to assess the impact of economic, social, technological, and environmental factors on a company’s business goals. Within the framework of the proposed model, it is quite possible to assess the impact of such factors on the company’s target indicators, both in aggregate and for each group of indicators (

Table 4. Linguistic evaluations.

	C1			C2			C3			C4			C5
	DS1	DS2	DS3	DS1	DS2	DS3	DS1	DS2	DS3	DS1	DS2	DS3	DS1	DS2	DS3
Research and Development (Criterion 1)	-	-	-	H	H	M	M	L	L	VH	H	M	H	L	M
Commercialization (Criterion 2)	M	M	VH	-	-	-	L	L	H	H	VL	VL	VL	L	L
Cost (Criterion 3)	H	H	M	H	VH	H	-	-	-	M	VL	VL	L	M	M
Operational issues (Criterion 4)	M	L	M	H	H	VH	VH	VH	H	-	-	-	VH	H	M
Functionality (Criterion 5)	H	H	L	H	VH	M	H	H	VH	L	VL	M	-	-	-

and

Table 5. Decisions matrix.

Decision Maker 1
	D1				D2				D3				D4				D5
	µ	η	ν	π	µ	η	ν	π	µ	η	ν	π	µ	η	ν	Π	µ	η	ν	π
C1	0	0	0	0	0.3	0.3	0.3	0	0.3	0.3	0.3	0.1	0.8	0.3	0.3	0.3	0.6	0.2	0.2	0
C2	0.3	0.3	0.3	0.1	0.6	0.2	0.2	0	0.2	0.3	0.3	0.3	0.6	0.6	0.2	0.2	0.1	0.3	0.3	0.3
C3	0.6	0.2	0.2	0	0.3	0.3	0.3	0	0	0.6	0.2	0.2	0.3	0.3	0.3	0.3	0.2	0.6	0.2	0.2
C4	0.3	0.3	0.3	0.1	0.6	0.2	0.2	0	0.8	0.3	0.3	0.3	0	0.6	0.2	0.2	0.8	0.3	0.3	0.3
C5	0.6	0.2	0.2	0	0.6	0.2	0.2	0	0.6	0.6	0.2	0.2	0.2	0.2	0.4	0.2	0	0.6	0.2	0.2
Decision Maker 2
	D1				D2				D3				D4				D5
	µ	η	ν	π	µ	η	ν	π	µ	η	ν	π	µ	η	ν	π	µ	η	ν	π
C1	0	0	0	0	0.6	0.3	0.3	0.3	0.2	0.3	0.3	0.3	0.6	0.2	0.2	0	0.2		0.6	0.2
C2	0.3	0.3	0.3	0.3	0	0.6	0.2	0.2		0.6	0.2	0.2	0.1	0.1	0.5	0.3	0.2	0	0.3	0.3
C3	0.6	0.6	0.2	0.2	0.8	0.3	0.3	0.3	0	0.3	0.3	0.3		0.6	0.2	0.3	0.3	0.8	0.2	0.2
C4	0.2	0.3	0.3	0.3	0.6	0.6	0.2	0.2	0.8	0.2	0.2	0.2	0	0.3	0.3	0	0.6	0.2	0.2	0
C5	0.6	0.6	0.2	0.2	0.8	0.1	0.1	0	0.6	0.2	0.2	0	0.8	0.2	0.2	0.3	0	0	0	0
Decision Maker 3
	D1				D2				D3				D4				D5
	µ	η	ν	π	µ	η	ν	π	µ	η	ν	π	µ	η	ν	π	µ	η	ν	π
C1	0	0	0	0	0.3	0.3	0.3	0.1		0.6	0.2	0.2	0.3	0.3	0.3	0.1	0.3	0.3	0.3	0.1
C2	0.8	0.1	0.1	0	0	0	0	0	0	0.3	0.3	0	0.1	0.1	0.5	0.3	0.2		0.6	0.2
C3	0.6	0.2	0.3		0.6	0.2	0.2	0	0.8	0.2	0.2	0		0.6	0.2	0.3	0.3	0	0.3	0.3
C4	0.3	0.3	0.3	0	0.3	0.3	0.1	0	0.6	0.2	0.2	0	0	0.3	0.3	0	0.3	0.8	0.2	0.2
C5	0.2	0.2	0.4	0.8	0.2	0.2	0.3	0.1	0.8	0.1	0.1	0	0.8	0.2	0.2	0.1	0	0	0	0

).

