Navigating the green shift with innovative techniques in petrochemical emission control

Abstract

This analysis delves into the profound influence of the petrochemical sector on carbon emissions, highlighting the insufficient data that impedes the formulation of effective emission reduction strategies. By concentrating on the unique challenges within this industry, the study employs a sophisticated decision-making model to explore the complex interconnections between carbon emissions, mitigation approaches, and investment choices. The primary objectives include boosting energy efficiency, refining CO₂ reduction initiatives, and cutting associated costs. To navigate the intricacies of carbon footprint assessment, the research introduces a novel hybrid framework that merges scientific modeling with a code-based prototype to aid in strategic planning. The efficacy of this approach is validated by experts, demonstrating its versatility and adaptability through CNHS mapping, which enables the customization of emission reduction strategies across different scenarios.

Introduction

Carbon emissions, the release of greenhouse gases into the atmosphere, presents a formidable global challenge, disrupting the Earth’s climate equilibrium and impacting human health through air pollution. Recognized universally as an urgent issue¹, the primary culprits include unbridled population growth, industrialization, and escalating energy demands. Nations are actively investing in renewable energy and promoting energy conservation² to curb reliance on fossil fuels and mitigate carbon emissions. Addressing this challenge necessitates a nuanced understanding of its root causes, with economic growth playing a pivotal role. Investments crucial to GDP drive economic expansion, leading to heightened energy consumption and increased carbon emissions during industrial production³. Globalization further exacerbates the issue, compelling corporations to expand production capacities, resulting in heightened energy consumption and carbon emissions^4–6. Insufficient environmental consciousness intensifies carbon emissions, as profit-driven businesses often favor cost-effective fossil fuels over cleaner alternatives^7–9. This research makes a significant contribution by addressing the critical gap in comprehensive data and strategy development within the petrochemical sector’s impact on carbon emissions. By focusing on the unique challenges inherent in this industry, the study introduces an innovative hybrid framework that merges scientific modeling with a code-driven prototype, offering a sophisticated decision-making paradigm. This approach enhances energy efficiency, optimizes CO2 emission reductions, and minimizes associated costs. The efficacy of this methodology is demonstrated through expert validation and the application of CNHS mapping, showcasing its versatility and adaptability in providing tailored emission reduction strategies across diverse contexts. The manuscript proceeds with a literature review, methodology, analysis results, and concludes with discussions and conclusions.

Literature

The surge in global carbon emissions has sparked increased scholarly research, with a notable focus on the direct correlation between economic expansion and heightened carbon emissions (e.g.,¹⁰). Business investments, integral for economic growth, not only foster employment opportunities but also contribute to increased emissions, primarily through extensive energy consumption in enterprise Flaring and Venting^11–16. Globalization further compounds the issue, as multinational businesses invest abroad to meet diverse consumer demands, leading to increased production capacities and energy consumption^17–26. Bathrinath et al.²⁷ offered valuable insights for industrial managers on curbing carbon emissions within the petrochemical industry. Li et al.²⁸ introduced a technology selection framework that minimizes information loss, enhances group consensus, and offers a viewpoint for petrochemical companies seeking energy-saving and emission-reduction technologies. Wu et al.²⁹ proposed a comprehensive decision-making framework for sustainable supplier selection within the chemical industry. Akhtar et al.³⁰ explored a stochastic fuzzy multi-criteria group decision-making approach for sustainable vendor selection in the Indian petroleum refining sector. Studies emphasize the significant role of globalization in exacerbating carbon emissions, especially in G20 countries. Some scholars argue that globalization’s reduced sensitivity to environmental concerns drives increased global trade and economic growth but also results in drawbacks such as heightened energy demands and waste production^31–34. The importance of environmental awareness among individuals and businesses is stressed as a crucial factor in addressing this challenge^35,36. Financial considerations also contribute to increased carbon emissions, as businesses prefer fossil fuels over renewable sources due to cost disparities^37,38. Mitigating this issue requires enhancing the cost competitiveness of renewable energy investments through research and development, financial incentives, and government support^39–43.

Motivation

This study seeks to overcome the shortcomings in carbon emission reduction strategies^44–48 by replicating real-world conditions and integrating cutting-edge techniques. Current models are inadequate in managing sub-parametric values and intricate data dimensions, leading to the integration of bipolar fuzzy, multipolar neutrosophic assessments, hypersoft sets, and a neutrosophic framework. The suggested paradigm, which employs an Argand plane for parametric values and a unit circle for periodic data, effectively addresses the uncertainties in emission methodologies. This model links various parameters, offering a comprehensive framework for emission reduction in the petrochemical sector, reinforced by an inverse mapping for adaptive recovery and continuous progress monitoring.

Methodology

Addressing urgent carbon emissions, this study prioritizes criteria for efficient resource allocation, utilizing a mapping-based CNHSS to identify and propose cost-effective techniques for precise emission management within the petrochemical sector.

Advanced strategies and influential factors in petrochemical carbon emission reduction

This subsection delves into innovative methodologies, like CNHSS mapping, to mitigate carbon emissions in the petrochemical industry. Key contributors-feedstock, energy consumption, transportation, and flaring-are analyzed for effective reduction^49–52. Additionally, a comprehensive exploration of diverse influences on carbon emissions, including CO₂, methane, nitrous oxide, VOCs, particulate matter, and sulfur dioxide, underscores the complexity. A proposed framework integrates production volume, energy sources, technology, and regulations for quantifiable analysis, emphasizing the need for strategic interventions.

Algorithm

Step 1. To categorize the carbon emission factors, consider a set $R=\{r_1,r_2,r_3,...,r_n\}$ representing four different petrochemical industries, and $A=\{s_1,s_2,s_3,...,s_v\}$ as indicators of these carbon emission factors, each associated with parameters within sets $S_i$s’, where $S={\displaystyle \prod _{i=1}^v{S}_i}$. Daily reports denoted as “t” over time aid in analyzing and identifying carbon emission factors using a computational framework such as a CNHS. After significant evaluations at $\epsilon$th times, the CNHS set chart is configured as follows:

$$\begin{array}{c}\hfill z_S^{\epsilon }=z_p^{\epsilon }=\{r,⟨T^{\epsilon }p(r),I^{\epsilon }p(r),F^{\epsilon }p(r)⟩:r\in R,p\in S\}\end{array}$$ 1

where $T^{\epsilon }p(r)$, $I^{\epsilon }p(r)$, and $F^{\epsilon }p(r)$ represent degrees of effectiveness, uncertainty, and non-membership grades of carbon emission factors for i-th indicators and j-th methods respectively, $(\epsilon =1,2,3,...,t;k=1,2,3,...,|S|;j=1,2,3,...,n)$. The amalgamation of CNHS sets is utilized to collate comprehensive information.

