Developing a decision support system for sustainable urban planning using machine learning-based scenario modeling

Abstract

Urbanization is rapidly transforming cities, posing intricate issues for sustainable urban development. Conventional urban planning techniques frequently encounter difficulties in incorporating several variables, including environmental, social, and economic issues. This research presents an innovative decision support system (DSS) aimed at tackling these difficulties through the application of machine learning and fuzzy decision-making methodologies. The approach utilizes random forest recursive feature elimination (RF-RFE) to determine the most significant criterion from a collection of 15 parameters, such as environmental impact, energy efficiency, social equity, and economic viability. The logarithmic percentage change-driven objective weighting (LOPCOW) approach is employed to determine the weights of these criteria according to their importance. The evaluation based on relative utility and nonlinear standardization (ERUNS) method is employed to rank different urban development methods, utilizing q-rung fuzzy sets (q-ROFS) to address uncertainty and imprecision. The analysis indicates that Green Urbanization is the most advantageous option among the assessed alternatives, demonstrating its compatibility with sustainable development objectives. The proposed DSS integrates machine learning-based feature selection with fuzzy multi-criteria decision-making, providing a comprehensive framework for navigating the intricacies of urban planning and facilitating data-driven, sustainable urban development decisions.

Introduction

Urbanization and the fast expansion of civilization have made it more difficult than ever for cities throughout the globe to achieve sustainable development¹. The pursuit of sustainable urban development² is a global objective that has sparked a variety of lines of thought and a reevaluation of city dynamics. The three main pillars of society, environment, and economics form the basis of this conceptual investigation. Cities must rethink and restructure the delicate interactions between ecosystem, inhabitants, the economy, politics, and society since they are dealing with complex demands and expectations. To adapt to the shifting landscape of urban sustainable development, a stronger reliance on the unique attributes and possibilities that come with urban life is required³. Apart from meeting quantifiable physical requirements such as air quality indices, green space ratios, population densities, and resource consumption, a thriving and growing city must also promote interpersonal relationships and human interactions to enhance its overall quality⁴. Rong et al.⁵ present Du-Bus, a real-time bus waiting time estimation system leveraging multi-source data, demonstrating enhanced accuracy and reliability in intelligent transportation systems. From the perspective of human life’s needs, Agenda 21 (1992), the framework for sustainable development in the twenty-first century, incorporates the environment into the social and economic domains. As the pinnacle of advancements in both the environmental and socioeconomic spheres, it emphasis’s the essential role that a flourishing existence plays in sustainable development. The World health organization (WHO) launched the healthy city (HC) initiative in 1997 with the goal of bringing urban sustainable development to life in line with this viewpoint⁶.An integrative approach to urban development and administration, sustainable urban planning aims to balance social, economic, and environmental goals. It entails developing resilient, resource-efficient urban landscapes that can sustain thriving, healthy communities. places a strong emphasis on small, transit-oriented development that promotes walking, protects open areas, and lessens urban sprawl. uses natural systems-like parks, green roofs, and urban forests-in urban planning to control storm water, improve air quality, and increase ecosystem services. Emphasis’s reducing waste, encouraging the use of renewable resources, and minimizing energy and water use. addresses concerns including affordable housing, access to green areas, and community involvement in planning procedures to guarantee that all inhabitants can benefit from urban growth. increases urban areas’ ability to endure and bounce back from social, economic, and environmental shocks, such as natural catastrophes, climate change, and economic downturns. The importance of sustainable urban planning concepts in tackling the many problems associated with urbanization is becoming more widely acknowledged. But putting them into reality calls for combining a number of methods and instruments that can efficiently assess and rank sustainable activities.

When considered in urban location, environmental impacts reduction is related to application of strategies that mitigate environmental repercussions of urbanization. Such tactics frequently focus on means for reducing the emission of the air, the water and the soil by employing cleaner technology and higher standards of law and more effective means of handling waste. For instance, there is something known as permeable pavements, rain gardens; these are examples of green infrastructures may help manage storm water, and fight pollution of water. Reduction of heat island effect strategies which include cool roofing materials and green roofs lower the urban temperature thus reducing energy use and negative impacts on health Green transport options such as walking, bicycling and the use of public transport instead of cars reduces air pollution and greenhouse gas emissions. Two common concepts that integrate land use and transportation are transit-oriented development (TOD), predetermining that spatial development measures are friendly to local animals, preserve the balance of ecological niches, and enhance natural environment. Conservation of biological diversity in urban regions can be achieved by green avenues and urban timber zones. With the help of renewable energy, efficient isolation, and utilization of passive solar light, urban planning potentially can reduce the energy consumption. Thus, practical activities in this field include retrofitting of old buildings and adherence to energy efficient construction regulations. Both of these strategies are critical to reducing emissions and improving sustainability of cities. As Norton and Soon highlight the common image of the endeavor of making urban landscapes into bases of health, sustainability, resilience, intelligence, inclusion, and accommodate is well served by the often summary idea of quality of life (QOL) , this is inevitably a contingent experience of residents in the dynamic context of the development of cities. Qi et al.⁷ examine the relationship between daily precipitation and wind speed over China’s coastline, providing critical evidence for coastal climate dynamics. This gross concept excellently intertwines ecological, social and economic factors which define life in cities. Quality of life or QOL is one of the fundamental success factors in sustainable urban development that has become necessary because of the threatening ecological challenges facing the entire world. The “Life-City” concept (LC), a novel paradigm for the construction of a city that outperforms existing standards of urban planning and construction, is the focus within this framework.

For this reason, urban planning has been complicated as cities grapple with social demands, the environment and unprecedented enlargements. As the focus on sustainability increased, the demand for complex that integrates social aspects such as justice or well-being along with economical and environmental factors arises. Albeit useful, these classical approaches to decision making are inadequate at describing urban systems and therefore, the decisions made lack the necessary optimality level set out by cities’ sustainable development goals. But much more sophisticated DSS that is capable in dealing with uncertainty, in integrating several criteria, and adapting to changing urban condition is indeed urgently required.

The Solitaire approach and other forms of MCDM methods applied to sustainable development choices in urban planning context has been underlined in current studies. It allows decision makers to assess and compare different aspects such as profitability, fairness, environment impact and energy yield. Some of these studies, however, use conventional methods that either generalize the urban systems’ complexity, or use little data, which in turn makes their conclusions not as accurate or efficient as desired during this time. However, most of the current planning models are of relatively more effectiveness in episodic decision making because they focus on a fixed set of conditions and cannot update themselves according to dynamics of urban systems. This work proposes a novel DSS for sustainable urban planning which uses ERUNS approach, LOPCOW method, and machine learning feature selection to address these challenges. Random Forest for feature removal helps to make a decision quicker and more accurate as it provides certainty that only the most valuable variables are included. However, with the usage of the q-ROFS, there is an added level of complexity since more effective managing of uncertainty present within the assessment process. In addition, this framework enables the incorporation of current data during the analysis, and can be modified as the environment evolves due to ongoing trends in urban scenarios.

The incorporation of q-ROFS into our DSS greatly improves its capacity to tackle the uncertainties present in urban planning. In contrast to conventional fuzzy or intuitionistic fuzzy sets, q-ROFS provide an enhanced level of flexibility and uncertainty in representing subjective or incomplete data. This positions them as highly effective in understanding the intricate and frequently unclear elements that impact sustainable urban development. Nonetheless, acknowledging specific limitations is crucial. The precision and reliability of decisions are significantly influenced by accurately defined membership functions and the caliber of stakeholder contributions, which can occasionally be inconsistent or imprecise. Moreover, elevating the q-rung parameter may introduce additional computational complexity, which could hinder the clarity of results for those who are not technically inclined. To tackle these challenges, integrating hybrid methods that merge q-ROFS with probabilistic or stochastic approaches may offer a more thorough framework for modeling uncertainty. Furthermore, employing methods like sensitivity analyses and scenario testing strengthens decision-making reliability by assessing system stability across different assumptions and data inputs. Future investigations could enhance the applicability of q-ROFS by examining their implementation in various urban environments and incorporating iterative approaches, like Delphi techniques, to unify stakeholder viewpoints. The developments guarantee that the suggested system continues to be flexible and efficient in facilitating sustainable urban planning.

Literature review

The aim of MCDM to finding the best solutions taking into account as many factors as possible is one of the largest components of decision science. To do this, a team of specialists has to assess each option according to the many criteria and then, to put it simply and to the point, come to the conclusion. However, in today’s complicated and demanding environment, uncertainty affects almost every decision-making process. Therefore, it is crucial to consider the possibility of discrepancies if one is involved in the interpretation process. Data managers find it difficult to provide precise answers when dealing with data that is inaccurate, incomplete, or otherwise poorly defined. Their work may demonstrate these difficulties. In the real world, these kinds of difficulties may sometimes manifest themselves in a number of tasks, such as assessing providers, selecting choices, and organising and classifying items. Originally introduced by Zadeh⁸, the fuzzy set (FS) paradigm is widely used to express uncertainty in real-world interactions. A fuzzy set is used to assign a real number between 0 and 1 to every single object in the universe. However, FS does not always work as intended. For example, it does not work as intended when a DM is presented with human opinion in the variety of positive and negative values. To address these issues, Atanassov⁹ created an intuitionistic fuzzy set (IFS) with membership degree (MG) and non-membership degree (N-MG) values. The need that the values of MG and N-MG fall within the unit interval between 0 and 1 is one of the many disadvantages of this novel technique. The modelling of uncertain information in IFSs is more successful than in FSs due to the superior environment. It is the better atmosphere that makes this feasible.

