Design of global climate control based on fuzzy systems with concept of carbon emissions

PLOS ONE OPEN ACCESS Citation: Naseer S, Chang W, Aslam S, Hashim Bukhari M, Bilal H, Nawaz MJ (2025) Design of global climate control based on fuzzy systems with concept of carbon emissions. PLoS One 20(10): e0333846. https://doi.org/10.1371/journal.pone.0333846 Editor: Morteza Taki, Agricultural Sciences and Natural Resources University of Khuzestan, IRAN, ISLAMIC REPUBLIC OF Received: July 2, 2025 Accepted: September 18, 2025 Published: October 14, 2025 Copyright: © 2025 Naseer et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data availability statement: All data are in the manuscript and/or supporting information files. Funding: This research was founded by the National Science and Technology Council of the Republic of China under contract NSTC114-2221-E-019-067. Competing interests: The writers claim to have no conflicts of interest and Aramco company on RESEARCH ARTICLE Design of global climate control based on fuzzy systems with concept of carbon emissions Saira Naseer1, Wer-Jer Chang2∗, Muhammad Shamrooz Aslam 3∗, Muhammad Hashim Bukhari4, Hazrat Bilal5, Muhammad Javid Nawaz6 1 School of Economics and Management, Quanzhou University of Information Engineering, Quanzhou, Fujian, People’s Republic of China, 2 Department of Marine Engineering, National Taiwan Ocean University (NTOU), Keelung, Taiwan, 3 School of Computer Science and Technology/School of Artificial

Intelligence, China University of Mining and Technology, Xuzhou, People’s Republic of China, 4 Saudi AramcoStar Building LIP, Dhahran, Saudi Arabia, 5 School of Information Science and Technology, University of Science and Technology of China, Hefei, Anhui, People’s Republic of China, 6 School of Economics and Management, Nanjing University of Science and Technology, Nanjing, People’s Republic of China ∗ wjchang@mail.ntou.edu.tw (W-JC); shamroz_aslam@cumt.edu.cn (MSA) Abstract The global carbon–climate system is a highly complex and dynamic network character- ized by multiple feedback loops between interconnected components. Addressing the risks of climate change requires active intervention across these components (Atmo- spheric level, Surface ocean, and Terrestrial biosphere). Consequently, this research introduces a new mathematical fuzzy control theory to explore how control mechanisms, incorporating both open and closed–loop, can help guide the carbon–climate system toward more stable and sustainable levels. First, a fuzzy mathematical generalization as a compartmental dynamical model is proposed for a formal analysis of closed–loop con- trol strategies for climate regulation. Second, the challenge of managing carbon–climate dynamics is reframed as a network congestion control problem, incorporating critical con- cepts to highlight gaps in current scientific approaches to climate feedback management. Third, an algorithm based on an implicit open–loop control assumption, incorporating the

need for continuous adjustments when discrepancies arise between targets and actual measurements, is introduced. Additionally, taking into account nonlinear behavior and feedback from an international carbon monitoring system, the authors show how the task of regulating the global carbon cycle may be viewed as an abstracted network conges- tion problem using a reduced complexity model. Finally, a simulation scenario demon- strating how closed–loop control could be developed to more effectively manage the carbon–climate structure is presented. PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 1/ 30

PLOS One Design of global climate control based on fuzzy systems this research. Author Muhammad Hashim Bukhari is employed by Saudi Aramco. Saudi Aramco provided funding, but had some additional role in study design, simulation analysis, decision to publish, and preparation of the manuscript. All other authors declare no competing interests. 1 Introduction One of the most important global issues of the present time is climate change, which is unquestionably a result of human activity. The term “climate change” refers to a general alter- ation of the earth’s climate, which includes changes to land and ocean temperatures as well as precipitation and snowfall amounts. The following are some pertinent climate–related factors: rays of the sun, earth, the oceans, the wind, the rain, the snow, the woods, the deserts, the savannas, and all human activity. Before industrialization, greenhouse gases were naturally balanced and their impact on climate was relatively stable. The greenhouse effect, which pre- vents the earth’s atmosphere from reflecting the sun’s heated infrared radiation, has been the primary driver of climate change since industrialization. The intricate relationships between several natural elements and human–caused impacts make it difficult to study and predict climate dynamics [1]. To deal with this complexity, researchers have developed novel mathe- matical models that can capture the uncertainties and non-linear interactions inherent in the climate system. One such model that has gained recognition for its ability to convey intricate

relationships, adjust to shifting circumstances, and provide insightful predictions in the con- text of climate change is the T–S (Takagi–Sugeno) fuzzy framework [2]. Based on fuzzy logic principles, the T–S fuzzy model offers a structured framework for representing complex sys- tems by breaking them down into the smallest, locally valid sub–models [3]. A comprehensive representation of the entire system is then produced by combining these sub–models. Given the complex interactions between multiple components in the subject of climate change, the T–S fuzzy model’s capacity to capture nonlinearities and uncertainty proved crucial. This paradigm provides a means of representing complex processes using fuzzy sets and linguistic variables, which is ideally suited to the inherently vague and imprecise nature of climate data. Earth’s climate dynamics are defined by a variety of elements, such as temperature, precipi- tation, concentrations of greenhouse gases, ocean currents, and others. These variables exhibit feedback loops, thresholds, and nonlinear interactions that are challenging to incorporate into conventional linear models [4]. By segmenting the input space into numerous parts, each of which is linked to a locally dependable linear sub-model, the T–S fuzzy model gets around this problem. This localized modeling approach can be used to depict nonlinear behaviors for certain ranges of input variables. In addition, due to natural fluctuations, lack of data, and changes in human activities, there are still unknown factors contributing to climate change.