Step 2. Consider a set $B=\{s_1^{\prime },s_2^{\prime },s_3^{\prime },...,s_w^{\prime }\}$ representing correlated parameters for A, associated with sets $S^{\prime }i$s’, where $S^{\prime }={\displaystyle \prod _{i=1}^w{S}_i^{\prime }}$ and compute a CNHS set (with weights derived from expert assessments of the significance of $\epsilon$ fundamental indicators on a daily basis).

Step 3. Develop a mapping based on characteristics as follows: $\vartheta :R\to R$ and $\sigma :S\to S^{\prime }$ characterized by

$$\begin{array}{c}\hfill \vartheta (r_j)=r_j,\sigma (p_k)=(p_{\prime }^{\prime }),\end{array}$$ 2

where $(k=1,2,3,...,|S|;k^{\prime }=1,2,3,...,|S^{\prime }|;j=1,2,3,...,n)$ based on the relationship between primary and secondary indicators. Consider the CNHS-mapping $\mho =(\vartheta ,\sigma ):CNHS(R)\to CNHS(R)$ defined as follows:

$$\begin{array}{cc}\hfill T_{\mho (z_S)}(p^{\prime })(r)=& |T_{p^{\prime }{k}^{\prime }}|\left\{\begin{array}{cc}{max}_{r\in {\vartheta }^{-1}(r)}\left({max}_{p\in {\sigma }^{-1}(p^{\prime })\cap S},T_{z_S}\right)(r),\hfill & \text{if}{\vartheta }^{-1}(r)\ne \mathrm{\varnothing },{\sigma }^{-1}(p^{\prime })\cap S\ne \mathrm{\varnothing },\hfill \\ 0,\hfill & \text{otherwise.}\hfill \end{array}\right)\hfill \end{array}$$ 3

$$\begin{array}{cc}\hfill I_{\mho (z_S)}(p^{\prime })(r)=& |I_{p^{\prime }{k}^{\prime }}|\left\{\begin{array}{cc}{min}_{r\in {\vartheta }^{-1}(r)}\left({min}_{p\in {\sigma }^{-1}(p^{\prime })\cap S},I_{z_S},(r)\right),\hfill & \text{if}{\vartheta }^{-1}(r)\ne \mathrm{\varnothing },{\sigma }^{-1}(p^{\prime })\cap S\ne \mathrm{\varnothing },\hfill \\ 1,\hfill & \text{otherwise.}\hfill \end{array}\right)\hfill \end{array}$$ 4

$$\begin{array}{cc}\hfill F_{\mho (z_S)}(p^{\prime })(r)=& |F_{p^{\prime }{k}^{\prime }}|\left\{\begin{array}{cc}{min}_{r\in {\vartheta }^{-1}(r)}\left({min}_{p\in {\sigma }^{-1}(p^{\prime })\cap S},F_{z_S},(r)\right),\hfill & \text{if}{\vartheta }^{-1}(r)\ne \mathrm{\varnothing },{\sigma }^{-1}(p^{\prime })\cap S\ne \mathrm{\varnothing },\hfill \\ 1,\hfill & \text{otherwise.}\hfill \end{array}\right)\hfill \end{array}$$ 5

where $T_{p_{\prime }^{\prime }}$, $I_{p_{\prime }^{\prime }}$, and $F_{p_{\prime }^{\prime }}$ are weights derived from $z_{S^{\prime }}$ that are interconnected. Obtain the $\bigsqcup z^{\epsilon }S$ image using the defined mapping $\mho$, which can be constructed as $z_{\prime }^{\prime }$.

Step 4.

To obtain weighted aggregation values, convert the CNHS set to the Neutrosophic Hypersoft set using the formula:

$$\begin{array}{cc}\hfill T_{\mho (z_S)}(p^{\prime })(r)=& w_1{\mu }_{z^{\prime }(r)}(p^{\prime })+w_2\left(\frac{1}{2\pi }\right){\omega }_{z^{\prime }}(p^{\prime })(r),\hfill \end{array}$$ 6

$$\begin{array}{cc}\hfill I_{\mho (z_S)}(p^{\prime })(r)=& w_1{\mu }_{z^{\prime }}(p^{\prime })(r)+w_2\left(\frac{1}{2\pi }\right){\omega }_{z^{\prime }}(p^{\prime })(r),\hfill \end{array}$$ 7

$$\begin{array}{cc}\hfill F_{\mho (z_S)}(p^{\prime })(r)=& w_1{\mu }_{z^{\prime }}(p^{\prime })(r)+w_2\left(\frac{1}{2\pi }\right){\omega }_{z^{\prime }}(r)(p^{\prime })\hfill \end{array}$$ 8

where ${\mu }_{z^{\prime }(s^{\prime })}(p)$ and ${\omega }_{z^{\prime }(p^{\prime })}(r)$ are the amplitude and phase terms in the CNHS set respectively, $T_{\mho (z_S)}(p^{\prime })(r)$, $I_{\mho (z_S)}(p^{\prime })(r)$, $F_{\mho (z_S)}(p^{\prime })(r)$ are the membership, indeterminacy, non membership functions in the Neutrosophic Hypersoft set respectively, where $w_1,w_2\in [0,1]$ are the weights for the amplitude terms (degrees of influence) and the phase terms (time of influence).

Step 5.

Compute the score function values for the achieved the carbon emission factors set denoted as $z_{\prime }^{\prime }$. Subsequently, determine the average score value associated with each relevant carbon emission factors using the following equation:

$$\begin{array}{c}\hfill \frac{1}{2}|T^{\epsilon }s(r)-2I^{\epsilon }s(r)-F_s^{\epsilon }(r)|.\end{array}$$ 9

Next, refer to Table 1 to ascertain the final assessment based on the calculated values.

Table 1.

Ranges of carbon emission reduction rechniques.

Carbon emission reduction rechniques	Various ranges within [0, 1]
Feedstock	[0.6, 1]
Energy consumption	[0.5, 0.6)
Transportation and distribution	(0.2, 0.5)
Flaring and venting	[0.1, 0.2]
No carbon emission reduction	[0, 0.1)

Step 6.