Yager¹⁰ was the first to suggest the “Pythagorean fuzzy set” (PFS), which is an extension of the original IFS. The goal of this update was to expand the range of values that may be assigned to both MG and N-MG. The PFS is comparable to the IFS as it is composed of MG and N-MG values. However, the PFS could provide decision makers greater freedom in selecting MG and N-MG values since the total of their squares is limited to the range [0, 1]. In order to address the issue of unclear data, which occurs when the sum of the MG and N-MG q-powers is less than or equal to 1, Yager¹¹ developed the idea of q-ROFSs. “to offer a general theoretical framework to represent imprecise information while, at the same time and to give users more freedom in expressing their belief about membership grade,” Yager said in his paper. He scored twice. In comparison to IFSs and PFSs, q-ROFSs are definitely a more comprehensive kind of system architecture. In order to aggregate assessment data, this paper aims to provide a “q-rung orthopair fuzzy weighted averaging (q-ROFWA) operator and the q-rung orthopair fuzzy weighted geometric (q-ROFWG) operator”¹². Liu et al.^13,14 concurrently provided further ideas for q-ROF AOs. These ideas may be able to include the judgement data provided by DMs by using the “Bonferroni mean” and the “power Maclaurin symmetric mean.” Wei et al. conducted a study on the q-ROF “Heronian mean” AOs in MCDM¹⁵. Peng et al.¹⁶ used energy-efficient technology for a building project after their investigation of exponential operation and AOs for q-ROFS utilising a unique scoring function. Liu et al.¹⁷ apply machine learning to simulate urban land subsidence, offering innovative solutions for environmental management in urban areas.

A probabilistic linguistic q-ROF technique was presented by Saha et al. et al.^18,19 and was generalised. Dombi and Bonferroni’s test contains the definition of AOs. Du²⁰ supplied the Minkowski type distance measurements for q-ROFSs. The Euclidean, Chebyshev, and Hamming distances were among these distance measurements. Furthermore, the possibility of using Minkowski-type distance measurements for MCDM tasks was investigated. Several recent advances in simulation modelling (SM) have focused on the presentation of a logical SM for q-ROFSs. This is by far the most significant issue in relation to the others. Shi et al.²¹ develop an ensemble regression model integrating polynomial regression-based decision trees to analyze tunnel boring machine data for enhanced predictive performance.

According to Ecer and Pamucar²², a new method for the MCDM methodology has been introduced. This approach unites DOBI, which is used for alternative evaluation, and LOPCOW, which is used for weighing, into a single solution. The objective weighing approach, called LOPCOW, has the potential to reduce the inherent instability of entropy weight systems. As a consequence, the target audience will find the criteria weights more palatable and reliable. You may always rely on the outcomes, regardless of the situation. The approach minimises the number of calculation and execution steps that are even remotely possible while producing a good result. The process’s remarkable practicality, clarity, and understandability make all of this feasible. This is the approach’s most important benefit. Zhang et al.²³ assess the techno-environmental-economical impacts of energy storage allocation in urban forms, contributing to low-carbon district planning. The data structure has fewer dimensional disparities, or gaps, and the criteria’s features, such its cost-benefit status, have less of an effect. In order to extend the LOPCOW methodology into the fermatean cubic fuzzy environment, Niu et al.²⁴ used EDAS methodologies. In order to assess and compare the performance of Indian companies’ IPOs, Biswas and Joshi²⁵ used the LOPCOW technique. Biswas et al.²⁶ published a strategy that calls for hiring salespeople with previous experience. Nila and Roy²⁷ integrated the LOPCOW, full consistency method (FUCOM), and DOBI techniques into their MCDM model, which allowed them to rank options using triangular fuzzy numbers while also evaluating criteria. Pan et al.²⁸ propose a two-step optimization model for location-allocation in health planning, showing significant improvements in spatial accessibility to tertiary hospitals. In their literature study, Uluta et al.²⁹ made the following assertions. In the aforementioned study, a hybrid MCDM model is established using techniques including MCRAT, MEREC, the LOPCOW, and the preference selection index (PSI). This model’s goal, along with the other workers’, is to determine which natural fibre insulation option is the most practical. Gorcun et al.³⁰ presented the LOPCOW and MARCOS methods for assessing and choosing eco-friendly refrigerated road vehicles (IFSs) for use in food logistics. In order to assess the possible risks associated with research and development projects in offline programming systems for industrial robots, the authors Rong et al.³¹ created an MCDM model that made use of LOPCOW-ARAS and interval-valued Fermat fuzzy information.

Allaoui et al.³² used a two-stage hybrid multi-objective analytical hierarchy process decision-making technique to examine the sustainable agro-food supply chain design. Li et al.³³ predict socioeconomic indicators using structural urban imagery, demonstrating the utility of machine learning in urban planning and development. In order to lower the overall cost of the supply chain and its environmental effect, Mele et al.³⁴ looked at an example of a sugarcane supply chain. Thus, the authors created a DSS based on a mixed integer linear programming model. Naik and Suresh³⁵ examined the difficulties in developing agri-retail supply networks that are sustainable. The project’s main goal was to figure out how to integrate small farmers into an agri-retail supply chain that is sustainable. Banaeian et al.³⁶ used an integrated multi-criteria decision-making tool, VIKOR and GRA, to choose green suppliers in a fuzzy environment using a case study from the agri-supply chain business. It was shown that fuzzy GRA may provide comparable outcomes with less computational work. Banasik et al.³⁷ used a multi-objective optimisation linear programming technique to assess trade-offs between economic and environmental concerns in a case study of agricultural supply chains using mushrooms. The productivity of manufacturers and farmers who rely heavily on short-term planning during harvest season was the subject of Ahumada and Villalobos’³⁸ investigation of the operational model for scheduling the harvest and distribution of perishable agricultural items. According to the research, the required money might be collected by controlling the trade-off between the product’s cleanliness during transit and the additional labour and expenses incurred by the farmer. Gokarn and Kuthambalayan³⁹ used exploratory factor analysis and the ISM technique to identify 33 issues related to waste reduction in the Indian agri-food supply chain.

The evaluation and optimisation of supply chains for sustainable agriculture have greatly improved as a result of earlier research, however there are still some significant issues that have not been resolved. In the paragraphs that follow, these issues will be covered in more detail. Allaoui et al.³² and Mele et al.³⁴ state that their work’s main goal is to use hybrid multi-objective decision-making models to maximise supply chain costs and environmental impacts. The economic and environmental factors are the primary focus of these models. However, one of the most crucial elements of the agriculture sector’s decision-making process-the absorption of uncertainty-is not sufficiently addressed by them. Although Gardas et al.⁴⁰ examined challenges in post-harvest and agri-retail supply chains, their research lacked a comprehensive framework that connected a variety of sustainability criteria into a logical model. The application of MCDM techniques in handling of sustainability challenges has been embraced in the present literature on DSS for urban planning to a greater extend. However, there exists several gaps that this paper intends to fill. First, While MCDM approaches have been employed in numerous studies for urban planning, the most of them do not consider actual time data which are effective in dynamic urban environment and rely on archive data. The complexity of urban systems is also in most cases disregarded by decision frameworks which reduce the relevance of the solutions by simplifying the criteria or having limited choices for evaluation. Moreover, it is a challenge that the urban planner, with their reliance on customary fuzzy logic modes face in handling the doubt and confusion arising from the convoluted social, environmental and economic complications.