The proposed model also allows one to evaluate the mutual influence of target indicators. The range of use in picture fuzzy rough sets is extensive. This study used modeling to analyze the impact of the internal and external environmental factors on the resulting indicators. The defuzzified and stable data are shown in

Table 6. Defuzzified matrix.

	D1	D2	D3	D4	D5
D1	0.00	0.34	0.00	0.18	0.22
D2	0.34	0.37	0.26	0.00	0.20
D3	0.34	0.00	0.18	0.22	0.00
D4	0.37	0.26	0.00	0.20	0.20
D5	0.21	0.26	0.35	0.18	0.00

and

Table 7. Stable matrix.

	D1	D2	D3	D4	D5
D1	0.20	0.34	0.00	0.18	0.22
D2	0.24	0.37	0.26	0.00	0.20
D3	0.34	0.00	0.18	0.18	0.00
D4	0.37	0.26	0.00	0.19	0.19
D5	0.26	0.35	0.18	0.17	0.17

, respectively.

A set of indicators for assessing the state of socio-economic and ecological systems in the Arctic and regular assessments that track progress toward sustainable development of the Arctic territory can be used within the framework of the considered picture fuzzy rough sets. The environmental sphere can be assessed using the indicator emissions of pollutants into the atmospheric air from stationary and mobile (i.e., automobile transport) sources. The economic sphere can be estimated using the following indicators: the gross regional product; the volume of cargo transportation by road, rail, and air transport; and the volume of inter-port cargo transportation by sea (in terms of cargo sent and received). An indicator for assessing the social sphere is the average monthly monetary income of the population in the Arctic zone (

Table 8. Weighted decision matrix.

	B	F	DL	Ps
C1	(⎡0.07; 0.15⎦; ⎡0.05; 0.07⎦; ⎡0.05; 0.07⎦; ⎡0; 0.01⎦)	(⎡0.10; 0.10⎦; ⎡0.05; 0.15⎦; ⎡0.01; 0.05⎦; ⎡0; 0⎦)	(⎡0.05; 0.15⎦; ⎡0.05; 0.07⎦; ⎡0.05; 0.10⎦; ⎡0; 0.05⎦)	(⎡0.05; 0.07⎦; ⎡0.05; 0.07⎦; ⎡0.07; 0.10⎦; ⎡0.01; 0.05⎦)
C2	(⎡0.17; 0.13⎦; ⎡0.01; 0.05⎦; ⎡0.01; 0.05⎦; ⎡0; 0⎦)	(⎡0.17; 0.13⎦; ⎡0.01; 0.05⎦; ⎡0.01; 0.05⎦; ⎡0; 0⎦)	(⎡0.05; 0.08⎦; ⎡0.05; 0.08⎦; ⎡0.08; 0.11⎦; ⎡0.01; 0.05⎦)	(⎡0.01; 0.17⎦; ⎡0.01; 0.08⎦; ⎡0.05; 0.14⎦; ⎡0; 0.08⎦)
C3	(⎡0.07; 0.15⎦; ⎡0.05; 0.07⎦; ⎡0.05; 0.07⎦; ⎡0; 0.01⎦)	(⎡0.15; 0.10⎦; ⎡0.01; 0.05⎦; ⎡0.01; 0.05⎦; ⎡0; 0⎦)	(⎡0.05; 0.15⎦; ⎡0.05; 0.07⎦; ⎡0.05; 0.10⎦; ⎡0; 0.05⎦)	(⎡0.01; 0.05⎦; ⎡0.01; 0.05⎦; ⎡0.10; 0.11⎦; ⎡0.05; 0.07⎦)
C4	(⎡0.04; 0.14⎦; ⎡0.04; 0.07⎦; ⎡0.04; 0.09⎦; ⎡0; 0.04⎦)	(⎡0.14; 0.18⎦; ⎡0.01; 0.04⎦; ⎡0.01; 0.04⎦; ⎡0; 0⎦)	(⎡0.04; 0.07⎦; ⎡0.04; 0.07⎦; ⎡0.07; 0.09⎦; ⎡0.01; 0.04⎦)	(⎡0.04; 0.14⎦; ⎡0.04; 0.07⎦; ⎡0.04; 0.09⎦; ⎡0; 0.04⎦)
C5	(⎡0.06; 0.11⎦; ⎡0.04; 0.06⎦; ⎡0.04; 0.06⎦; ⎡0; 0.01⎦)	(⎡0.11; 0.16⎦; ⎡0.01; 0.04⎦; ⎡0.01; 0.04⎦; ⎡0; 0⎦)	(⎡0.04; 0.11⎦; ⎡0.04; 0.06⎦; ⎡0.04; 0.08⎦; ⎡0; 0.04⎦)	(⎡0.04; 0.06⎦; ⎡0.04; 0.06⎦; ⎡0.06; 0.08⎦; ⎡0.01; 0.04⎦)