The T–S fuzzy framework [5] is highly effective at handling uncertainties, as it incorporates fuzzy set theory to explicitly model imprecision. This competency is crucial when working with climate projections, as evaluating uncertainty is necessary for making wise decisions. This study of climate change modeling using the T–S fuzzy framework covers the fundamen- tal concepts of the T–S model, its application to climate systems, and its advantages over tra- ditional modeling approaches. By accepting the inherent complexity and uncertainty of cli- mate dynamics, the T–S fuzzy model opens up new avenues for enhancing our understanding of climate change, assisting with well–informed policy decisions, and fostering a sustainable future. In order to combat atmospheric systems, recent research emphasizes the expanding con- vergence of energy systems, environmental sustainability, and artificial intelligence. In their investigation of cellular and biochemical pathways, Li et al. [6] offered insights into reg- ulatory mechanisms that may have consequences for climate–resilient systems and bio- engineering. Multi-source information fusion strategies were developed in [7] and can improve predictive environmental models by increasing accuracy in the face of ambiguity. By directly connecting advanced analytics to the monitoring and mitigation of climate–related PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 2/ 30

PLOS One Design of global climate control based on fuzzy systems pollutants, Wu et al. [8] highlighted the potential of geospatial AI in air pollution prediction. In order to maximize the integration of renewable energy sources and minimize emissions, Meng et al. [9] suggested low–carbon dispatching solutions for integrated energy systems. In their evaluation of district sharing plans for heating and cooling using ground source heat pump (GSHP) systems, Zhang et al. [10] highlighted workable ways to reduce carbon emis- sions in urban energy use. In order to show how large-scale interactions affect global climate variability, Zhu et al. [11]looked at the effects of tropical regions on Arctic climate patterns. Lastly, in [12] looked at how cloud computing may decouple urban carbon footprints and provided solutions for sustainable urbanization. When taken as a whole, these works are sig- nificant because they tackle climate change from various but complementary angles, such as urban carbon management, predictive AI, and system optimization. This lays the groundwork for creating integrated frameworks that integrate sustainability objectives, technology, and policy. 1.1 Significance of T-S fuzzy model for Climate Change The use of Takagi–Sugeno Fuzzy Models (T–S models) in climate change study is crucial to comprehending the many facets of this worldwide problem. By addressing nonlinear link- ages within climate systems, these models offer a unique perspective and transcend the limi- tations of traditional linear methodologies. By effectively managing uncertainty, they address

the inherent ambiguity in climate data [13]. It is also essential to incorporate expert infor- mation, which allows climate scientists to offer qualitative insights and increase forecast accuracy. T–S models have a revolutionary effect on a number of applications, from predict- ing short–term climate changes to assessing the potential effects on sectors like agriculture, water resources, and energy. Their ability to facilitate scenario analysis and policy evaluation empowers decision-makers to make educated choices, directing society toward effective miti- gation and adaptation strategies for climate change [14]. In a world grappling with the sever- ity of climate change, Takagi–Sugeno Fuzzy Models are an essential tool that offer insights into the complex interplay of variables and uncertainties affecting our planet’s future [15]. A comprehensive overview of global greenhouse gas (GHG) emissions by sector for 2016– when total emissions reached 49.4 billion tonnes of CO2–is shown in Fig 1’s block diagram. With 38.2% of global emissions, the energy sector is the largest contributor, as the graphic Fig 1. Emissions of greenhouse gases worldwide by sector [16]. https://doi.org/10.1371/journal.pone.0333846.g001 PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 3/ 30

PLOS One Design of global climate control based on fuzzy systems makes clear. Energy consumption in buildings (14.2%), and transportation (7.2%), and are the main sources of energy in this sector, with residential and commercial buildings account- ing for the majority of contributions. Livestock, deforestation, and soil management are the main drivers of the 12.4% contribution from the Agriculture, Forestry & Land Use sector. Waste (1.2%) and Industry (5.2%), on the other hand, are lesser but nonetheless important sources. The graphic also shows possible ways to improve resource efficiency through dig- ital transformation, which makes it possible for improved automation, optimization, and monitoring. GHG emissions worldwide by sector (derived from [Ref [16]). The baseline data supporting the fuzzy control method used in this investigation is shown in this picture. The urgent need for adaptive control strategies–which are further explored in Sects 3–6, which is demonstrated by the significant contributions from the energy, building, and transporta- tion industries. In order to improve sustainability and lower emissions, the green–highlighted section describes significant research applications such as smart buildings, intelligent ware- houses, and wireless industrial automation. Industries may fix inefficiencies, reduce their environmental effect, and aid in the fight against climate change by incorporating these cutting–edge solutions. For more comprehensive review, readers can refer the references [17, 18].