Additionally, although random forests, a class of machine learning techniques, have been successfully used in feature selections of MCDM, little is understood of how to introduce these approaches to sustainable urban planning models. Most scientific papers do not report a systematic way of selecting features which leads to models that are either excessively complex, or, conversely, too simplified. In addition, criteria in urban planning priorities are normally assigned by the weightage by the perceived view by experts therefore making it somewhat biased and the objectives of decisions are not wholly objective. To address these gaps, this study presents a DSS framework of ERUNS methodology, the LOPCOW method, and the use of machine learning to eliminate unimportant features. The RF-RFE selection improves the accuracy of the model and reduces the excess of complicated features in the object thanks to the effective filtration of those characteristics that are most informative. The application of q-ROFS provide a better picture of the degrees of fuzziness represented in decision makes and an enhanced method for handling the uncertainties in the criteria in urban planning. The study also faces the issue dealing with the REAL TIME DATA problem by suggesting a framework that can be fixed to accept data in real time, and therefore make the study very valuable as a research study useful for long term planning for cities. The described LOPCOW method for defining the objective weights free from disadvantage of the traditional expert-weighting techniques ensure the evaluation of criteria in an open and unbiased manner, while also providing the potential drawbacks of the conventional expert-based weighing techniques. In addition to addressing current research gaps, this study offers a thorough, adaptable, and scalable approach to sustainable urban planning decision-making. Breiman⁴¹ created the popular machine learning method known as Random Forest (RF), which employs an ensemble of unpruned decision trees for regression or classification. The candidate set of variables is selected at random from all variables in a fixed number at each split, and the RF method is constructed using a bootstrap sampling of the data⁴². The majority classification voting or average of their outputs determines the final outcome of an input sample in the RF algorithm. It’s crucial to remember that the RF classifier may identify many variable significance metrics. Out-of-Bag (OOB) samples are input samples that are not utilised during training; they are the data that are not included in each tree. The OOB error estimate is used to provide an objective assessment of the accuracy, and the omitted data is used to evaluate the classifiers’ generalisation ability.

Using different statistical and knowledge discovery in data methods to reduce noise and redundant data is one of the most popular and widely used strategies in many high-dimensional machine learning issues⁴³. Recursive feature elimination (RFE) using different classifiers is a well-liked KDD and data mining strategy for machine learning issues to minimise the amount of features^44,45. RFE is an efficient technique that chooses a subset of the most relevant features to train the model and eliminates the weakest feature or features until the desired number of features is obtained, according to Rao & Rao⁴⁶. Research investigations shown that this approach aids in eliminating co-linearity and dependencies from any model⁴⁷. The use of several classifiers, including support vector machines⁴⁸, partial least squares⁴⁹, Kernel Fisher discriminant analysis⁵⁰, and Naïve Bayes⁵¹, is one of the main components of the RFE approach. Lin et al.⁵² introduced a landscape-driven patch-based cellular automaton (LP-CA) model that integrates landscape patterns and cell-level agreement, significantly improving the accuracy of urban land-use change simulations. This model provides valuable support for urban planning by enabling better prediction of urban expansion under different scenarios. Xiao et al.⁵³ employed GPS trajectory data to develop emergency rescue stations customized to the spatiotemporal patterns of outdoor adventure tourists, accounting for their seasonal preferences and activity hotspots. Utilizing a genetic algorithm, they determined best placements for rescue stations, providing essential insights for improving outdoor safety and disaster readiness.

Motivation and contribution

Motivation

The growing pace of urbanization presents an urgent need for cities to develop in a sustainable and efficient manner, balancing economic growth with environmental and social responsibilities. However, urban planning decisions are often hindered by the complexity and uncertainty of integrating multiple factors, such as infrastructure development, resource management, social equity, and environmental protection. Traditional methods struggle to cope with the dynamic and multifaceted nature of these decisions, making it difficult to prioritize strategies that ensure long-term sustainability. The impetus for this research is a recognized lack of an adaptive solution that can help urban planners make informed decisions based on the available data. First, feature selection based on machine learning algorithms is expected to help identify the most important decision factors, while the use of fuzzy MCDM will help urban planners receive valuable recommendations on how to rank and choose potential strategies for further development of cities. The segregation of RF-RFE makes it easy to identify the most important criteria; this leads to reduction of dimension and increased efficiency of the system. Of course, using the LOPCOW method to determine weights for each criterion allows for the proper quantization of those criteria based on each criterion’s role in planning. The ERUNS method, which focuses on the implementation of q-ROFS, makes it possible for the system to manage uncertainties and imprecision, and which provide a high level of flexibility and stability for performing the decisions-making.

Contribution

• The paper integrates machine learning-based feature selection RF-RFE with fuzzy MCDM methods to create a robust DSS for sustainable urban planning.

• By using RF-RFE, the system identifies the most influential criteria among a set of 15, reducing dimensionality and improving the efficiency of the decision-making process.

• The LOPCOW method is applied to accurately calculate the weights of selected criteria based on their significance and impact on urban planning decisions.

• The ERUNS method is used for ranking urban development alternatives, incorporating uncertainty management through q-ROFS.

• The use of q-ROFS allows the DSS to handle uncertainty and imprecision in criteria evaluation, providing a flexible and adaptable framework for decision-making under complex, dynamic conditions.

• The DSS facilitates informed, evidence-based decision-making, providing urban planners with actionable insights to prioritize sustainable urban development strategies.

• Relationship to previous research:

  • This paper outlines the foundational contributions of MCDM methods, encompassing both traditional approaches and recent advancements in fuzzy logic extensions, such as FS, IFS, and q-ROFS.

  • As said, Zadeh, Atanassov, and Yager’s investigations laid the groundwork for our work on uncertainty in decision-making.

• Differences from previous research:

  • We explained how our study addressed earlier research’s lack of real-time data integration, simplicity of complicated urban systems, and subjective expert-weighting methodologies.

  • Our DSS new combination of q-ROFS, machine learning and RF-RFE, and LOPCOW methodology outperforms previous urban planning frameworks.

  • The incorporation of machine learning for feature selection significantly improves model efficiency and robustness, distinguishing our research from studies that depend exclusively on traditional MCDM methods.

• 1. Lack of real-time data handling in urban planning: Many existing studies in urban planning and DSS primarily rely on archived data, overlooking the dynamic nature of urban environments. As a result, these studies fail to consider the evolving and real-time aspects of urban development, making them less effective in addressing current urban planning challenges. The gap here is the need for integrating real-time data into urban planning decision-making processes, allowing for more accurate and adaptable solutions.

• 2. Inadequate consideration of complex urban system interactions: The interactions between various urban criteria, such as social, environmental, and economic factors, are oversimplified by the majority of urban planning decision frameworks. This simplification may result in suboptimal decision-making, as it fails to account for the interdependencies and complexity of urban systems. There is a research void in the development of a more comprehensive model that accurately represents these intricate relationships, thereby ensuring more effective urban planning solutions.

• 3. Restricted utilization of sophisticated machine learning methods: Although machine learning techniques like random forests have gained popularity in feature selection for various domains, their application in sustainable urban planning models has been limited. Furthermore, the challenge of selecting the most relevant features from high-dimensional datasets is often underexplored. This research gap is addressed by incorporating advanced machine learning algorithms, such as Random Forest Recursive Feature Elimination (RF-RFE), to optimize the feature selection process and improve the accuracy of decision-making models.

• 4. Inadequate handling of uncertainty in decision-making: Uncertainty is an intrinsic element of urban planning, particularly when addressing inadequate, vague, or ambiguous data. Although fuzzy logic models and intuitionistic fuzzy sets are employed in decision-making, they frequently prove inadequate for managing increasingly intricate uncertainty. The research gap pertains to the utilization of advanced fuzzy systems, specifically q-ROFS, which provide superior techniques for addressing uncertainty and imprecision in decision-making.

• 5. The proposed DSS incorporates three innovative methods RF-RFE the LOPCOW and the ERUNS methods to tackle the intricate challenges associated with sustainable urban planning. RF-RFE was selected for its capacity to manage large data sets by integrating the strengths of Random Forest with the iterative process of RFE, thereby ensuring the identification of the essential characteristics while reducing overfitting and preserving interpretability. The LOPCOW method was chosen for its objective, data-driven approach to weighting and ranking criteria. It employs logarithmic percentage changes to derive weights based on intrinsic data variability, especially useful for balancing diverse and often conflicting sustainability criteria. The ERUNS method enhances these approaches by integrating uncertainty analysis into the evaluation process, allowing decision-makers to evaluate the robustness of urban sustainability scenarios in dynamic and uncertain contexts. These methods collectively create a comprehensive DSS that addresses the drawbacks of traditional approaches, including subjectivity, overfitting, and insufficient consideration of uncertainty, thereby offering urban planners a more precise, transparent, and actionable instrument for sustainable and resilient urban development.

Structure of the paper

The structure of this paper begins in Section “Preliminaries” with an introduction to the q-rung fuzzy set, providing a foundation for handling uncertainty and vagueness in multi-criteria decision-making, which is essential for evaluating complex urban planning alternatives. Section “Algorithm based on e RF-RFE technique with LOPCOW-ERUNS” describes the detailed algorithmic steps used, including the Random Forest feature elimination method for initial criterion selection, the LOPCOW method for calculating criterion weights, and the ERUNS method for ranking alternatives. Section “Applications of the proposed framework” focuses on the case study, explaining the implementation of the developed algorithm to assess sustainable urban planning scenarios, with emphasis on practical application and evaluation of the selected criteria and alternatives. Finally, Section “Conclusion” presents the results of the case study, followed by a conclusion that discusses the findings, highlights the model’s efficacy in sustainable urban planning, and suggests future research directions. This structure ensures a clear flow from theoretical background to practical application, providing a comprehensive approach to decision-making in sustainable urban planning.