Consider a set of indications denoted as $B=\{s_1^{\prime },s_2^{\prime },s_3^{\prime },...,s_w^{\prime }\}$, representing relevant indicators of reduced carbon emission- techniques related issues. Here, $k={\displaystyle \prod _{i=1}^w|S^{\prime }i|}$, and $C=\{c_1,c_2,c_3,...,c_x\}$ signifies a collection of potential carbon emission reduction techniques. Formulate ${\chi }_{S^{\prime }}$, where $\chi$ represents a function from the carbon emission reduction techniques set $S^{\prime }$ to P(C), signifying the experts’ recommendations corresponding to the most appropriate carbon emission reduction techniques in response to the identified emission-related indications.

Step 7.

Utilizing a defined methodology (e.g., from a predetermined set of procedures), derive $R_C^1$ by employing a min-max composition approach involving $z_{\prime }^{\prime }$ and ${\chi }_{S^{\prime }}$.

Step 8.

Opt for carbon emission reduction techniques that offer more significant benefits while minimizing adverse effects on the environment. The petrochemical industry emission reduction progress history necessitates the following steps for assessment and management. This revised version adapts the content to focus on carbon emission reduction techniques in the petrochemical industry, modifying terminologies, and preserving the structure and order of the original paragraph.

Step 9.

Define a distinct set of generalised mappings; ${\vartheta }^{\prime }:R^{q-1}\to R^q$ and ${\sigma }^{\prime }:C^{q-1}\to C^q$ such that

$$\begin{array}{c}\hfill {\vartheta }^{\prime }(r_j)=r_j\end{array}$$ 10

and

$$\begin{array}{c}\hfill {\sigma }^{\prime }(c_x)=c_x.\end{array}$$ 11

Then CNHS-mapping is defined in the form of ${\mho }^{\prime }=({\vartheta }^{\prime },{\sigma }^{\prime }):R_C^{q-1}\to R_C^q$ and can be evaluated as:

$$\begin{array}{cc}\hfill R_C^q=& {\mho }^{\prime }(R_C^{q-1})(c)(r)\hfill \\ \hfill =& \frac{1}{q}\left\{\begin{array}{cc}\underset{\pi \in {\vartheta }^{\prime -1}(r)}{⨆}\left(\underset{\vartheta \in {\sigma }^{\prime -1}(c)\cap C}{⨆},R_C^{q-1}\right)(\pi ),\hfill & \text{if}{\vartheta }^{\prime -1}(r)\ne \mathrm{\varnothing },{\sigma }^{\prime -1}(c)\cap C\ne \mathrm{\varnothing },\hfill \\ 0,\hfill & \text{otherwise.}\hfill \end{array}\right)\hfill \end{array}$$ 12

where $q=2,3,4...$ is the number of episodes and $c\in {\sigma }^{\prime }(C)\subseteq C$, $r\in R^q$, $\pi \in R^{q-1}$, $\vartheta \in {(C)}^{q-1}$.

Step 10. Continue the iterative process from Step 10 until the intended objectives concerning carbon emission reduction techniques are accomplished.

Proposed strategy for illustrating carbon emission factors and recommended reduction methods

This section proposes a specialized algorithm for petrochemical carbon emission factors, incorporating data input to generate actionable strategies and establish tracking tables (Table 2) and maps (Table 1), presenting a real-time data-driven methodology for emissions reduction through a Coding-Based Prototype (Figs. 1, 2, 3, 4, 5, 6, 7, 8).

Table 2.

Carbon emission reduction tactics and their day-to-day concentration.

Strategies	First day	Day two and day three	After day 3
High-Intensity Feedstock (HIF)	[0.72, 0.8)	[0.8,1)	$=1$
Moderate-Intensity Feedstock (MIF)	[0.75,0.82)	[0.82,0.87)	[0.87,0.92)
Low-Intensity Feedstock (LIF)	[0.59,0.65)	[0.65,0.69)	[0.69,0.74)
High-Efficiency Energy Consumption (HEEC)	[0.55,0.57)	[0.57,0.58)	[0.58,0.59)
Moderate-Efficiency Energy Consumption (MEEC)	[0.51,0.53)	[0.53,0.54)	[0.54,0.55)
Low-Efficiency Energy Consumption (LEEC)	[0.49,0.50)	[0.50, 0.501)	[0.501,0.51)
High-Performance Transportation and Distribution (HPTD)	[0.2,0.3)	[0.3,0.4)	[0.4,0.49)
Moderate-Performance Transportation and Distribution (MPTD)	[0.23,0.25)	[0.25,0.27)	[0.27,0.4)
Low-Performance Transportation and Distribution (LPTD)	[0.22,0.23)	[0.23,0.235)	[0.235,0.37)
High-Effectiveness Flaring and Venting (HEFV)	[0.1,0.15)	[0.15,0.17)	[0.17,0.176)
Moderate-Effectiveness Flaring and Venting (MEFV)	[0.12,0.13)	[0.13,0.15)	[0.15,0.157)
Low-Effectiveness Flaring and Venting (LEFV)	[0.123,0.125)	[0.125,0.129)	[0.129,0.189)
No Carbon Emission Reduction (NCER)	[0.00,0.01)	[0.01,0.06)	[0.06,0.08)

Fig. 1.

CFHS mapping: coding for petrochemical industry’s carbon emission reduction techniques.

Fig. 2.

CFHS mapping: coding for petrochemical industry’s carbon emission reduction techniques.

Fig. 3.

CFHS mapping: coding for petrochemical industry’s carbon emission reduction techniques.

Fig. 4.

CFHS mapping: coding for petrochemical industry’s carbon emission reduction techniques.

Fig. 5.

CFHS mapping: coding for petrochemical industry’s carbon emission reduction techniques.

Fig. 6.

CFHS mapping: coding for petrochemical industry’s carbon emission reduction techniques.

Fig. 7.

CFHS mapping: coding for petrochemical industry’s carbon emission reduction techniques.

Fig. 8.

CFHS mapping: coding for petrochemical industry’s carbon emission reduction techniques.