Climate mechanism and global warming are complicated environmental issues brought on by both natural and human–caused causes. The interrelated causes, feedback systems, and ensuing effects on the environment and human society are depicted in this block dia- gram. The main contributors to climate change include deforestation, agriculture, and the use of fossil fuels, all of which increase the emission of greenhouse gases including nitrous oxide, carbon dioxide, and methane. These gases exacerbate the greenhouse effect and fuel global warming by trapping heat in the Earth’s atmosphere. The Fig 2 emphasizes the func- tion of feedback loops, wherein thawing permafrost, increasing water vapor, and decreased snow cover all contribute to the acceleration of climate change. Environmental effects of these changes include habitat loss, ecosystem collapse, biodiversity loss, increased weather, glacial retreat, and sea level rise. Human problems including agricultural failure, flooded towns, pop- ulation displacement, and health hazards are further exacerbated by these environmental repercussions. The root causes and effects of global warming and climate change. The nonlin- ear feedback loops (such as water vapor amplification and permafrost thawing) that are sub- sequently modeled using fuzzy rules (Table 1) and assessed in simulation tests (Figs 12–20) are highlighted in this schematic. It is clear from comprehending the chain reactions shown in this graphic that climate change is a complex problem that needs immediate attention to

lessen its profound effects on ecosystems and human culture. Applying T–S fuzzy models in climate change has practical significance. These models offer an easy and efficient approach to incorporate uncertainty in input and output variables, such as projected greenhouse gas (GHG) emissions and temperature increases. T–S fuzzy mod- els help capture the relationships between GHG concentrations and temperature variations by using linguistic rules derived from emission scenarios and climate models [19,20]. Fuzzy models can also account for climate sensitivity uncertainty, giving a more thorough evalua- tion of temperature rises [21]. Decision–makers can test alternative strategies and analyze their results at different levels by using fuzzy models to measure regional sustainability develop- ment under climate change [22]. In general, T–S fuzzy models provide useful tools for making decisions and comprehending the effects of climate change. In [23], two strategies for controlling complex dynamical systems are outlined: open–loop control, also known as pre-computed control (OCLC), and closed-loop control. As shown in Figs 3 and 4, feedback (closed–loop) control adjusts actions based on observations of the sys- tem state, allowing it to correct deviations and account for random perturbations caused by PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 4/ 30

PLOS One Design of global climate control based on fuzzy systems Fig 2. Causes and effect of Climate change and Global warming. https://doi.org/10.1371/journal.pone.0333846.g002 Fig 3. Traditional open–loop controller representation for controlling dynamical systems and their counterpart strategies in managing carbon climate systems. https://doi.org/10.1371/journal.pone.0333846.g003 noise or model uncertainties [24]. In cutting–edge research on carbon–climate policy, how- ever, open–loop models are often employed (See Figs 5 and 6). Studies on carbon–climate PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 5/ 30

PLOS One Design of global climate control based on fuzzy systems Fig 4. Conventional description of a closed-loop controller for controlling dynamical systems and their counterpart strategies in managing carbon climate systems. https://doi.org/10.1371/journal.pone.0333846.g004 Fig 5. Policies for open-loop control and climate change mitigation for controlling dynamical systems and their counterpart strategies in managing carbon climate systems. https://doi.org/10.1371/journal.pone.0333846.g005 feedback heavily rely on scenario–driven analyses using long–term emission pathways to fore- cast climate impacts [25], and their results significantly shape climate mitigation strategies aligned with particular scenario trajectories [26]. Control theory plays an essential role in climate change mitigation, providing a framework for analyzing and managing the complex systems that influence Earth’s climate. Encompass- ing a range of methodologies and techniques, it enables the regulation of key drivers such as greenhouse gas emissions, deforestation, and industrial pollution. By applying control princi- ples, policymakers and scientists can design strategies and interventions that guide environ- mental systems toward sustainability and resilience. This multidisciplinary approach draws PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 6/ 30

PLOS One Design of global climate control based on fuzzy systems Fig 6. Closed–loop control, measurements design and assessment of policies pertaining to climate change adaptation. https://doi.org/10.1371/journal.pone.0333846.g006 on engineering, mathematics, and environmental sciences to develop effective mechanisms for mitigating climate change at a global scale. The primary contributions can be outlined as follows: • Introduces a novel fuzzy logic–based mathematical representation of the carbon–climate system to formalize the closed–loop control problem. • Develops a segmented mathematical representation of the global carbon system that high- lights characteristics such as dynamical stability, demonstrating through simulations that fuzzy logic rules can effectively regulate fossil fuel demand and carbon transfer to geological reserves like the deep sea. • Derives a mathematical decision-making guideline from system demand and internal dynamics, enabling adaptive carbon cycle management as an alternative to long–term scenario–based recommendations, with policy decisions supported on shorter time scales. The subsequent part of this article is organized as follows. Sect 2 delves into the principles of Control Theory in the context of Climate Change Mitigation. Our mathematical depiction of the Global Carbon Climate Model (GCCM) is outlined in Sect 3. Sect 4 elaborates on a novel fuzzy model for the Global Climate Model (GCM). The interconnected control methodology for the Global Climate System (GCS) is expounded in Sect 5. Lastly, the ultimate findings are

disclosed in Sect 6. PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 7/ 30

PLOS One Design of global climate control based on fuzzy systems 2 Concepts of control theory in the Mitigation of Climate Model Control theory encompasses many concepts, strategies, and techniques involving optimiza- tion ideas. Although optimization concepts have long been applied in areas such as economics (e.g., inflation control) and in recognizing the benefits of mitigating global warming, applica- tions of contemporary control theory to climate systems remain relatively new. In addition, the concepts of optimization were instrumental in the creation of Integrated Assessment Mod- els (IAMs) [27], which can provide optimal prescriptions that can be used as policy responses. Their central tenet is cost–benefit optimization, which incorporates societal costs of climate impacts to maximize social welfare by exploring a space of future emission trajectories with associated environmental effects [28]. Emissions time trajectories offer data for policymakers, but they lack official feedback and corrective procedures grounded in actual observations. Few studies have employed coupled carbon–climate AI models, which is surprising given their significant potential for modeling and managing the global carbon cycle. In contrast to Solar Radiation Management (SRM), which faces significant uncertainties regarding envi- ronmental impacts and may never be fully deployed, substantial progress has been made in reducing emissions and sequestering carbon in long–term reservoirs. To the best of current