Preliminaries

Definition 2.1

¹¹ Consider q-ROFS R in X and it is characterized as

$$R=\{\langle {\kappa ^{\varpi }},{D^{\chi }}_{R}({\kappa ^{\varpi }}),{{R}^{\chi }}_{R}({\kappa ^{\varpi }})\rangle :{\kappa ^{\varpi }}\in X\}$$

where ${D^{\chi }}_{R},{{R}^{\chi }}_{R}:X\rightarrow [0,1]$ interpret the MD and NMD of the alternative ${\kappa ^{\varpi }}\in X$ and $\forall ~ {\kappa ^{\varpi }}$ we have

$$0\le {D^{\chi }}^q_{R}({\kappa ^{\varpi }})+{{R}^{\chi }}^q_{R}({\kappa ^{\varpi }})\le 1.$$

Definition 2.2

¹² Let $\breve{{{Y}^\tau }}_{1}= \langle {D^{\chi }}_{1},{{R}^{\chi }}_{1}\rangle$ and $\breve{{{Y}^\tau }}_{2}= \langle {D^{\chi }}_{2},{{R}^{\chi }}_{2}\rangle$ be q-ROFNs. $\sigma> 0$, Then

• (1) $\breve{{{Y}^\tau }}_{1}^c= \langle {{R}^{\chi }}_{1}, {D^{\chi }}_{1} \rangle$

• (2) $\breve{{{Y}^\tau }}_{1} \vee \breve{{{Y}^\tau }}_{2}= \langle max\{{D^{\chi }}_{1}, {{R}^{\chi }}_{1}\}, min\{{D^{\chi }}_{2}, {{R}^{\chi }}_{2}\} \rangle$

• (3) $\breve{{{Y}^\tau }}_{1} \wedge \breve{{{Y}^\tau }}_{2}= \langle min\{{D^{\chi }}_{1}, {{R}^{\chi }}_{1}\}, max\{{D^{\chi }}_{2}, {{R}^{\chi }}_{2}\} \rangle$

• (4) $\breve{{{Y}^\tau }}_{1} \oplus \breve{{{Y}^\tau }}_{2}= \langle ({D^{\chi }}_{1}^{q}+{D^{\chi }}_{2}^{q}-{D^{\chi }}_{1}^{q}{D^{\chi }}_{2}^{q})^{1/q},{{R}^{\chi }}_{1}{{R}^{\chi }}_{2}\rangle$

• (5) $\breve{{{Y}^\tau }}_{1} \otimes \breve{{{Y}^\tau }}_{2}= \langle {D^{\chi }}_{1}{D^{\chi }}_{2},({{R}^{\chi }}_{1}^{q}+{{R}^{\chi }}_{2}^{q}-{{R}^{\chi }}_{1}^{q}{{R}^{\chi }}_{2}^{q})^{1/q}\rangle$

• (6) $\daleth \breve{{{Y}^\tau }}_{1} = \langle (1-(1-{D^{\chi }}_{1}^{q})^{\daleth })^{1/q},{{R}^{\chi }}_{1}^{\daleth } \rangle$

• (7) $\breve{{{Y}^\tau }}_{1}^{\daleth }= \langle {D^{\chi }}_{1}^{\daleth }, (1-(1-{{R}^{\chi }}_{1}^{q})^{\daleth })^{1/q} \rangle$

• (8) $\breve{{{Y}^\tau }}_{1} \ominus \breve{{{Y}^\tau }}_{2} =\left( \root q \of {\frac{{D^{\chi }}_{1}^{q}-{D^{\chi }}_{2}^{q}}{1-{D^{\chi }}_{2}^{q}}}, \frac{{R}_{1}}{{R}_{2}}\right)$, if ${D^{\chi }}_{1} \ge {D^{\chi }}_{2}, {R}_{1} \le \min \left\{ {R}_{2}, \frac{{R}_{2} \pi _{1}}{\pi _{2}}\right\}$

• (9) $\breve{{{Y}^\tau }}_{1} \oslash \breve{{{Y}^\tau }}_{2} =\left( \frac{{D^{\chi }}_{1}}{{D^{\chi }}_{2}}, \root q \of {\frac{{R}_{1}^{q}-{R}_{2}^{q}}{1-{R}_{2}^{q}}}\right)$ if ${R}_{1} \ge {R}_{2}, {D^{\chi }}_{1} \le \min \left\{ {D^{\chi }}_{2}, \frac{{D^{\chi }}_{2} \pi _{1}}{\pi _{2}}\right\}$

Definition 2.3

¹¹ Let $\breve{{{Y}^\tau }}= \langle {D^{\chi }},{{R}^{\chi }} \rangle$ be the q-ROFN, “score function” (SF) $\Lambda$ of $\breve{{{Y}^\tau }}$ is defines as

$$\begin{aligned} \Lambda (\breve{{{Y}^\tau }})= {D^{\chi }}^{q}-{{R}^{\chi }}^{q} \end{aligned}$$

(1)

$\Lambda (\breve{{{Y}^\tau }}) \in [-1,1 ]$.Its q-ROFN score determines its ranking; a high score suggests that q-ROFN is significant. On the other hand, the SF may sometimes be detrimental to q-ROFN. This indicates that the SF-based q-ROFN assessment is inadequate.

Definition 2.4

¹¹ Let $\breve{{{Y}^\tau }}= \langle {D^{\chi }},{{R}^{\chi }} \rangle$ be the q-ROFN, then an “accuracy function” AF $H^{\Gamma }$ of $\breve{{{Y}^\tau }}$ is defines as

$$H^{\Gamma }(\breve{{{Y}^\tau }})= {D^{\chi }}^{q} + {{R}^{\chi }}^{q}$$

$H^{\Gamma }(\breve{{{Y}^\tau }}) \in [0,1 ]$.

Definition 2.5

Consider $\breve{{{Y}^\tau }}= \langle {D^{\chi }}_{\breve{{{Y}^\tau }}}, {{R}^{\chi }}_{\breve{{{Y}^\tau }}} \rangle$ and ${\lambda }= \langle {D^{\chi }}_{\lambda }, {{R}^{\chi }}_{\lambda } \rangle$ are two q-ROFN, and $\Lambda (\breve{{{Y}^\tau }}), \Lambda ({\lambda })$ are the SFs of $\breve{{{Y}^\tau }}$ and ${\lambda }$, and $H^{\Gamma }(\breve{{{Y}^\tau }}), H^{\Gamma }({\lambda })$ are the AFs of $\breve{{{Y}^\tau }}$ and ${\lambda }$, respectively, then

• (i) If $\Lambda (\breve{{{Y}^\tau }})> \Lambda ({\lambda })$, then $\breve{{{Y}^\tau }}> {\lambda }$

• (ii) If $\Lambda (\breve{{{Y}^\tau }}) = \Lambda ({\lambda })$, then

if $H^{\Gamma }(\breve{{{Y}^\tau }})> H^{\Gamma }({\lambda })$ then $\breve{{{Y}^\tau }}> {\lambda }$,

if $H^{\Gamma }(\breve{{{Y}^\tau }}) = H^{\Gamma }({\lambda })$, then $\breve{{{Y}^\tau }}= {\lambda }$.

Always keep in mind that the SF might have values between -1 and 1. Prioritised relations have been advantageously used in the following studies: further SF is $\mathscr {H}(\breve{{{Y}^\tau }})= \frac{1+ {{D^{\chi }}}_{\breve{{{Y}^\tau }}}^q \, - \,{{R}^{\chi }}_{\breve{{{Y}^\tau }}}^q }{2}$. We can see that $0 \le \mathscr {H}(\breve{{{Y}^\tau }}) \le 1$.

Algorithm based on e RF-RFE technique with LOPCOW-ERUNS

Step 1:Introducing the q-RFNs dataset, where alternatives are evaluated based on a variety of criteria and represented by ${B^{S}_{i}}$ (for $i=1,2,...,f$). If $j=1,2,...,e$, then ${{Q^{S}}_{j}}$. DMs provide the following decision matrix: ${D}=[{G_{ij}}]_{f\times e}$

.

In our dataset, which we refer to as q-RFNs, each ${Q_{ij}}$ is a $\left( {D}_{ij},{R}_{ij}\right)$. A variety of criteria, each indicated by an index between i and j, have been used to assess the alternatives in this collection. Additionally, as Table 2 shows, we have improved these claims by using language words that decision makers have supplied, such as Table 1 for knowledge.

Table 1 Linguistic Terms.

Table 2 Key decision-makers for sustainable urban planning.