Step 1: Consider a set $E=\{r_1,r_2,r_3,r_4\}$ that represents four unique carbon emission sources within the petrochemical industry. Let $p_1=$Pressure, $p_2=$Temperature, and $p_3=$Gas Composition, denote various properties of emissions categorized within sets $P_1$, $P_2$, and $P_3$ respectively. Define $P_1=\{p_{11}=\text{Fluctuations},p_{12}=\text{Acidity}\}$, $P_2=\{p_{21}=\text{Vapour Presence}\}$, and $P_3=\{p_{31}=\text{Particulate Matter},p_{32}=\text{Chemical Composition Changes}\}$. Following a comprehensive assessment, experts evaluate the emission situation. Utilizing the expert-derived data $(\delta =1,2)$, develop a two-day emission chart $c^{\delta }P\in \text{CNHS}(E)$ for the initial and subsequent days represented as (Table 3) and (Table 4) correspondingly. These tables encapsulate the primary emission data categorized within CNHS based on defined emission attributes. Merge $z_S^1$ and $z_S^2$ using the CNHS-union operation. Table 5 exhibits the resulting CNHS $\bigsqcup c^{\delta }P$, where $0\le \theta \le 2\pi$.

Table 3.

$z_S^1$: First day report of all four petrochemical industry based on their influencing factors.

Factors/industries	$r_1$	$r_2$	$r_3$	$r_4$
$(s_{11},s_{21},s_{31})$	$(0.2e^{i0.4\theta },0.3e^{i0.6\theta },0.6e^{i0.1\theta })$	$(0.4e^{i0.7\theta },0.4e^{i0.7\theta },0.1e^{i0.9\theta })$	$(0.2e^{i0.5\theta },0.3e^{i0.4\theta },0.4e^{i0.7\theta })$	$(0.5e^{i0.1\theta },0.6e^{i0.4\theta },0.3e^{i0.8\theta })$
$(s_{11},s_{21},s_{32})$	$(0.3e^{i0.8\theta },0.1e^{i0.5\theta },0.3e^{i0.9\theta })$	$(0.2e^{i0.7\theta },0.4e^{i0.6\theta },0.2e^{i0.5\theta })$	$(0.6e^{i0.9\theta },0.3e^{i0.4\theta },0.4e^{i0.6\theta })$	$(0.2e^{i0.5\theta },0.7e^{i0.8\theta },0.4e^{i0.5\theta })$
$(s_{12},s_{21},s_{31})$	$(0.2e^{i0.6\theta },0.6e^{i0.6\theta },0.3e^{i0.6\theta })$	$(0.2e^{i0.7\theta },0.4e^{i0.2\theta },0.4e^{i0.8\theta })$	$(0.6e^{i0.4\theta },0.5e^{i0.9\theta },0.4e^{i0.7\theta })$	$(0.1e^{i0.5\theta },0.3e^{i0.8\theta },0.4e^{i0.7\theta })$
$(s_{12},s_{21},s_{32})$	$(0.5e^{i0.2\theta },0.6e^{i0.5\theta },0.4e^{i0.9\theta })$	$(0.2e^{i0.5\theta },0.1e^{i0.5\theta },0.9e^{i0.2\theta })$	$(0.5e^{i0.4\theta },0.8e^{i0.2\theta },0.4e^{i0.5\theta })$	$(0.8e^{i0.3\theta },0.2e^{i0.5\theta },0.5e^{i0.4\theta })$

Table 4.

$z_S^2$: 2nd day report of all four petrochemical industry based on their influencing factors.

Factors/industries	$r_1$	$r_2$	$r_3$	$r_4$
$(s_{11},s_{21},s_{31})$	$(0.2e^{i0.5\theta },0.6e^{i0.4\theta },0.5e^{i0.5\theta })$	$(0.6e^{i0.4\theta },0.2e^{i0.4\theta },0.6e^{i0.2\theta })$	$(0.7e^{i0.1\theta },0.5e^{i0.7\theta },0.8e^{i0.2\theta })$	$(0.4e^{i0.8\theta },0.2e^{i0.6\theta },0.7e^{i0.5\theta })$
$(s_{11},s_{21},s_{32})$	$(0.5e^{i0.3\theta },0.1e^{i0.7\theta },0.2e^{i0.5\theta })$	$(0.6e^{i0.2\theta },0.4e^{i0.7\theta },0.6e^{i0.9\theta })$	$(0.4e^{i0.5\theta },0.3e^{i0.4\theta },0.7e^{i0.6\theta })$	$(0.5e^{i0.8\theta },0.5e^{i0.6\theta },0.7e^{i0.3\theta })$
$(s_{12},s_{21},s_{31})$	$(0.6e^{i0.9\theta },0.1e^{i0.5\theta },0.5e^{i0.6\theta })$	$(0.1e^{i0.5\theta },0.7e^{i0.3\theta },0.5e^{i0.3\theta })$	$(0.5e^{i0.6\theta },0.4e^{i0.2\theta },0.5e^{i0.5\theta })$	$(0.1e^{i0.7\theta },0.3e^{i0.5\theta },0.5e^{i0.7\theta })$
$(s_{12},s_{21},s_{32})$	$(0.4e^{i0.8\theta },0.2e^{i0.6\theta },0.4e^{i0.7\theta })$	$(0.2e^{i0.8\theta },0.3e^{i0.6\theta },0.4e^{i0.7\theta })$	$(0.5e^{i0.7\theta },0.1e^{i0.6\theta },0.3e^{i0.8\theta })$	$(0.4e^{i0.6\theta },0.1e^{i0.6\theta },0.2e^{i0.4\theta })$

Table 5.

$\bigsqcup z_S^{\epsilon }$: CNHS union of $z_S^1$ and $z_S^2$.