).

Table 9. Defuzzified decision matrix.

	B	F	DL	P
D1	0.15	0.18	0.11	0.14
D2	0.23	0.16	0.12	0.09
D3	0.16	0.11	0.14	0.09
D4	0.16	0.11	0.14	0.14
D5	0.13	0.12	0.09	0.09

demonstrates that rapid environmental and social changes in the Arctic increase the need for understanding and for conducting the systematic discussion of various potential futures. For such purposes, the analyzed model may well be suitable. A fundamental problem in the Arctic is the complex dynamics of multiple drivers of change with feedback loops that can accelerate the pace of changes in the following set of indicators used for assessing the state of socio-economic and ecological systems in the Arctic: bulk storage, flexible energy, dynamic lines, and phasor measurement units.

The processes of modeling the company’s internal and external environmental factors are usually considered from the point of view of constructing nonlinear adaptive models with an assessment of the risks and consequences of the decisions made. Modern agent-based models take into account, first of all, innovative research models and strategies. Emerging technological innovations often lead to a realignment of the agent-based models of established companies, thus requiring them to incorporate new external knowledge into their internal activities. Established agent-based models are changing in response to the emergence of Industry 4.0.

Information system analysts widely use business process models in companies to represent complex business requirements and environmental constraints. This understanding is extracted from graphical processes models, as well as from production and business rules. A representative integrated modeling method allows you to improve the representation of such models by focusing primarily on the performance factor of the modeled system itself. Linking rules is superior to separate modeling in terms of understanding efficiency, productivity, perceived mental effort, and visual attention.

One of the most important problems faced by a company’s modeling practices is that the simulated systems are presented more from the technical side and do not have a social orientation. A company’s architecture frameworks are of interest from the point of view of social aspects—these are the soft aspects of the organization that lead to the organic development of the company.

5. Discussion: Carbon Emissions and AI in the Context of International Companies

This article proposes a valuable framework for understanding the complex relationship between carbon emissions, economic factors, and the performance of international companies. The researchers of this study recommend a discussion that attempts to gain a deeper understanding of the challenges and opportunities that lie ahead for international companies in the context of climate change and technological innovation. This discussion should delve deeper into this topic, and it should draw upon insights from two relevant approaches. The insights from the work of [37] and the research of [38] suggest that carbon emissions and AI are two important factors that can significantly impact the performance of international companies. While carbon policies may increase production costs in the short term, they can also incentivize investment in clean technologies and create opportunities for companies in countries with lower emissions. AI, on the other hand, can help companies optimize their operations, reduce their environmental impact, and improve their overall efficiency.