Step 2: The weights of the DMs and the scoring function may be obtained using Eq. (1). After obtaining the scores, you need to enter them into Eq. (2). This approach includes a comprehensive evaluation that conforms to the framework for decision-making.

$$\begin{aligned} B^{S}_{pq}= \frac{\sum _{p}^{3} ( {D^{q}_{pq}}-{R^{q}_{pq}})}{\sum _{q}^{3}({\sum _{p}^{3} ( {D^{q}_{pq}}-{R^{q}_{pq}})})}\quad i = 1, 2, \ldots , f; \ j = 1, 2, \ldots , e; \end{aligned}$$

(2)

Step 3: Equation (3), which is expressed as $M = [M_{ij}]_{u \times v}$, serves as a guide for constructing the whole decision matrix.

$$\begin{aligned} \operatorname {q-RFSSPWA}\left( {\kappa ^{\varpi }}_{1}, {\kappa ^{\varpi }}_{2}, {\kappa ^{\varpi }}_{3}\right) = \left( \root q \of {1-\left( \sum _{\wp =1}^{3} \mu ^{\zeta }_{\wp }\left( 1-\left( D_{{\kappa ^{\varpi }}_{\wp }}\right) ^q\right) ^{\sigma }\right) ^{\frac{1}{\sigma }}}, \root q \of {\left( \sum _{\wp =1}^{3} \mu ^{\zeta }_{\wp }\left( {R}_{{\kappa ^{\varpi }}_{\wp }}\right) ^{q \sigma }\right) ^{\frac{1}{\sigma }}} \right) \end{aligned}$$

(3)

Step 4: Use the given Eq. (4) to get the combined decision matrix score.

$$\begin{aligned} {V(Q)_{ij}}= {D^{q}_{ij}}-{R^{q}_{ij}} \end{aligned}$$

(4)

Step 5: Recursive Feature Elimination with Random Forest

The procedures for normalising the decision matrix, using Recursive Feature Elimination (RFE) with a Random Forest model, and determining the significance of certain criteria are described in this section.

Step 5.1: Start with all features, $\textbf{X} = \{x_1, x_2, \ldots , x_n\}$ corresponding to each alternative in the form of LiDFNs. Then set the number of features to select, let’s say k.

Step 5.2: Calculate the importance of each feature by using Equation (5).

$$\begin{aligned} I_j = \frac{1}{m} \sum _{i=1}^{m} x_{j} \end{aligned}$$

(5)

Step 5.3: In order to create test and training samples, 80% of the input data related to the first collection of features was randomly selected as the training dataset, while the remaining 20% was designated as the test dataset. The random seed for random sampling is used to standardise the RF-RFE technique’s random process.

Step 5.4: To show the original criteria together with their normalised accuracy scores, standard deviation values, and RF-RFE important measurements, we lastly produce a results Table .

LOPCOW method

Step 6: The normalized matrix $T^{\alpha }=\left( {\mu }_{i j}^{G}\right) _{r\times s}$ was created by transforming the score matrix as follows:

$$\begin{aligned} {\mu }_{i j}^{G}=\left\{ \begin{array}{l} \frac{V(Q)_{i j}-V(Q)_j^{-}}{V(Q)_j^{+}-V(Q)_j^{-}}, \hspace{2mm}\text{ if } j \in S_{b}, \\ \frac{V(Q)_j^{+}-V(Q)_{i j}}{V(Q)_j^{+}-V(Q)_j^{-}}, \hspace{2mm}\text{ if } j \in S_{c}, \end{array}\right. \quad i = 1, 2, \ldots , f; \ j = 1, 2, \ldots , e; \end{aligned}$$

(6)

where $J^{+}=\max _i V(Q)_{i j}$ and $V(Q)_j^{-}=\min _i V(Q)_{i j}$ , $S_{b}$ and $S_{c}$ represent the cost-type and benefit-type criteria, respectively.

Step 7:

The percentage values (P) for each criterion are found using Eq. 7.

$$\begin{aligned} {\nu ^{\eta }}{j}=\left| \ln \left( {\frac{\sqrt{\frac{\sum _{i=1}^{m} {{\mu }_{i j}^{G}}_{i j}}{m}}}{{B^{\vartheta }}_{j}}}\right) .100\right| \quad j = 1, 2, \ldots , f; j = 1, 2, \ldots , e; \end{aligned}$$

(7)

where m is the number of selections and the SD, which is calculated as follows, is ${B^{\vartheta }}_{j}$.

$$\begin{aligned} {B^{\vartheta }}_j=\sqrt{\frac{\displaystyle \sum _{i=1}^m\left( {\mu }_{i j}^{G}-\bar{\omega }_j\right) ^2}{m}}, ~~where ~~\bar{\omega }_j=\displaystyle \sum _{i=1}^m {{\mu }_{i j}^{G}}/m \quad j = 1, 2, \ldots , e; \end{aligned}$$

(8)

Step 8:

Developed the weights shown below for the goals:

$$\begin{aligned} \textrm{w}_{j}=\frac{{\nu ^{\eta }}{j}}{\displaystyle \sum _{i=1}^{m} {\nu ^{\eta }}{j}}\quad j = 1, 2, \ldots , e; \end{aligned}$$

(9)

Proposed method: ERUNS

Step 9:Equation (10) is used to standardise the elements of the matrix ${\nabla } = \left[ {V(Q)}_{i j}\right] _{m \times n}$ to the interval $[G^{\beta }, \tau ]$

$$\begin{aligned} {{\varsigma ^{\upsilon }}}_{i j} = \left( \frac{{{V(Q)}}_j^{\min }}{{{V(Q)}_{i j}}} \right) ^3 \tau + \frac{Y^{S}}{{{V(Q)}}_j^{\min }} \quad i = 1, 2, \ldots , f; \ j = 1, 2, \ldots ,e; \end{aligned}$$

(10)

Here, ${{V(Q)}}_j^{\min } = \displaystyle \min _{1 \le i \le u} ({{V(Q)}_{i j}})$. The decision-maker’s preferences and the particulars of the problem-solving process define the values of the interval $[Y^{S}, \tau ]$.

Step 10: The values of ${\nabla } = \left[ {V(Q)}_{i,j}\right]$ represents the maximum kind of criterion using the following formula: (11).

$$\begin{aligned} {\Re ^{\wp }}_{i j}= {\left\{ \begin{array}{ll} -{{\varsigma ^{\upsilon }}}_{i j}+\displaystyle \max _{1 \le i \le m}\left( {{\varsigma ^{\upsilon }}}_{i j}\right) +\displaystyle \min _{1 \le i \le m}\left( {{\varsigma ^{\upsilon }}}_{i j}\right) , \\ {{\varsigma ^{\upsilon }}}_{i j}\end{array}\right. }\quad i = 1, 2, \ldots , f; \ j = 1, 2, \ldots ,e; \end{aligned}$$

(11)

Step 11: To calculate the weighted standardised decision matrix, use equation (12).

$$\begin{aligned} {\Pi ^{\textrm{u}}}_{i j}=\frac{\exp \left( C\left( {\Re ^{\wp }}_{i j}\right) / {P}^{N}\right) w_{j}}{\sum _{j=1}^{v} \exp \left( C\left( {\Re ^{\wp }}_{i j}\right) / {P}^{N}\right) w_{j}} \quad i = 1, 2, \ldots , f; \ j = 1, 2, \ldots ,e; \end{aligned}$$

(12)

where $C\left( {\Re ^{\wp }}_{i j}\right) =\frac{{\Re ^{\wp }}_{i j}}{\sum _{j=1}^{v} {\Re ^{\wp }}_{i j}}, j \in \{1,2,3 \ldots v\}$.

Step 12:Calculate the utility degrees for the ideal and anti-ideal solutions. The $i {\text{ th } }$ option has utility degrees for both ideal and anti-ideal solutions: $\mathcal {A}_{i}^{+}=\frac{\displaystyle \prod _{j=1}^{v}\left( {\Re ^{\wp }}_{i j}\right) ^{{\Pi ^{\textrm{u}}}_{i j}}}{\displaystyle \sum _{j=1}^{v}{\Pi ^{\textrm{u}}}_{j}^{+}}$

$\mathcal {A}_{i}^{-}=-\frac{\displaystyle \sum _{j=1}^{v}{\Pi ^{\textrm{u}}}_{j}^{-}}{\displaystyle \prod _{j=1}^{v}\left( {\Re ^{\wp }}_{i j}\right) ^{{\Pi ^{\textrm{u}}}_{i j}}}+\displaystyle \max _{1 \le i \le u}\left( \frac{\displaystyle \sum _{j=1}^{v}{\Pi ^{\textrm{u}}}_{j}^{-}}{\displaystyle \prod _{j=1}^{v}\left( {\Re ^{\wp }}_{i j}\right) ^{{\Pi ^{\textrm{u}}}_{i j}}}\right) +\displaystyle \min _{1 \le i \le u}\left( \frac{\displaystyle \sum _{j=1}^{v}{\Pi ^{\textrm{u}}}_{j}^{-}}{\displaystyle \prod _{j=1}^{v}\left( {\Re ^{\wp }}_{i j}\right) ^{{\Pi ^{\textrm{u}}}_{i j}}}\right)$

Where ${\Pi ^{\textrm{u}}}_{j}^{+}=\displaystyle \max _{1 \le i \le u}\left( {\Re ^{\wp }}_{i j} \cdot w_{j}\right)$ and ${\Pi ^{\textrm{u}}}_{j}^{-}=\displaystyle \min _{1 \le i \le u}\left( {\Re ^{\wp }}_{i j} \cdot w_{j}\right) \quad (i=1,2 \ldots f; j=1,2 \ldots e)$.