Factors/industries	$r_1$	$r_2$	$r_3$	$r_4$
$(s_{11},s_{21},s_{31})$	$(0.1e^{i0.7\theta },0.4e^{i0.9\theta },0.3e^{i0.7\theta })$	$(0.5e^{i0.6\theta },0.2e^{i0.8\theta },0.3e^{i0.6\theta })$	$(0.1e^{i0.9\theta },0.4e^{i0.4\theta },0.6e^{i0.7\theta })$	$(0.2e^{i0.5\theta },0.3e^{i0.5\theta },0.7e^{i0.4\theta })$
$(s_{11},s_{21},s_{32})$	$(0.3e^{i0.5\theta },0.5e^{i0.1\theta },0.2e^{i0.6\theta })$	$(0.3e^{i0.9\theta },0.2e^{i0.5\theta },0.2e^{i0.7\theta })$	$(0.3e^{i0.7\theta },0.2e^{i0.5\theta },0.2e^{i0.6\theta })$	$(0.1e^{i0.3\theta },0.5e^{i0.3\theta },0.1e^{i0.2\theta })$
$(s_{12},s_{21},s_{31})$	$(0.6e^{i0.4\theta },0.3e^{i0.7\theta },0.2e^{i0.7\theta })$	$(0.4e^{i0.9\theta },0.5e^{i0.6\theta },0.6e^{i0.5\theta })$	$(0.7e^{i0.2\theta },0.5e^{i0.9\theta },0.3e^{i0.7\theta })$	$(0.4e^{i0.7\theta },0.3e^{i0.7\theta },0.9e^{i0.2\theta })$
$(s_{12},s_{21},s_{32})$	$(0.4e^{i0.5\theta },0.4e^{i0.7\theta },0.2e^{i0.5\theta })$	$(0.8e^{i0.3\theta },0.4e^{i0.7\theta },0.3e^{i0.6\theta })$	$(0.1e^{i0.5\theta },0.6e^{i0.1\theta },0.5e^{i0.i9\theta })$	$(0.1e^{i0.6\theta },0.3e^{i0.2\theta },0.5e^{i0.8\theta })$

Step 2.

Within the realm of emission factors in the petrochemical industry, various strategies are employed to mitigate environmental impact. Let $t_1^{\prime }=$Economic development, $t_2^{\prime }=$Industrial structure, $t_3^{\prime }=$Operational Risk, represent different factors of carbon emission in the petrochemical industry, each with distinct methodologies and operational frameworks. These techniques are organized within sets $T_1^{\prime },T_2^{\prime },T_3^{\prime }$, where $T_1^{\prime }=\{t_{11}^{\prime }=\text{Investment},t_{12}^{\prime }=\text{Gross Domestic Product (GDP) Contribution}\}$, $T_2^{\prime }=\{t_{21}^{\prime }=\text{Processes Market Dynamics}\}$, $T_3^{\prime }=\{t_{31}^{\prime }=\text{Process Safety Incidents},t_{32}^{\prime }=\text{Supply Chain Disruptions}\}$. In assessing emission reduction measures, experts evaluate diverse factors based on industry-specific data. Utilizing a numerical representation system akin to the Carbon Neutralization and Reduction Scale ($z_{T^{\prime }}$), verbal descriptions are translated into quantitative values. This translation process is outlined in the accompanying numerical table (Table 6).

Table 6.

$z_{S^{\prime }}$: Past report Reports of $S^{\prime }$ for each petrochemical industry in the form of CNHS.

Factors/industries	$r_1$	$r_2$	$r_3$	$r_4$
$(s_{11}^{\prime },s_{21}^{\prime },s_{31}^{\prime })$	$(0.5e^{i0.6\theta },0.2e^{i0.4\theta },0.1e^{i0.6\theta })$	$(0.1e^{i0.5\theta },0.2e^{i0.9\theta },0.1e^{i0.5\theta })$	$(0.1e^{i0.2\theta },0.4e^{i0.7\theta },0.2e^{i0.4\theta })$	$(0.5e^{i0.7\theta },0.2e^{i0.9\theta },0.1e^{i0.2\theta })$
$(s_{11}^{\prime },s_{21}^{\prime },s_{32}^{\prime })$	$(0.1e^{i0.5\theta },0.2e^{i0.6\theta },0.1e^{i0.5\theta })$	$(0.2e^{i0.5\theta },0.8e^{i0.2\theta },0.5e^{i0.1\theta })$	$(0.6e^{i0.1\theta },0.2e^{i0.6\theta },0.5e^{i0.7\theta })$	$(0.2e^{i0.1\theta },0.4e^{i0.5\theta },0.1e^{i0.3\theta })$
$(s_{12}^{\prime },s_{21}^{\prime },s_{31}^{\prime })$	$(0.1e^{i0.7\theta },0.3e^{i0.6\theta },0.2e^{i0.9\theta })$	$(0.2e^{i0.1\theta },0.5e^{i0.2\theta },0.7e^{i0.6\theta })$	$(0.1e^{i0.4\theta },0.4e^{i0.9\theta },0.6e^{i0.1\theta })$	$(0.4e^{i0.7\theta },0.2e^{i0.9\theta },0.3e^{i0.3\theta })$
$(s_{12}^{\prime },s_{21}^{\prime },s_{32}^{\prime })$	$(0.5e^{i0.1\theta },0.4e^{i0.7\theta },0.2e^{i0.7\theta })$	$(0.8e^{i0.2\theta },0.1e^{i0.6\theta },0.3e^{i0.7\theta })$	$(0.6e^{i0.2\theta },0.1e^{i0.9\theta },0.4e^{i0.2\theta })$	$(0.1e^{i0.7\theta },0.5e^{i0.2\theta },0.1e^{i0.7\theta })$

Step 3.

Suppose two mappings in such a way; $\vartheta :R\to R$ and $\sigma :S\to S^{\prime }$ such that

$$\begin{array}{c}\hfill \vartheta (r_1)=r_1,\vartheta (r_2)=r_2,\vartheta (r_3)=r_3,\vartheta (r_4)=r_4\end{array}$$ 13

and

$$\begin{array}{cc}\hfill \sigma (s_{11},s_{21},s_{31})=& (s_{11}^{\prime },s_{21}^{\prime },s_{31}^{\prime }),\hfill \end{array}$$ 14

$$\begin{array}{cc}\hfill \sigma (s_{11},s_{21},s_{32})=& (s_{12}^{\prime },s_{21}^{\prime },s_{31}^{\prime }),\hfill \end{array}$$ 15

$$\begin{array}{cc}\hfill \sigma (s_{12},s_{21},s_{31})=& (s_{11}^{\prime },s_{21}^{\prime },s_{32}^{\prime }),\hfill \end{array}$$ 16

$$\begin{array}{cc}\hfill \sigma (s_{12},s_{21},s_{32})=& (s_{12}^{\prime },s_{21}^{\prime },s_{32}^{\prime }).\hfill \end{array}$$ 17

Then $\mho =(\vartheta ,\sigma ):CNHS(R)\to CNHS(R)$ is used to represent CNHS-mapping. Using the aforementioned mapping in Step 3 of the method, assess the image of $\bigsqcup z_S^{\epsilon }$ supplied as $z_{\prime }^{\prime }$ in Table 7.