knowledge, formal closed–loop control concepts have not been applied within emission trad- ing policy frameworks based on fuzzy model. Furthermore, very few scientific studies have examined feedback regulation processes in the global carbon cycle using similar ideas. Using locally linear sub–models, the data–driven T–S fuzzy identification described above provides a systematic approach to approximating nonlinear systems. We apply this method to the global carbon–climate system in the next section. Specifically, climatic drivers such as greenhouse gas emissions, solar radiation, and biosphere feedbacks serve as fuzzy inputs, while the model’s state variables–carbon reservoirs and surface temperature–are represented as outputs of fuzzy sub–models. The nonlinear dynamics outlined in Eq (1) can thus be expressed within the T–S fuzzy framework. 3 Mathematical representation of the Global Climate Model At any particular point in time domain (t, R), the global carbon–climate system can be rep- resented as a vector s(t) ∈ Rn with components representing carbon levels and temperatures across earth system reservoirs. The function s(t) representing the state at a given time span can be formally articulated as the outcome of a specific organizing 𝟋 ∶ (s0, 𝜈) ↦ s with ini- tial condition s0 ∶= s(t0) and 𝜈(t) denotes the driving signal in term of vector. For instance, one may consider 𝟋 as a representation of the Earth system, incorporating the initial condi- tion s0 along with a set of time–varying driving parameters 𝜈(t) defined over the time span

T = [t0, tmax] and produces the complete evolution of the state s(t) over the time interval T within the overarching carbon–climate model. Although 𝟋 can be expressed in various ways, the authors will confine its definition in this case study to an initial value problem (IVP) for an interconnected set of ordinary differential equations that represent carbon accumulation within Earth reservoirs denoted as ℂE(t), and surface temperatures expressed through block matrices as 𝕋S(t). ̇ s(t) = [̇ ℂE(t) ̇ 𝕋S(t) ] = [ 𝔹(ℂE, 𝕋E, t).ℂE + s(t) f(ℂE, ℝ, t) ] (1) In the next section, the authors will present the new concept of T–S fuzzy model for the climate control plant. PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 8/ 30

PLOS One Design of global climate control based on fuzzy systems Remark 1. The climate model presented here is the particular application area in which the generic T–S fuzzy methodology of Sect 2 is used; it is not separate from the fuzzy identification framework. By approximating the temperature feedback functions f(⋅) and nonlinear transfer rates (matrix 𝔹) in Eq (1), the fuzzy sub–models integrate data–driven fuzzy identification into the climate control environment. 4 New fuzzy model for Global Climate Model We model the global carbon–climate plant as a nonlinear augmented system (1), building on the fuzzy identification concepts discussed in Sect 2. Fuzzy rules convert qualitative climate knowledge (such as ”high CO2 with high temperature → accelerated warming”) into quantita- tive model structure, and T–S fuzzy sub–models derived from available data capture the com- partmental dynamics (carbon exchange among atmosphere, biosphere, and ocean). Our focus here is still on carbon–climate dynamics, but the framework is broad enough to be applied to other environmental problems. The above model (1) illustrates how Fuzzy Models can be used to predict changes in climate environment due to rising sea levels. The main steps have been listed below: Scenario: Fuzzy carbon climate prediction under sea level rise in the following way: Step 1 (Variable Identification): Sea level rise (SLR) and wave energy (WE) are two climatic factors to consider. Define the terms ”low,” ”medium,” and ”high,” as well as their membership criteria, for each.

Step 2 (Fuzzy Rules): Specify the linguistic effects of SLR and WE on fuzzy carbon climate by developing fuzzy rules. Consider this: • If both SLR and WE are high, then there will be severe fuzzy carbon climate. • If both SLR and WE are low, then there will be little fuzzy carbon climate. Step 3 (Fuzzy Inference System): In order to forecast the severity of fuzzy carbon climate based on the current sea level rise and wave energy conditions, apply the fuzzy rules. The model predicts severe fuzzy carbon climate (0.65), for instance, if SLR is medium (0.6) and WE is high (0.7). Step 4 (Defuzzification): From the fuzzy output, generate a precise value that, under the given circumstances, indicates the extent of fuzzy carbon climate. This can be achieved by taking a weighted average of the fuzzy rule’s output values. 4.1 From compartmental dynamics to a T–S fuzzy model Let 𝜉(t) = ⎛ ⎜ ⎝ 𝜉A(t) 𝜉T(t) 𝜉S(t) ⎞ ⎟ ⎠ T , denote the carbon stock in atmosphere, terrestrial biosphere, and surface ocean (PgC). The Eqs (12)–(9) give: ̇ 𝜉(t) = 𝔹(𝜉, t) 𝜉(t) + m(t), m(t) = [𝜆F→A(t), 0, 𝜆D→S]⊤, (2) with entries of 𝔹(𝜉, t) defined by the fluxes 𝜆X→Y (Eq (12)) with parameters 𝛾1, 𝛾2. We define the scheduling vector: z(t) = [z1(t), z2(t), z3(t)] = [ 𝜉A(t) 700 , 𝜉T(t) 3000 , 𝜉S(t) 1000 ] , (3) where augment z(t) with exogenous radiative forcing. PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 9/ 30