Step 13: Equation (13) may be used to calculate the utility function’s values based on total utility levels.

$$\begin{aligned} \begin{aligned}&C\left( \mathcal {A}_{i}^{+}\right) =\frac{\mathcal {A}_{i}^{+}}{\mathcal {A}_{i}^{+}+\mathcal {A}_{i}^{-}} \quad i = 1, 2, \ldots , f; \\&C\left( \mathcal {A}_{i}^{-}\right) =\frac{\mathcal {A}_{i}^{-}}{\mathcal {A}_{i}^{+}+\mathcal {A}_{i}^{-}}\quad i = 1, 2, \ldots , f; \end{aligned} \end{aligned}$$

(13)

Step 14: Equation (14) calculates the evaluation scores of the alternatives using the parameter ${G^{\beta }} \in [0,1]$.

$$\begin{aligned} A S_{i}=\left( \mathcal {A}_{i}^{+}+\mathcal {A}_{i}^{-}\right) \frac{\left( 1+C\left( \mathcal {A}_{i}^{+}\right) \right) ^{{G^{\beta }}}\left( 1+C\left( \mathcal {A}_{i}^{-}\right) \right) ^{1-{G^{\beta }}}-\left( 1-C\left( \mathcal {A}_{i}^{+}\right) \right) ^{{G^{\beta }}}\left( 1-C\left( \mathcal {A}_{i}^{-}\right) \right) ^{1-{G^{\beta }}}}{\left( 1+C\left( \mathcal {A}_{i}^{+}\right) \right) ^{{G^{\beta }}}\left( 1+C\left( \mathcal {A}_{i}^{-}\right) \right) ^{1-{G^{\beta }}}+\left( 1-C\left( \mathcal {A}_{i}^{+}\right) \right) ^{{G^{\beta }}}\left( 1-C\left( \mathcal {A}_{i}^{-}\right) \right) ^{1-{G^{\beta }}}}\quad i = 1, 2, \ldots , f; \end{aligned}$$

(14)

Applications of the proposed framework

Population density is one of the key challenges and opportunities of the twenty-first century, as more and more people are becoming interested in living in cities to receive better payment, medical care and education. However, rapid urban growth is realised by several problems including environmental degradations, traffic jams, lack of adequate accommodation, depleted resource base, and increasing social inequity. Therefore, urban planners as well as policy makers are under pressure to build efficient urban settings that support economic growth, social health, and environmental conservation. In some cities despite the availability of technology in planning, and various methodologies, there is still a problem of resource allocation, increased transport jam, poor quality air, increased use of energy, and poor infrastructure among others. Furthermore, the decision making in urban planning reflects a variety of multifaceted issues that cannot be relatively easily translated into volume, priority or be solved independently of other interdependent factors such as social, environmental, economical and technological factors. The existing urban planning paradigms and principles could not deliver adequate and relevant solutions for such problems, mainly due to the fact that traditional approaches has not been able to cope with the complexities intensifying and uncertainties growing in the modern city system. Additionally, there is the superposition of a number of interests represented by numerous stakeholders, the scarcity of high quality data, and the absence of comprehensive DSSs which all create significant difficulties in the formation and putting into practice of sustainable strategies in urban planning that can be effectively used in various conditions and within reach of long-term objectives.

Along this line, a machine learning-based scenario modeling deployed within a DSS provides the most suitable way to solve for problems of sustainable urban planning. As we shall later see, such a system can assist in decision making by running a set of possible urban developmental strategies and evaluating the likely long term effects of such a closure/implementation and provide pointers towards the best course of action. Yet, constructing an efficient DSS for urban planning that could take into consideration numerous factors, could work with the uncertainty, and present feasible decisions still has to be recognized as a significant and unresolved issue. Consequently, the objective of this research is to design and implement an integrated DSS that utilizes machine learning regarding the scenario approach to empower the urban planner towards making informed decisions for sustainable city evolution. The system will make a comprehensive comparison of the different strategies for the development of urban areas by considering numerous factors that include physical environmental, social, economic, and cogent factors such as energy consumption and or utilization, public health, and financial feasibility among others. It is in this context that the present study aims to provide a contribution to tackling the problems of current urban design and including the following recommendations for generating better, more sustainable, and less vulnerable cities in the future.

Definition of alternatives

In this study, five quite different urban planning options are compared with the aim of advancing sustainability. All the alternatives are different scenarios of urban development, which is tried to accomplish specific criteria with the consideration of environmental, economic, and social factors.

• ${B^{S}}_1$: Transit-oriented development (TOD)

• Description: Established to promote development based on well-organized systems of transport that minimize the use of individual cars.

• Objective: For enhanced mobility and environmental sustainability by using a combined public transport centre.

• Advantages: Eases congestion, pollutes less and improves access.

• Disadvantages: High capital intensity in transport infrastructure and can result in congestion in those areas with densities.

• ${B^{S}}_2$: Smart City Integration

  • Description: Uses the interconnections of computers and physical devices - IoT, computer intelligence - AI and big data to boost urban frameworks and services.

  • Objective: For purposes of enhancing operational efficiency, cutting on the expenses which are incurred during operations, and making the best use of resources through the utilization of technology.

  • Advantages: Reduces costs and overall time consumption, improves data-oriented decision-making, and improves quality of life.

  • Disadvantages: High cost of implementation, and maintenance as well as some privacy issues.

• ${B^{S}}_3$: Green Urbanization

  • Description: Strengthens green infrastructure by focusing on increase in green areas, green energy, green constructions, etc.

  • Objective: In order to promote environmental conservation and fostering of a sustainable physical environment for a city.

  • Advantages: Reduces air pollution levels, preserves the gene pool and beautifies cities.

  • Disadvantages: Cost of initial implementation is high and there are certain restrictions in the usage of land since considerable area is dedicated to green space.

• ${B^{S}}_4$: Eco-Industrial Development

  • Description: Deals with promoting the creation of environmentally friendly areas for production that encourage environmentally friendly industrial activities.

  • Objective: And as measures towards minimizing industrial pollution and wastage, their accomplishment of environmental sustainable initiatives in specified manufacturing areas.

  • Advantages: Reduces pollution in the environment, encourages waste recycling, and the sustainable production within industries.

  • Disadvantages: May slow down industrial development because of high standards of environmental policies and can also be expensive to undertaking.

• ${B^{S}}_5$: Mixed-Use Zoning

  • Description: Organizes both living, working, and play in close relation to one another within the city so that the parts form a complete and compact whole.

  • Objective: To decrease the amount of travel time, increase pedestrian accessibility and create a friendly and cohesive environment.

  • Advantages: Cuts the time taken in travelling, encourages contacts within the society and effectively use of space.

  • Disadvantages: The above type may face some legal issues and may take long time and planning to address the various zoning requirements.

Definition of criteria

• ${Q^{S}}_1$ : Environmental Impact

  • Explanation: This criterion evaluates the adverse this issue in evaluating and deciding on urban development with special reference to ecosystems, water, and air.

  • Advantages: Enhances conservation of biophysical resources, controls pollution and conserves nature resources.

  • Disadvantages: Can be harder to quantify because if different conditions in the environment.

• ${Q^{S}}_2$: Energy Efficiency

  • Explanation: It concentrates particularly to efficient use of energy in tackling urban infrastructures that include the importance of renewable energy and energy-saving technologies.

  • Advantages: Decreases expenses, effects a cut in greenhouse gas emissions, raises awareness for green energy.

  • Disadvantages: May need large initial capital investment for systems improvement.

• ${Q^{S}}_3$: Noise Pollution Control

  • Explanation: Evaluates measures for controlling and minimising noise pollution with a special focus to crowded human settlements.

  • Advantages: Improves population density, recreation, and quality of life by lowering severities of stress-related and noise sickness illnesses.

  • Disadvantages: Difficult to supervise and control especially in ‘hot’ areas where high population is expected.

• ${Q^{S}}_4$: Economic Viability

  • Explanation: Analyses the City’s financial effectiveness to support urban projects and its ability to correspondingly generate economic growth, and, thus, new job vacancies.

  • Advantages: Retained for efficiency and fosters Ivestment attraction while supporting employment and lasting efficiency.

  • Disadvantages: May fail to focus on proximate economic issues and may have the tendency of pursuing long-term benefits.

• ${Q^{S}}_5$: Social Equity and Accessibility

  • Explanation: Assesses how well resources and services are distributed across populations to ensure inclusivity.

  • Advantages: Enhances social inclusion, supports fair access to resources and services.

  • Disadvantages: Quantifying social equity can be challenging due to subjective factors.