Table 7.

Under CNHS mapping,the image ($z_{\prime }^{\prime }$) of $\bigsqcup z_S^{\epsilon }$.

Factors/industries	$r_1$	$r_2$	$r_3$	$r_4$
$(s_{11}^{\prime },s_{21}^{\prime },s_{31}^{\prime })$	$(0.3e^{i0.2\theta },0.1e^{i0.5\theta },0.8e^{i0.2\theta })$	$(0.1e^{i0.9\theta },0.2e^{i0.4\theta },0.2e^{i0.6\theta })$	$(0.2e^{i0.7\theta },0.2e^{i0.9\theta },0.1e^{i0.7\theta })$	$(0.1e^{i0.9\theta },0.6e^{i0.2\theta },0.1e^{i0.8\theta })$
$(s_{12}^{\prime },s_{21}^{\prime },s_{31}^{\prime })$	$(0.1e^{i0.8\theta },0.2e^{i0.6\theta },0.2e^{i0.8\theta })$	$(0.8e^{i0.5\theta },0.2e^{i0.6\theta },0.1e^{i0.8\theta })$	$(0.4e^{i0.3\theta },0.2e^{i0.9\theta },0.2e^{i0.7\theta })$	$(0.1e^{i0.2\theta },0.5e^{i0.6\theta },0.2e^{i0.3\theta })$
$(s_{11}^{\prime },s_{21}^{\prime },s_{32}^{\prime })$	$(0.6e^{i0.2\theta },0.1e^{i0.5\theta },0.1e^{i0.4\theta })$	$(0.1e^{i0.4\theta },0.2e^{i0.5\theta },0.1e^{i0.7\theta })$	$(0.2e^{i0.9\theta },0.1e^{i0.7\theta },0.2e^{i0.5\theta })$	$(0.1e^{i0.7\theta },0.4e^{i0.8\theta },0.1e^{i0.3\theta })$
$(s_{12}^{\prime },s_{21}^{\prime },s_{32}^{\prime })$	$(0.4e^{i0.5\theta },0.2e^{i0.4\theta },0.1e^{i0.6\theta })$	$(0.5e^{i0.2\theta },0.1e^{i0.2\theta },0.1e^{i0.2\theta })$	$(0.1e^{i0.5\theta },0.6e^{i0.2\theta },0.4e^{i0.5\theta })$	$(0.1e^{i0.4\theta },0.3e^{i0.2\theta },0.7e^{i0.6\theta })$

Step 4.

To acquire weighted aggregate values in Table 8, use the formula (given in step 4 algorithm portion with weights $w_1=0.2$, $w_2=0.4$) to convert Table 7 CNHS set to Neutrosophic Hypersoft set (Tables 9, 10).

Table 8.

$z_{\prime }^{\prime }$: CNHS to Neutrosophic Hypersoft set.

Factors/industries	$r_1$	$r_2$	$r_3$	$r_4$
$(s_{11}^{\prime },s_{21}^{\prime },s_{31}^{\prime })$	(0.12, 0.23, 0.23)	(0.41, 0.51, 0.23)	(0.12, 0.12, 0.61)	(0.24, 0.23, 0.12)
$(s_{12}^{\prime },s_{21}^{\prime },s_{31}^{\prime })$	(0.67, 0.21, 0.72)	(0.15, 0.12, 0.12)	(0.23, 0.34, 0.21)	(0.23, 0.34, 0.12)
$(s_{11}^{\prime },s_{21}^{\prime },s_{32}^{\prime })$	(0.62, 0.34, 0.24)	(0.6, 0.34, 0.61)	(0.62, 0.34, 0.51)	(0.12, 0.51, 0.23)
$(s_{12}^{\prime },s_{21}^{\prime },s_{32}^{\prime })$	(0.67, 0.51, 0.54)	(0.21, 0.32, 0.13)	(0.34, 0.24, 0.42)	(0.24, 0.43, 0.72)

Table 9.

The emission technique score values data concerning linked indications.

Factors/industries	$(s_{11}^{\prime },s_{21}^{\prime },s_{31}^{\prime })$	$(s_{11}^{\prime },s_{21}^{\prime },s_{32}^{\prime })$	$(s_{12}^{\prime },s_{21}^{\prime },s_{31}^{\prime })$	$(s_{12}^{\prime },s_{21}^{\prime },s_{32}^{\prime })$	Average score
$r_1$	0.5	0.13	0.07	0.3	0.34
$r_2$	0.12	0.67	0.45	0.51	0.51
$r_3$	0.784	0.412	0.31	0.73	0.445
$r_4$	0.781	0.51	0.29	0.25	0.44

Table 10.

${\chi }_{S^{\prime }}$: Recommendations from experts regarding the appropriate methods to reduce carbon emissions within the petrochemical industry.

Techniques/factors	$(s_{11}^{\prime },s_{21}^{\prime },s_{31}^{\prime })$	$(s_{11}^{\prime },s_{21}^{\prime },s_{32}^{\prime })$	$(s_{12}^{\prime },s_{21}^{\prime },s_{31}^{\prime })$	$(s_{12}^{\prime },s_{21}^{\prime },s_{32}^{\prime })$
$c_1$	(0.9, 0.1, 0.2)	(0.7, 0.2, 0.1)	(0.6, 0.1, 0.2)	(0.8, 0.1, 0.2)
$c_2$	(0.8, 0.2, 0.1)	(0.7, 0.2, 0.1)	(0.9, 0.1, 0.2)	(0.7, 0.1, 0.2)
$c_3$	(0.7, 0.1, 0.2)	(0.9, 0.2, 0.1)	(0.2, 0.1, 0.1)	(0.7, 0.1, 0.1)
$c_4$	(0.9, 0.2, 0.3)	(0.8, 0.1, 0.2)	(0.9, 0.2, 0.2)	(0.7, 0.1, 0.1)

Step 5.

Calculate the fusion of two CNHS sets

${\chi }_{S^{\prime }}$ and $z_{\prime }^{\prime }$ to derive the correlation between the suggested reduction technique for carbon emissions and the petrochemical industries as a Neutrosophic soft set

$$\begin{array}{c}\hfill {\chi }_{S^{\prime }}\circ z_{\prime }^{\prime }=R_C^1\end{array}$$ 18

, as presented in Table 11.

Table 11.