PLOS One Design of global climate control based on fuzzy systems 4.1.1 Partition and membership functions. For each zk we select nk overlapping fuzzy sets (e.g., Low/High triangles as in Figs 7, 8, 9, and 10, with membership 𝜇k,j(zk). The i–th rule corresponds to one set per k, with normalized weight hi(z) = ∏3 k=1 𝜇k,𝜎i(k)(zk) ∑r ℓ=1 ∏3 k=1 𝜇k,𝜎ℓ (k)(zk) , r = ∏ k nk, (4) where hi(z) ≥ 0 and ∑r i=1 hi(z) = 1. Fig 7. Membership function for global climate model for internal temperature (○C) with solid line and signal groups (points). https://doi.org/10.1371/journal.pone.0333846.g007 Fig 8. Membership function for global climate model for external temperature (○C) with solid line and signal groups (points). https://doi.org/10.1371/journal.pone.0333846.g008 PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 10/ 30

PLOS One Design of global climate control based on fuzzy systems Fig 9. Membership function for global climate model for Internal humidity with solid line and signal groups (points). https://doi.org/10.1371/journal.pone.0333846.g009 Fig 10. Membership function for global climate model for member of radiation with solid line and signal groups (points). https://doi.org/10.1371/journal.pone.0333846.g010 4.1.2 Local affine sub-models. Within each fuzzy region, the state–dependent coeffi- cients in 𝔹(𝜉, t) are approximated at the region’s nominal point, yielding: ̇ 𝜉(t) = 𝔸i 𝜉(t) + 𝔹i u(t) + m(t), (5) with 𝔸i ∶= 𝔹(̄𝜉(i),̄ t(i)) PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 11/ 30

PLOS One Design of global climate control based on fuzzy systems Here u(t) = 𝜓(𝜅(t)) is the control input, and p(t) is the disturbance or demand term. The global T–S fuzzy model is then obtained as: ̇ 𝜉(t) = r ∑ i=1 hi(z(t)) (𝔸i 𝜉(t) + 𝔹i u(t) + m(t)) . (6) With z1 = 𝜉A/700 (Low/High); z2 = CO2 (Low/High); z3 = Terrestrial biosphere 𝜉T (Low/High); z4 = Sea surface 𝜉S/1000 (Low/High); z5 = Wind speed (Low/High); and z6 = Climate risk (Low/High), ten rules are obtained: • ℜ1: If z1 is Low and z2 is Low, then chance of high temperature. • ℜ2: If z1 is Low and z2 is Low, then chance of high snowfall. • ℜ3: If z1 is High and z3 is High, then increase of risk of species extinction temperature. • ℜ4: If z1 is Low and z3 is Low, then decrease of risk of species extinction temperature. • ℜ5: If z4 is High and z3 is Low, then increase in biodiversity. • ℜ6: If z4 is Low and z3 is High, then decrease in biodiversity. • ℜ7: If z5 is High and z4 is High, then structural damage in buildings & trees. • ℜ8: If z5 is Low and z4 is Low, then no effect. • ℜ9: If z5 is High and z6 is High, then increase energy sources. • ℜ10: If z5 is Low and z6 is Low, then decrease in power output. This framework ties the compartmental dynamics (Eqs (5)–(7)), membership functions (Fig 7, 8, 9, and 10, and the control law 𝜓(𝜅) into a unified T–S fuzzy representation of the carbon–climate system. Remark 2. The main contribution of this research has been the following: ● For compartmen- talized reservoirs (atmosphere, terrestrial biosphere, and surface ocean), T–S fuzzy logic is used.

● Integrating uncertainty and nonlinear dynamics into carbon feedback circuits. ● Fuzzy rule development for adaptive carbon cycle management (as demonstrated in Figs 8–10 and Table 1.) Figs 7, 8, 9, and 10 show the outcomes for each input, indicating the groupings created by the fuzzy approach and the functions for membership of the fuzzy plant. To reduce the amount of rules in the T–S fuzzy structure, we choose a limited number of groups for every input. Four subplots depicting fuzzy membership functions for environmental variables such as tem- perature, humidity, and radiation are included in Figs 7, 8, 9, and 10. The link between envi- ronmental parameters and their respective membership functions is depicted in each sub- plot. Every subplot adheres to a similar structure, such as using red stars (*) to symbolize data points. In other words, those indicate data points from the first group (e.g., ’Hot’, ’Dry’, or ’Low’). ’Cold’, ’Wet’, or ’High’ data points are represented by blue circles (o) in category two. Additionally, the membership functions for the first and second groups are shown by solid red and blue lines, respectively. Every graphic exhibits the fuzzy logic properties of soft transitions between two states (hot/cold, dry/wet, etc.). This is a basic feature of fuzzy logic that deals with overlapping con- ditions and uncertainty. Since it can be challenging to set exact thresholds, these fuzzy mem- bership functions are commonly used in heating, ventilation, and air conditioning (HVAC)

PLOS One Design of global climate control based on fuzzy systems in the red and blue data points, the system’s capacity to filter noise while still maintaining effi- cient environmental control is shown by the smooth membership functions. A clearly spec- ified fuzzy logic system for climate and environmental control is depicted in this collection of charts. The data sets’ logical grouping, adaptive crossover points, and seamless transitions demonstrate a reliable technique for simulating overlapping or uncertain situations that are frequently present in real-world settings. To establish the fuzzy rules for the climate plant, we have some certain range for climate change model. For the variable identification, we assume with a range of 0 → 1, let SLR and WE stand for sea level rise and wave energy, respectively. Fuzzy rules can be modeled as: • SLR must be high (0.8) and WE must also be high (0.7) for fuzzy carbon climate to be severe (0.75). • In the event where both SLR and WE are low (0.2 and 0.3, respectively), fuzzy carbon cli- mate is minimal (0.25). Under the existing circumstances, the fuzzy inference system combines these criteria to estimate the severity of fuzzy carbon climate. This example shows how T–S models can fore- cast how climatic factors would affect it. These models, which make use of fuzzy logic to rep- resent the intricate interactions between sea level rise, wave energy, and erosion susceptibility, provide light on the possible threats that climate change may pose to coastal communities.