• ${Q^{S}}_6$: Resilience and Adaptability

  • Explanation: Focuses on the urban area’s ability to adapt to environmental and social changes, including natural disasters and climate shifts.

  • Advantages: Enhances long-term stability, helps cities recover from adverse events.

  • Disadvantages: Requires investment in resilient infrastructure, which can be costly.

• ${Q^{S}}_7$: Water Management

  • Explanation: Examines water usage, conservation strategies, and the management of stormwater and wastewater.

  • Advantages: Conserves valuable water resources and reduces waste, enhancing sustainability.

  • Disadvantages: Requires substantial infrastructure and maintenance costs.

• ${Q^{S}}_8$: Air Quality Control

  • Explanation: Monitors and manages urban air pollution sources, aiming to reduce emissions and improve air quality.

  • Advantages: Improves public health, reduces respiratory issues, and enhances overall livability.

  • Disadvantages: Enforcement can be challenging, and requires consistent monitoring and regulation.

• ${Q^{S}}_9$: Transportation Efficiency

  • Explanation: Assesses the efficiency of public and private transportation, focusing on reducing traffic congestion and enhancing public transit options.

  • Advantages: Reduces travel time and emissions, improves quality of life, and supports mobility.

  • Disadvantages: Infrastructure development is costly and time-consuming.

• ${Q^{S}}_{10}$: Resource Efficiency

  • Explanation: Focuses on the efficient use of resources like water, energy, and materials to minimize waste and maximize sustainability.

  • Advantages: Reduces resource depletion, lowers costs, and promotes green technology.

  • Disadvantages: Implementation can require substantial initial investments in green infrastructure.

• ${Q^{S}}_{11}$: Public Health

  • Explanation: Focuses on the health outcomes of urban residents, including access to healthcare, recreational spaces, and pollution control.

  • Advantages: Directly improves residents’ quality of life and reduces healthcare costs.

  • Disadvantages: Direct impacts on health can be challenging to measure and link to specific planning decisions.

• ${Q^{S}}_{12}$: Green Space Allocation

  • Explanation: Examines the availability and quality of parks, green belts, and recreational areas in urban planning.

  • Advantages: Enhances biodiversity, improves air quality, and offers recreational spaces for residents.

  • Disadvantages: Limits the amount of land available for commercial or residential purposes.

• ${Q^{S}}_{13}$: Land Use and Zoning Flexibility

  • Explanation: Involves adaptable planning that can respond to future needs, demographic changes, and technological advancements.

  • Advantages: Provides resilience against urban sprawl and enables flexible development over time.

  • Disadvantages: Requires detailed planning and may lead to regulatory and zoning challenges.

• ${Q^{S}}_{14}$: Job Creation

  • Explanation: Evaluates urban planning initiatives based on their potential to create new employment opportunities.

  • Advantages: Promotes economic growth and supports community development.

  • Disadvantages: Job sustainability can vary based on economic conditions and industry volatility.

• ${Q^{S}}_{15}$: Climate Resilience

  • Explanation: Focuses on the capacity of urban systems to adapt to climate-related challenges, such as extreme weather events.

  • Advantages: Minimizes disaster impacts, reduces future risk, and ensures city longevity.

  • Disadvantages: Requires substantial upfront investment, and benefits may not be immediately visible.

Experimental results

Step 1: Tables 3, 4, and 5 provide a tabular record of the DMs’ remarks. They used linguistic terms from the DMs to communicate their ideas.

Table 3 Decision matrix for decision maker 1.

Table 4 Decision matrix for decision maker 2.

Table 5 Decision matrix for decision maker 3.

Step 2: The weights of DMs assess the significance ascribed to each DM’s area of competence. This case study consists of three DMs. Equation (2) was utilised to explain the q-RFS linguistic values for the several DMs shown in Table 6.

Table 6 Linguistic terms about DMs.

Step 3: Individual tables are methodically collected and categorised according to the various DMs’ perspectives in order to build the aggregated q-RFNs. Equation (3) defined the q-RFWG operator, which was used to integrate them. Table 7 shows the results.

Table 7 Aggregated decision matrix.

Step 4: The score matrix $S^{*}$ was calculated using equation (4) as given in Table 8.

Table 8 Score of aggregated decision matrix.

Step 5: Recursive Feature Elimination with Random Forest

This section describes how to normalise the decision matrix, use Recursive Feature Elimination (RFE) with a Random Forest model, and determine the relevance of specified criterion.

Step 5.1 5.2, 5.3, 5.4: Feature importance results given in Table 9. The updated data is given in the Table 10.

Table 9 Feature Importance and Selection Results.

Table 10 Updated aggregated score matrix.

Step 6:

Equation (6) generated the normalised matrix $T^{\alpha }$ from the score matrix $M^*$. Table 11 presents the findings.

Table 11 Normalized score matrix.

Step 7:

SD and P are computed using Eqs. (8) and (7), with results shown in Table 12.

Table 12 Standard deviation.

Step 8:

The objective weights of the criteria are determined using Eq. (9) and displayed in Table 13.

Table 13 Weights of criteria.

Step 9, 10: Equation (10) is used to standardise the matrix $\nabla$ elements to the interval [0, 1]. The criteria are of the max kind, and the values of $\mathfrak {X}^{N}=\left[ {{\varsigma ^{\upsilon }}}_{i j}\right]$. Equation (11) modifies $_{m \times n}$, as seen in the matrix below.

$${{\varsigma ^{\upsilon }}}_{i j}=\begin{bmatrix} 1.0000 & 0.1618 & 0.2081 & 0.2204 & 0.7464 & 0.3569 \\ 0.0029 & 0.1090 & 0.3562 & 0.4508 & 0.2987 & 1.0000 \\ 0.1383 & 0.0412 & 0.2089 & 1.0000 & 0.1947 & 0.3658 \\ 0.0400 & 1.0000 & 0.4533 & 0.5691 & 0.4321 & 0.3496 \\ 0.0033 & 0.1699 & 1.0000 & 0.4888 & 1.0000 & 0.4423 \\ \end{bmatrix}$$

$${\Re ^{\wp }}_{i j}=\begin{bmatrix} 1.0000 & 0.8795 & 1.0000 & 0.2204 & 0.4482 & 0.3569 \\ 0.0029 & 0.9322 & 0.8519 & 0.4508 & 0.8960 & 1.0000 \\ 0.1383 & 1.0000 & 0.9991 & 1.0000 & 1.0000 & 0.3658 \\ 0.0400 & 0.0412 & 0.7548 & 0.5691 & 0.7626 & 0.3496 \\ 0.0033 & 0.8713 & 0.2081 & 0.4888 & 0.1947 & 0.4423 \\ \end{bmatrix}$$

Step 11: Equation (12) calculates the weighted standardised decision matrix ${\Pi ^{\textrm{u}}}_{i j}$, as given below.

$$\Gamma =\begin{bmatrix} 0.2561 & 0.2252 & 0.2561 & 0.0564 & 0.1148 & 0.0914 \\ 0.0007 & 0.2255 & 0.2061 & 0.1090 & 0.2168 & 0.2419 \\ 0.0307 & 0.2221 & 0.2219 & 0.2221 & 0.2221 & 0.0812 \\ 0.0159 & 0.0164 & 0.2998 & 0.2261 & 0.3029 & 0.1389 \\ 0.0015 & 0.3945 & 0.0942 & 0.2213 & 0.0882 & 0.2003 \end{bmatrix}$$

$${\Pi ^{\textrm{u}}}_{i j}=\begin{bmatrix} 0.1262 & 0.2171 & 0.2406 & 0.2679 & 0.1472 & 0.0010 \\ 0.1245 & 0.2153 & 0.2398 & 0.2694 & 0.1469 & 0.0011 \\ 0.1274 & 0.2182 & 0.2415 & 0.2667 & 0.1483 & 0.0009 \\ 0.1238 & 0.2168 & 0.2421 & 0.2681 & 0.1476 & 0.0012 \\ 0.1251 & 0.2179 & 0.2402 & 0.2690 & 0.1468 & 0.0008 \end{bmatrix}$$

$${\Pi ^{\textrm{u}}}_{i j}=\begin{bmatrix} 0.1262 & 0.2171 & 0.2406 & 0.2679 & 0.1472 & 0.0010 \\ 0.1245 & 0.2153 & 0.2398 & 0.2694 & 0.1469 & 0.0011 \\ 0.1274 & 0.2182 & 0.2415 & 0.2667 & 0.1483 & 0.0009 \\ 0.1238 & 0.2168 & 0.2421 & 0.2681 & 0.1476 & 0.0012 \\ 0.1251 & 0.2179 & 0.2402 & 0.2690 & 0.1468 & 0.0008 \end{bmatrix}$$

Step 12, 13, 14: Table 14 displays the utility degrees of the ideal, anti-ideal, and utility functions. Equation (14) generates the appraisal scores of the alternatives using the parameter ${G^{\beta }}=0.5$.

Table 14 Results for final ranking.