$R_C^1$: Relating the proposed emission reduction method to the petrochemical industry involves combining ${\chi }_{S^{\prime }}$ and $z_{\prime }^{\prime }$ in a concise composition.

industries /techniques	$c_1$	$c_2$	$c_3$	$c_4$
$r_1$	(0.9, 0.31, 0.2)	(0.5, 0.23, 0.123)	(0.51, 0.23, 0.3)	(0.9, 0.31, 0.5)
$r_2$	(0.81, 0.4, 0.1)	(0.6, 0.21, 0.3)	(0.8, 0.1, 0.21)	(0.8, 0.12, 0.1)
$r_3$	(0.9, 0.1, 0.2)	(0.7, 0.2, 0.12)	(0.9, 0.12, 0.3)	(0.9, 0.2, 0.3)
$r_4$	(0.7, 0.3, 0.1)	(0.7, 0.2, 0.3)	(0.6, 0.2, 0.4)	(0.8, 0.12, 0.2)

Step 6.

Assessing petrochemical emission factors involves a comprehensive analysis based on industry-specific data. Utilizing a numerical rating system similar to carbon emission factors ($z_{C^{\prime }}$), verbal descriptions are translated into quantifiable values. This conversion mechanism is detailed in the corresponding numerical representation (Table 8). Using the formula

$$\begin{array}{c}\hfill \frac{1}{2}|T_s^{\epsilon }(r)-2I_s^{\epsilon }(r)-F_s^{\epsilon }(r)|,\end{array}$$ 19

the CNHS evaluates scores for various emission factors. Following the computation of scores for each technique, Table 9 demonstrates these numerical evaluations. Subsequently, Table 1, representing the implementation chart for carbon emission-related concerns, is utilized to validate the results presented in Table 9, showing that the petrochemical industries $r_1$, $r_3$, and $r_4$ are significant contributors to carbon emissions due to Transportation and Distribution, while the petrochemical industry $r_2$ is a major contributor to carbon emissions due to Energy Consumption.

Step 7.

Once the factors is confirmed, appropriate measures to alleviate the carbon emissions are prescribed by the environmental specialist. Our CNHS toolkit has been meticulously crafted by industry experts, offering tailored solutions for various carbon emission sources. Let $T=\{t_1=$ Carbon Capture and Storage, $t_2=$ Energy Efficiency Improvements, $t_3=$ Waste Heat Recovery, $t_4=$ Carbon Offsetting$\}$ denote distinctive methodologies. Establishing ${\mathrm{\Theta }}_{C^{\prime }}$ signifies a compilation of expert recommendations to mitigate carbon emissions within specific contexts. The collection ${\mathrm{\Theta }}_{C^{\prime }}\in CNHS(E)$ serves as the foundation, outlined as Table 10. The evaluations presented in Table 10 are tailored to each operational setting, factoring in historical emission data. Grades of inclusion demonstrate the affirmative impact of each method, while uncertainty grades portray the neutral effects, and grades of falsehood highlight potential adverse consequences associated with each carbon emission reduction technique, considering various emission sources and their characteristics.

Step 8.

Petrochemical industry can be experience significant benefits from employing emission reduction techniques that result in fewer adverse environmental impacts. To determine the efficacy of these methods, scores are computed by applying a scoring function to various emission reduction strategies for each operational context, as detailed in Table 12 within algorithm in step 4. Upon reviewing Table 12, it becomes evident that strategy $t_1$ is the most suitable option for petrochemical industries $r_1$ and $r_3$, while strategy $t_2$ is optimal for petrochemical industry $r_2$, and strategy $t_4$ is deemed most effective for petrochemical industry $r_4$. The final selection of the most suitable emission reduction technique in the petrochemical industry relies on the current operational context, historical emission patterns, and the precise characteristics of emission sources along with their environmental implications.

Table 12.

Petrochemical industry score values and suggested carbon emission techniques are shown in a tabulated form.

Industries/ techniques	$c_1$	$c_2$	$c_3$	$c_4$	Maximum esteems	Selected treatment
$r_1$	0.09	0.013	0.004	0.05	0.09	$c_1$
$r_2$	0.103	0.38	0.145	0.08	0.38	$c_2$
$r_3$	0.5	0.031	0.08	0.05	0.5	$c_1$
$r_4$	0	0	0.16	0.221	0.221	$c_4$

Step 9.

The condition of the emission source and its historical impact determine the status of the carbon emission reduction process. Repeated application of emission reduction techniques can persist until the complete mitigation of the emissions. Employing CNHS-mapping and establishing two sub-mappings ${ϵ}^{\prime }:E^{q-1}\to E^q$ and ${\mathrm{{\rm Y}}}^{\prime }:S^{q-1}\to S^q$ allows for tracking the improvement of each emission source over time.

$$\begin{array}{c}\hfill {\vartheta }^{\prime }(r_1)=r_1,{\vartheta }^{\prime }(r_2)=r_2,{\vartheta }^{\prime }(r_3)=r_3,{\vartheta }^{\prime }(r_4)=r_4;\end{array}$$ 20

and

$$\begin{array}{c}\hfill {\sigma }^{\prime }(c_1)=c_1,{\sigma }^{\prime }(c_2)=c_2,{\sigma }^{\prime }(c_3)=c_3.\end{array}$$ 21

Then CNHS-mapping defined as follows;

$$\begin{array}{c}\hfill {\mho }^{\prime }=({\vartheta }^{\prime },{\sigma }^{\prime }):R_C^{q-1}\to R_C^q\end{array}$$ 22

The CNHS-mapping is as shown in;

$$\begin{array}{c}\hfill R_C^q={\mho }^{\prime }(R_C^{q-1})(c)(r)=\frac{1}{q}\left\{\begin{array}{cc}\underset{\theta \in {\vartheta }^{\prime -1}(r)}{\bigvee }\left(\underset{\vartheta \in {\sigma }^{\prime -1}(c)\cap C}{\bigvee },R_C^{q-1},(\theta )\right)\hfill & \text{if}{\vartheta }^{\prime -1}(r)\ne \mathrm{\varnothing },{\sigma }^{\prime -1}(c)\cap C\ne \mathrm{\varnothing }\hfill \\ 0\hfill & \text{otherwise}\hfill \end{array}\right)\end{array}$$ 23

where $q=2,3,4,...$ represents the number of episodes of treatments and $c\in {\sigma }^{\prime }(C)\subseteq C$, $r\in R^q$, $\theta \in R^{q-1}$, $\vartheta \in C^{q-1}$ and treatment episodes can be written up in Tables 13, 14, 15 and 16 are given for $q=2,3,4$ and 5 respectively.