From Eq (1), the global carbon cycle can be seen to operate like a nonlinear augmented system whose outputs depend on time [29,30] which in turn influences its temperature nonlinearly. This system represents the active part of the carbon cycle. The matrix 𝔹 presents all trans- fer rates between system compartments and all mass inputs into it; its vector s accounts for mass inputs to it. A portion of its activity as a component of the carbon cycle is represented by this compartmental mechanism. Therefore, in terms of ocean sediments and geological reser- voirs, the atmosphere, terrestrial biosphere, and ocean are open in [31]. The temperature of the surface functions f are dependent on the state of carbon cycle activities, solar radiation, and other radiative forcing agents ℝ [32]. Some presumptions are listed below before mov- ing on to the core controllability and stability. In Sect 5, the authors expand the method to a worldwide carbon–climate control network, using the fuzzy model presented here as the basis for building interconnected control strategies. Assumption 1. All diagonal elements are negative. Assumption 2. All other variables other than diagonal elements entries are positive. Assumption 3. Sum of all columns are positive. 5 Novel approach for control theory interconnected Global Climate–Carbon Network In this section, the authors apply current control frameworks to the global climate–carbon system (e.g., [36] on congestion control in compartmental networks). Our contribution is

to adapt these concepts to the nonlinear, stochastic, and multi–scale dynamics of the Earth’s carbon cycle, whereas previous work has mostly concentrated on artificial or isolated sys- tems. In particular, the authors combine a compartmental carbon–climate model with fuzzy logic–based membership rules, allowing for adaptive control of carbon flows and greenhouse gas emissions in the face of uncertainty. By creating a closed–loop, feedback–oriented strat- egy that recommends shorter-horizon, adaptive control actions, this fusion enables us to go beyond long–term, scenario–driven projections. Therefore, we have developed completely PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 13/ 30

PLOS One Design of global climate control based on fuzzy systems new mathematical control laws, but rather because we have extended and reframed existing approaches for use in climate feedback management, where socioeconomic decision horizons, nonlinearities, and incomplete observability present particular difficulties. In order to address the issue of controlling the global climate–carbon network, we will now enhance the model of our plant to incorporate control signals denoted as u(t) and noise represented as p(t). The original mapping function 𝟋c will now involve the consideration of two additional variables. 𝟋c ∶ = (s0, 𝜈, u, p) ↦ s (7) The expression 𝟋c may be extremely complex, encapsulating the climate mechanism’s non- autonomous, unpredictable, multi–scale, and stochastic properties. We now isolate in u(t) parameters that are controllable, such as emissions from fossil fuels and decreases in emis- sions, carbon storage in biological products and earth’s reservoirs, and radiation from the sun management, even though 𝜈(t) still represents outside factors that affect the system’s behav- ior, such as variations in solar activity or Earth’s rotation. Additionally, the authors distin- guish between model unreliability and process disturbance using the vector–valued measure p(t). We usually only have access to a limited collection of data and measurements y(t) to com- prehend the framework, and we frequently do not know the full state s(t) of the entire system. The findings, which come from a measurement network, provide information on a number

of factors, including gross manufacturing, atmospheric CO2 concentrations, and atmospheric surface temperature. We now provide a mapping between these observations and the state of the system. 𝟋y ∶ = (s, u, 𝜔) ↦ s (8) From the above (Eq 8), the outcome may be influenced by the inputs u(t), which in turn can be influenced by measurement noise 𝜔(t). The combination of 𝟋c and 𝟋y forms our model, which is impacted by the inputs u(t) and output (y(t)) has been observed. Conse- quently, the task that society is confronted with is to ascertain the necessary course of action for u(t) in the coming years, such as for t ∈ [2020, 2100], to mitigate the risk of hazardous warming. Remark 3. To effectively address climate change, certain key variables and parameters must be controlled. These can be grouped into two main categories: Emissions of greenhouse gases and Climate Mitigation Techniques. Here’s a detailed breakdown: • Greenhouse Gas Emissions (GHGs). • Climate Mitigation Techniques. The primary causes of the burning of fossil fuels (power plants, automobiles), industrial oper- ations, deforestation, and changes in land use have an impact on control methods through the use of renewable energy, enhanced energy efficiency, forest restoration, and tree planting. On the other side, carbon sequestration can be described by planting trees and restoring forests to absorb CO2. The effectiveness is rely on the highly in suitable regions, with long-term benefits. Secondly, Soil Carbon Sequestration have capability to enhancing soil management practices to increase

carbon storage, which significant effect on potential, especially in agricultural regions. This fac- tor can further improving the efficiency of energy use in buildings, transportation, and industry. Reduces energy demand and emissions, cost-effective with immediate benefits. Effective control PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 14/ 30