Sensitive analysis

An investigation Table 15 depicts the complex interplay in our decision-making system between parameters ${{P}^{N}}$ and ${G^{\beta }}$. Figure 1 illustrates how the ranking varies with k while leaving ${G^{\beta }}$ unchanged. Figure 2 provides a line graph under the same situations. Figure 3 show 3D surface plots mapping the appraisal score (AS). Taken together, these statistics give a full understanding of how alternative representations and parameter modifications effect evaluation and ranking results. Furthermore, it is clear how computationally efficient the technique is since, in dynamic contexts and big datasets, changing parameters seldom affects ranking results, ensuring fast and reliable decision-making. To expand the approach’s flexibility and utility across a variety of decision-making situations, future research should look into adaptive parameter techniques tailored to specific datasets or choice scenarios.

Table 15 The impact of the parameter ${{P}^{N}}$ and ${G^{\beta }}$ on result.

Fig. 1

Bar graph of ranking with fixed ${G^{\beta }}$ and varying ${{P}^{N}}$.

Fig. 2

Line graph of ranking with fixed ${G^{\beta }}$ and varying ${{P}^{N}}$.

Fig. 3

Behavior of each alternative by variations of parameters.

Comparative analysis

The experiment proves the methodology’s reliability and robustness in an FF scenario by comparing the RF-RFE technique with LOPCOW-ERUNS outcomes to those of other well-known decision-making methodologies. This comparison shows that the method in Table 16 is resilient and reliable. Decision-makers may assess the validity and reliability of the RF-RFE technique with LOPCOW-ERUNS approach by comparing its results to those of other methods such as WASPAS, DEA, GLDS, CRITIC, and VIKOR procedures. Sensitivity tests may be done on each approach to have a better understanding of the reliability and robustness of the decision-making outcomes. These trials include adjustments to variables such as fuzzy function membership and criteria weights. Decision-makers should have trust in the RF-RFE technique with LOPCOW-ERUNS methodology’s applicability and usefulness in English teaching contexts, as this cross-case research supports its reliability in a variety of decision-making situations.

Table 16 Comparison with some exiting.

Marginal limitations of the method

This study, while advancing a novel decision support framework for sustainable urban planning, has some marginal limitations. First, the evaluation includes only five alternatives, which may not fully represent the range of options available in diverse urban planning scenarios. Expanding the scope of alternatives could provide a broader comparison, allowing decision-makers to explore a wider array of solutions. Additionally, although the q-ROFS effectively manage uncertainty, they may not capture the full complexity of highly subjective or context-specific criteria in urban planning. Refining these fuzzy set models could enhance the decision-making accuracy, especially for criteria involving nuanced social or environmental impacts.

Another marginal limitation is the dependence on expert judgment in the LOPCOW method for weighting criteria. While this method aims to reduce bias, slight variations in expert perspectives could influence the outcome, highlighting the potential for subjective bias. Moreover, the static scenario modeling applied in this study does not fully address the dynamic, rapidly changing nature of urban environments. Real-time or adaptive modeling would make the framework more relevant for continuous, long-term urban planning efforts. Finally, although the current model offers an effective approach to multi-criteria evaluation, its complexity may pose challenges for non-expert users. Simplifying the interface and enhancing user accessibility could make it a more practical tool for a wider range of urban planning professionals.

Discussion

The findings obtained from the proposed DSS for sustainable urban planning offer important theoretical and practical contributions to the development of smart city frameworks. This approach integrates RF-RFE, the LOPCOW method, and the ERUNS technique to create a robust framework for evaluating urban planning alternatives, emphasizing sustainability. This work significantly contributes to resolving enduring challenges in urban planning. Prior research has emphasized the capacity of machine learning to improve decision-making in urban environments; nonetheless, challenges including explainability, model complexity, and inadequate incorporation of domain-specific knowledge remain unresolved. The DSS addresses these challenges through the use of RF-RFE to identify the most pertinent criteria, thus enhancing the decision-making process and minimizing dimensional complexity. This simplification enhances computational efficiency and offers urban planners an accessible framework that does not necessitate extensive technical knowledge. The ERUNS methodology, which utilizes advanced fuzzy logic techniques, introduces a significant degree of flexibility in addressing the uncertainty that is characteristic of urban planning scenarios. The DSS utilizes q-ROFS to provide a detailed representation of ambiguous and subjective factors, especially those related to sustainability. The integration of fuzzy logic improves the system’s capacity to handle qualitative inputs, including expert opinions and stakeholder insights, which are frequently crucial in urban development initiatives. Sustainability serves as a fundamental goal in urban planning, involving intricate interrelationships among environmental, social, and economic dimensions. This study presents a fuzzy logic-based approach that enhances the formulation and prioritization of interconnected criteria, thereby providing a more comprehensive and realistic decision-making framework. This ability to process and integrate diverse inputs effectively addresses a gap identified in prior research, where conventional systems frequently encountered difficulties in accommodating qualitative or uncertain data. The LOPCOW method, utilized for determining criterion weights, provides a systematic and unbiased approach for assessing the relative significance of each factor. This methodological choice prevents biases associated with traditional expert-based approaches, resulting in fairer and more objective evaluations. The sensitivity analyses performed in this study illustrate the framework’s adaptability to different contexts. Customizing the DSS for various urban scenarios enables decision-makers to examine distinct strategic implications and align their actions with specific sustainability objectives. The DSS offers a transparent and objective decision-making framework, facilitating informed choices among stakeholders that are consistent with sustainability goals. The machine learning feature elimination process guarantees that decisions rely on the most pertinent factors, whereas the fuzzy logic system provides adaptability to variations in urban conditions and developmental priorities. The model’s compatibility with real-time data provides a distinct advantage, facilitating ongoing updates and refinements as new information emerges. The adaptability of the DSS renders it a versatile solution for addressing the diverse and evolving challenges encountered by cities globally.

Conclusion

The LOPCOW method adopted in the determination of the criterion weights is logical, to estimate the degree of importance of each factor. This is evidence that more impartial weighting is possible, with this method, by which fair judgments can be made for sustainable urban development. In the present study, based on the empirical context analysis, sensitivity analysis is carried out so as to show that the framework can be customized according to the various situations and it can offer different implications to the decision-makers by presenting the potential options under different contexts and emphases. It also reduces some gaps that have been noted in the recent literature. The difficulties of applying high-level machine learning models when making decisions on urban development, specifically, the need for application of automated tools which are aimed at simplifying the process of model identification as well as interpretation. Where RF-RFE is applied, the final decision is made, thus eliminating the need for planner intervention as we photocopy important features that have an impact on decision making as a result of this kind of work. Furthermore, Page et al. (2024) noted that in their analysis of potential and strategic AI applications for future urban sustainability, existing planning frameworks lack adequate means to fully capture uncertainties. These uncertainties, otherwise pose significant challenges with respect to the reliability of the DSS and factors such as fuzzy logic and machine learning help in controlling the above uncertainties of the system. In practical terms, the findings of our work are enormous. It essentially means that urban planners and policymakers will be able to use the proposed DSS to reach decisions that will be sustainable. Our framework makes the decision process more objective and transparent compared to different alternatives by a machine learning feature elimination process. Also, due to the fuzziness of the logic system, the model is rather immune to changes in urban conditions and objectives of sustainable development, which makes it adjusted to a rather wide range of different cities with renewed priorities. This does not arise from guesswork because our approach is structured and the methodology guarantees real-time updates and enhanced models from new data on the ever-evolving urban environment.

• Future research may incorporate real-time data from IoT sensors and smart city infrastructure into decision-making frameworks. This would enable urban planners to modify their strategies according to dynamic factors, including traffic patterns, air quality, and other essential elements affecting urban planning. The challenges associated with data collection, integration, and model robustness in the context of real-time information warrant further investigation.

• Enhancing the predictive capabilities of the DSS may be advantageous by integrating sophisticated methodologies such as deep learning and reinforcement learning. These methodologies, by analyzing historical urban planning decisions, could yield more precise and flexible forecasts for sustainable city development. Future studies should address challenges including data availability, computational complexity, and model interpretability.

• Future research may emphasize the integration of stakeholder perspectives, such as those of residents, city planners, and environmental experts, into the decision-making framework. The application of fuzzy logic and participatory tools in the DSS facilitates the effective integration of the needs and preferences of various community groups. An exploration of balancing stakeholder interests and ensuring the validity of subjective data is essential for improved implementation.

• The environmental and economic aspects of urban planning have garnered significant focus; however, the social sustainability dimension, which encompasses inclusivity, equity, and quality of life, is still insufficiently examined. Future research must integrate advanced social sustainability metrics into MCDM models to more effectively address the varied needs of urban populations, particularly in settings characterized by considerable socio-economic disparities.

• Applying the presented models to larger cities, diverse geographical locations, and other urban contexts will evaluate the framework’s scalability and robustness. Such investigations could reveal how effectively the methodologies generalize across urban areas and what adaptations may be needed to address diverse planning difficulties.