The authors of this study believe that further research could provide more evidence for the proposed model’s accuracy and generalizability, as well as allow for further refinement and improvement. Further research should perform the following:

–

Conduct empirical studies in different contexts: The current study focuses on international companies. It would be beneficial to test the model in other contexts, such as small- and medium-sized enterprises (SMEs), non-profit organizations, or specific industries. This would allow for a more comprehensive understanding of the model’s applicability and limitations.

–

Analyze specific case studies: In-depth case studies of individual companies could provide valuable insights into the proposed model’s strengths and weaknesses. This could involve comparing the model’s predictions with actual company data and then analyzing the reasons for any discrepancies.

–

Introduce additional control variables: The current model includes a range of factors that influence company performance. However, there may be other relevant variables that are not currently included. Further research could identify and incorporate these additional variables to improve the model’s accuracy.

–

Carry out additional regression, correlation, and variance analysis: Further types of analyses should be conducted as part of analyzing the reliability of the model.

–

Consider the impact of external shocks: The model currently focuses on the impact of factors within the company and its environment. However, external shocks, such as economic crises or natural disasters, can also significantly impact company performance. Further research could explore how the model can be adapted to account for these external factors.

–

Investigate the role of non-linear relationships: The current model assumes linear relationships between the variables. However, in reality, these relationships may be non-linear. Further research could explore the use of non-linear models to improve the model’s accuracy.

Further research could also consider the complex interplay between carbon emissions, AI, and the performance of international companies. This research should answer the following questions:

–

How can AI be used to develop more effective carbon mitigation strategies?

–

How can international companies adapt their business models to a low-carbon economy?

–

What are the ethical implications of using AI in the context of carbon emissions?

By addressing these questions, researchers can help international companies navigate the challenges and opportunities presented by a transition to a more sustainable future.

6. Conclusions

This paper widens the knowledge base on the problem of modeling the impact of internal and external environmental factors on the resulting indicators of a company as a whole. The research highlights the fact that there is an urgent need to develop modeling approaches. The proposed model offers a valuable tool for companies and policymakers to understand the complex interplay between internal and external factors, carbon emissions, and economic performance. By applying this model, companies can identify key areas for improvement and develop strategies to mitigate environmental impact while enhancing financial sustainability.

From the above, we can outline the direction of the further development of picture fuzzy rough sets. Through drawing upon the concept of picture fuzzy rough sets, it is recognized that achieving absolute similarity in most systems is unattainable. Therefore, the fundamental objective of employing picture fuzzy rough sets is to ensure that the model sufficiently represents the operations of the system being studied. To achieve this, it is essential to systematically enlarge the model. In other words, doing this will increase the number of endogenous and exogenous variables at each subsequent stage. The number of endogenous and exogenous variables can be increased at the expense of variables with high and low communication tightness.

The results of this paper have policy implications: government regulators and businesses can use the soft aspects of complex systems theory to understand organizations such that it leads to the organic development of a company (in terms of its communication, collaboration, culture, skills, and personal goal parameters). The development of a full-fledged methodology for picturing the fuzzy rough sets of the impact of factors on the target indicators of a production or territorial system will allow us to assess and overcome barriers that exist in real life, and it will also serve as a factor for the sustainable development of an analyzed system that is based on complex systems theory.

Further research is needed to refine the model and validate its accuracy in diverse contexts. Exploring the integration of AI and carbon mitigation strategies within the model framework could provide valuable insights for future research. Collaboration between researchers, businesses, and policymakers is crucial to address the challenges and opportunities presented by the transition to a more sustainable future.

The researchers of this study are committed to developing tools and insights that can help businesses and policymakers navigate the complexities of the modern world. The authors of this research believe that this model represents a significant step forward in our collective efforts to achieve a more sustainable future.