PLOS One Design of global climate control based on fuzzy systems of these variables and parameters involves a combination of reducing GHG emissions, enhanc- ing carbon sequestration, and exploring innovative climate mitigation techniques. Each strategy’s effectiveness can vary based on geographical, technological, and economic factors. A compre- hensive and integrated approach, supported by strong policies and international cooperation, is essential to achieve significant climate mitigation outcomes. 5.1 Designing control systems involves the process of creating control laws Measurements are mapped to control actions through a control law 𝕂. Control laws are typ- ically designed by tuning parameters or design structures using properties or system behav- ior. The majority of previous studies of closed-loop control have focused on controlling cli- mate or socio-ecological systems [33,34]. In all of these studies, linear or linearized models are employed and/or linear feedback control methods are utilized, with proportional–integral controllers and their modifications being the most commonly used. Many applications have been successfully implemented with PI controllers. The significant limitation of this method is the requirement that the system remain near the point at which it has been linearized, i.e., the point where the nonlinear system was linearized. Climate change, however, is by its very nature nonlinear. It is possible to exploit nonlinear interactions for control by linearizing

around a specific operating point, eliminating critical nonlinear interactions, which are criti- cal for prediction. It is also important to note that disturbances and uncertainties are likely to cause significant changes to the system and render the controller invalid as a result. A model– based control approach appears to be promising and can have a greater impact given the exis- tence of realistic climate models. Using a simple model as part of the model–based control strategy, [35] provide a good example of this concept. In addition to minimization or maxi- mization of the control objective, The control work as established by the control rule 𝕂 itself may likewise be penalized by u(t). When using a compartmentalized nonlinear closed–loop controller, [36] showed how to prevent mass congestion in compartmental networks automat- ically. To maximize the network’s throughput, reservoirs that temporarily store carbon can be designed and implemented to maximize the carbon management strategy. The controller can figure out how much mass can enter the network and calculate mass allowances. We think this control mechanism can be helpful as a model worldwide system for reducing climate change and the management of carbon. 6 Simulation test scenarios By contrasting the framework proposed by [36], which attempts to prevent congestion in compartmental networks, the authors demonstrate the effectiveness of closed–loop control in this example. The idea behind global CO2 cycling is that has been transferred across several

compartments before being released into the deep ocean. Our goal is to prevent the atmo- spheric compartment from overflowing when we release carbon from fossil fuels. The sur- face of the ocean and grassland biosphere exchange carbon with the atmosphere, but they are only able to capture and digest a certain quantity of it. Fig 11 shows the behavior of net fluxes between the deep seafloor and the surface, allowing us to develop a controller that will indicate the amount of carbon from fossil fuels that may enter the atmosphere. In this case, temperature feedback is not taken into account for convenience. This paper presents a modified version of [37,38] simple nonlinear global carbon cycle model. This can be seen in Fig 11 as the dashed rectangle within the green box, which repre- sents the following three carbon components: PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 15/ 30

PLOS One Design of global climate control based on fuzzy systems Fig 11. Nonlinear global carbon–cycle fuzzy control scheme using output feedback. https://doi.org/10.1371/journal.pone.0333846.g011 1. Atmospheric (𝜉A). 2. Terrestrial biosphere (𝜉T). 3. Surface ocean (𝜉S). Three carbon compartments are contained in the model: atmosphere (𝜉A), terrestrial bio- sphere (𝜉T), and surface ocean (𝜉S). Deep ocean and fossil fuel reserves are designated by the letters D and F. The amount of Carbon contents is always expressed in PgC and fluxes in PgC year–1. Adding carbon to the system is the result of two external fluxes. As 𝜆D→S is constant, As a result of the combustion of fossil fuels, CO2 is released into the atmosphere, whereas 𝜆F→A = 𝜆F→A(t) is depend upon the time, fossil fuel burns and releases carbon diox- ide into the atmosphere. Fig 6 shows how 𝜆F→A = u(t)p is defined by the input control u(t) and the output human demand p. Surface seawater and deep ocean water are the only two places where carbon can leave the system. A flux of this kind is denoted by the number 𝜆S→D. As a result of the model, the following fluxes exist from compartment X to compartment Y, all given in PgC year –1. 𝜆A→T = 60 (𝜉A/700)𝛾1 , 𝜆A→S = 100𝜉A/700 𝜆T→A = 60𝜉T/3000, 𝜆S→A = 100 (𝜉S/1000)𝛾2 𝜆S→D = 45𝜉S/1000, 𝜆D→S = 45. (9) It is controlled by two parameters, 𝛾1 = 0.2 and 𝛾2 = 10.0 which control the fluxes between the atmosphere and biosphere, as well as between the surface ocean and atmosphere. Three

PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 16/ 30

PLOS One Design of global climate control based on fuzzy systems Algorithm 1 FCC–I: Fuzzy closed-loop carbon–climate control. Given inputs T = {t0, … , tmax}, Δt, initial state 𝜉(t0) = [𝜉0 A, 𝜉0 T, 𝜉0 S ]⊤, demand p(t)≥0, rule base ℜ, membership functions (MFs), flux maps 𝜆●→●(⋅), and constants 𝜆S→D, 𝜆D→S. Choose bounds for tunable Θ = {𝛾1, 𝛾2, 𝜅max, MF thresholds/widths}. 1: Phase 1: Control variable configuration 2: ForAll 𝜃 ∈ Θ do ▷ 𝜃 groups 𝛾1, 𝛾2, 𝜅max, MF cut–points 3: For k = 1, 2, … , Tmax do 4: Randomly draw MF cut–points and 𝜅max from 𝜃-bounds 5: Using current (𝛾1, 𝛾2), compute one-step flux maps: 𝜆A→T = 60(𝜉A/700)𝛾1 , 𝜆A→S = 100(𝜉A/700), 𝜆T→A = 60(𝜉T/3000), 𝜆S→A = 100(𝜉S/1000)𝛾2 6: Build fuzzy antecedents from MFs; fire rules R to get weights; defuzzify → zfuzzy 7: Define controller shape 𝜓(𝜅): 𝜓(𝜅) = ⎧⎪⎪ ⎨ ⎪⎪⎩ g(𝜅), 𝜅 ≤ 𝜅max 1, 𝜅 > 𝜅max where g is cubic Hermite with g(0) = 0, g(𝜅max) = 1, g′(0) = 1/𝜅max, g′(𝜅max) = 0 8: Compute feedback y(t) = 𝜆S→D – 𝜆D→S and buffer update. 𝜅 ← 𝜅 + Δt (y – 𝜓(𝜅) p) 9: Go to previous Step. 10: Phase 2 : Output (Control) Determination 11: Set 𝜓(⋅) and MFs from HL; simulate over [t0, tmax]: 12: for dot = t0, t0 + Δt, … , tmax 13: u(t) ← 𝜓(𝜅(t)); 𝜆F→A(t) ← u(t) p(t) 14: ̇ 𝜉A ← 𝜆T→A + 𝜆S→A – 𝜆A→T – 𝜆A→S + 𝜆F→A 15: ̇ 𝜉T ← 𝜆A→T – 𝜆T→A; ̇ 𝜉S ← 𝜆A→S – 𝜆S→A – 𝜆S→D + 𝜆D→S 16: 𝜉 ← 𝜉 + Δt [̇𝜉A, ̇ 𝜉T, ̇ 𝜉S]⊤ 17: y(t) ← 𝜆S→D – 𝜆D→S; 𝜅 ← 𝜅 + Δt (y – u p) 18: end for 19: Return tuned parameters, trajectories {𝜉(t)}, control u⋆(t), and buffer 𝜅(t)