Table 13.

$R_C^2$: Petrochemical industry’ progress report after the second episode.

Industries/techniques	$c_1$	$c_2$	$c_3$	$c_4$
$r_1$	(0.9, 0.212, 0.03)	(0.78, 0.11, 0.121)	(0.781, 0.02, 0.3)	(0.8, 0.01, 0.1)
$r_2$	(0.751, 0.12, 0.2)	(0.9, 0.141, 0.02)	(0.71, 0.12, 0.124)	(0.8, 0.321, 0.2)
$r_3$	(0.7, 0.131, 0.5)	(0.9, 0.3, 0.1)	(0.8, 0.02, 0.122)	(0.8, 0.31, 0.61)
$r_4$	(0.9, 0.2, 0.31)	(0.6, 0.11, 0.02)	(0.9, 0.001, 0.003)	(0.741, 0.121, 0.1)

Table 14.

$R_C^3$: Petrochemical industry’ progress report after the second episode.

Industries/techniques	$c_1$	$c_2$	$c_3$	$c_4$
$r_1$	(0.09, 0.02, 0.02)	(0.61, 0.01, 0.02)	(0.6, 0.012, 0.021)	(0.09, 0.01, 0.02)
$r_2$	(0.8, 0.01, 0.02)	(0.08, 0.02, 0.01)	(0.7, 0.012, 0.012)	(0.08, 0.02, 0.01)
$r_3$	(0.7, 0.02, 0.01)	(0.8, 0.01, 0.01)	(0.8, 0.01, 0.02)	(0.8, 0.02, 0.01)
$r_4$	(0.8, 0.01, 0.02)	(0.9, 0.01, 0.01)	(0.7, 0.01, 0.012)	(0.09, 0.01, 0.02)

Table 15.

$R_C^4$: Petrochemical industry’ progress report after the second episode.

Industries/techniques	$c_1$	$c_2$	$c_3$	$c_4$
$r_1$	(0.06, 0.01, 0.002)	(0.0416, 0.006, 0.013)	(0.087, 0.005, 0.001)	(0.045, 0.001, 0.02)
$r_2$	(0.06, 0.0132, 0.0091)	(0.071, 0.011, 0.0021)	((0.081, 0.0213, 0.021)	(0.072, 0.011, 0.0012)
$r_3$	(0.035, 0.0012, 0.023)	(0.051, 0.0021, 0.011)	(0.061, 0.021, 0.003)	(0.045, 0.002, 0.0212)
$r_4$	(0.071, 0.0131, 0.0011)	(0.071, 0.0011, 0.0231)	(0.091, 0.0012, 0.001)	(0.091, 0.014, 0.012)

Table 16.

$R_C^5$: Petrochemical industry’ progress report after the second episode.

Industries/techniques	$c_1$	$c_2$	$c_3$	$c_4$
$r_1$	(0.004, 0.0022, 0.0013)	(0.0067, 0.0023, 0.0050)	(0.0061, 0.0013, 0.0021)	(0.007, 0.00121, 0.00212)
$r_2$	(0.0065, 0.0013, 0.0013)	(0.0068, 0.002, 0.00031)	(0.008, 0.002, 0.001)	(0.006, 0.0012, 0.001)
$r_3$	(0.007, 0.0013, 0.002)	(0.005, 0.0001, 0.0021)	(0.009, 0.001, 0.0021)	(0.008, 0.001, 0.0041)
$r_4$	(0.00721, 0.0019, 0.0006)	(0.008, 0.0011, 0.0021)	(0.007, 0.0001, 0.0002)	(0.004, 0.002, 0.003)

Step 10.

The process outlined in Step 9 iterates until the achieved carbon emission reduction results meet the predefined satisfaction criteria.

Limitations

The model heavily relies on expert evaluations and historical data, which may be limited or inaccurate. This reliance could affect the precision of emission factor assessments and the effectiveness of the proposed strategies. The intricate nature of CNHS operations could pose challenges for users unfamiliar with advanced fuzzy logic techniques. The model’s effectiveness may be constrained when applied to large-scale or diverse petrochemical operations. Variations in emission sources and operational conditions across different facilities might require additional customization or adjustments not covered by the current framework. The approach involves extensive calculations and data processing, which may require substantial computational resources and time. This could limit the feasibility of using the model for real-time decision-making in resource-constrained environments.

Concluding remarks

This investigation illuminates the triumphant implementation of a groundbreaking decision-making paradigm, adeptly addressing the complexities of carbon emissions in the petrochemical sector. The research eloquently showcases the efficacy of a hybrid set framework, amalgamating scientific modeling with a sophisticated coding-based prototype, in enhancing energy efficiency, optimizing CO2 emission reductions, and curtailing costs. The findings are as follows: Firstly, the petrochemical sectors $r_1$, $r_3$, and $r_4$ significantly contribute to carbon emissions primarily due to Transportation and Distribution, whereas the petrochemical sector $r_2$ is a major contributor due to Energy Consumption. Secondly, it is clear that strategy $t_1$ is the most appropriate for petrochemical sectors $r_1$ and $r_3$, while strategy $t_2$ is best suited for petrochemical sector $r_2$, and strategy $t_4$ is considered the most effective for petrochemical sector $r_4$. This methodology’s potency is further corroborated by domain experts, who extol its versatility and the capacity for bespoke emission diminution strategies in varied contexts, facilitated by CNHS mapping. Beyond surmounting the initial impediment of inadequate comprehensive data, this study lays the groundwork for more enlightened and potent approaches in curtailing carbon emissions in the petrochemical realm. In conclusion, this research not only represents a significant stride in the application of innovative, data-driven solutions for environmental challenges but also sets a precedent for future endeavors aiming to harmonize industrial processes with environmental sustainability.

Author contributions

Dr. Muhammad Ahsan was the primary author of the main manuscript, responsible for developing the concepts, conducting the investigation, gathering data, and composing the write-up. Professors Laxin Tian and Ruijin Du contributed by conducting the formal analysis.

Data availability

The data will be available on reasonable request. The data can be furnished by the primary author, Dr. Muhammad Ahsan.

Declarations

Competing interests

The authors declare no competing interests.