ordinary differential equations can now be used to describe the model, for t > t0 = 1765. ⎧⎪⎪⎪⎪ ⎨ ⎪⎪⎪⎪⎩ ̇ 𝜉A = 𝜆T→A + 𝜆S→A – 𝜆A→T – 𝜆A→S + 𝜆F→A(t),̇ 𝜉T = 𝜆A→T – 𝜆T→Ȧ 𝜉S = 𝜆A→S – 𝜆S→A – 𝜆S→D + 𝜆D→S (10) As shown in (10) the right–hand side of (9) depends on t and also on the state matrix 𝜉(t) = ⎛ ⎜ ⎝ 𝜉A(t) 𝜉T(t) 𝜉S(t) ⎞ ⎟ ⎠ T . In other words, fluxes between compartments are nonlinearly depen- dent upon the contents of those compartments. Here are the results of Eq (1), assuming 𝔹 = PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 17/ 30

PLOS One Design of global climate control based on fuzzy systems 𝔹(ℂ, t) is a state– and time–dependent compartmental matrix: ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ –𝜉–1 A (𝜆A→T + 𝜆A→S) 𝜉–1 T 𝜆T→A 𝜉–1 S 𝜆S→A 𝜉–1 A 𝜆A→T –𝜉–1 T 𝜆T→A 0 𝜉–1 A 𝜆A→S 0 –𝜉–1 S (𝜆S→A + 𝜆S→D) ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ (11) and m(t) ∶= (𝜆F→A(t), 0, 𝜆D→S)T , and then the plant fits into (1) without considering temper- ature. From the global climate carbon emissions theory, the authors presents the new fuzzy rules in Table 1. To describe the nature A compartmental nonlinear time–dependent system can be stated as follows: {̇ 𝜉(t) = 𝔹(ℂ, t)𝜉(t) + m(t), t > t0, 𝜉 (t0) = 𝜉0 (12) From the equilibrium point of the uncontrolled system (u(t) = 1), we ran it at the point 𝜉0 = (700, 3000, 1000)T from 1765 forward until 1900, at which point the control function was turned on, u(t) = 𝜓(𝜅(t)). The global carbon cycle was assumed to be controlled by humanity after 1900, as all fossil fuel emissions were allowed until this date. After selecting the fuzzy rules from the Sect 4, the effectiveness of our proposed algorithms can be found in Figs 12, 13, and 14 respectively. In Fig 12, the response of atmospheric (𝜉A) with and without fuzzy rules can be analyzed. While in Figs 13 and 14 presented the response of terrestrial biosphere (𝜉T) and surface ocean (𝜉S) with and without fuzzy rules. Fuzzy logic and fuzzy rules play a significant role in modeling and understanding complex systems like global climate. Here are the key aspects of how fuzzy rules contribute to global climate stud-

ies, e.g., Handling Uncertainty and Ambiguity, Modeling Complex Relationships, Integrating Diverse Data Sources, Improving Climate Prediction Models, Adaptive Systems, and Risk Assess- ment and Decision Support. However, there are some practical examples that can be effective by using our new proposed algorithm in Climate Change Impact Studies, Weather Forecast- ing, and Environmental Monitoring. In summary, fuzzy rules are invaluable in global climate studies for their ability to handle complexity, integrate diverse data, and improve predictive models, ultimately aiding in more effective climate management and decision–making. 6.1 Prediction analysis of external/internal air temperature Two figures are showing the predicted vs. measured air temperature data and the associated prediction error are included in Figs 15 and 16. The fact that the two lines closely follow one Table 1. Fuzzy rules for global climate system. Rule No. IF Condition 1 IF Condition 2 THEN Result 1 Temperature is High CO2 is High Chance of High Temperature 2 Temperature is Low CO2 is Low Chance of High Snowfall 3 Temperature is High Terrestrial biosphere (𝜉T) is High Increase the risk of Species Extinction 4 Temperature is Low Terrestrial biosphere (𝜉T) is Low Decrease the risk of Species Extinction 5 Sea surface is High Terrestrial biosphere (𝜉T) is Low Increase in Biodiversity 6 Sea surface is Low Terrestrial biosphere (𝜉T) is High Decrease in Biodiversity 7 Wind speed is High Surface ocean (𝜉S) is Large Structural damage in Buildings & Trees