Spherical bipolar fuzzy decision model for green infrastructure selection

Abstract

Increasing urbanization, brought on by population expansion and industrialization, is posing a number of environmental concerns for urban and suburban areas. Urban communities are adapting to the intricacies brought about by a number of factors, including pollution, temperature variations, and climate change. However, achieving adaptation sustainably remains a significant challenge because many existing adaptation strategies lack sustainability, particularly in the context of urban development. Sustainable urban development can be achieved through green initiatives, with green infrastructure (GI) practices playing an essential role in its implementation. Nevertheless, selecting one of the available GI practices might be challenging since their execution necessitates careful assessment of all relevant factors. To this end, we seek the aid of a fuzzy multi-criteria decision-making framework. This study considers six GI practices as alternatives, assessed based on environmental, economic, and social dimensions encompassing fourteen criteria. Spherical bipolar fuzzy sets (SBFS) are employed to represent the evaluation information. The significance of each criterion is established using the distance correlation-based criteria importance through inter-criteria correlation (D-CRITIC) technique, while the alternatives are ranked through the preference ranking on the basis of ideal-average distance (PROBID) approach. The proposed SBFS-based D-CRITIC-PROBID framework is a significant addition to the literature as a distinctive study on GI assessment. Further, the effectiveness and robustness of the findings are validated through comparison and sensitivity analyses.

Introduction

Rapid urbanization driven by increasing population and industrialization significantly impacts the natural ecosystem, primarily causing the degradation of green spaces as well as heightening environmental pollution. Currently, over half of the worldwide population dwells in urban and metropolitan regions, and predictions suggest that this figure could rise to 80% by 2050¹. Consequently, the usage of land has changed, with urban infrastructures taking the place of vegetation and unoccupied land². This shift has an effect on the climate of urban regions, leading to abnormally high or low levels of humidity, precipitation, evapotranspiration, and air temperature³. The primary drivers of climate change include escalating greenhouse gas emissions, population expansion challenges, and consumerist lifestyle patterns⁴. It also has an impact on biodiversity and poses a risk to the ecosystem and human wellness. Growing interest has been shown in the possible role of green initiatives, which are frequently addressed with the idea of sustainable development, in finding solutions to these issues. The proper balance of economic, social, and environmental factors at the domestic, city, locality, neighbourhood, and household scales leads to sustainable development on a worldwide basis in urban regions. The Brundtland Commission, formerly termed the World Commission on Environment and Development, described sustainable development as “the development that satisfies current requirements without compromising the capacity of future generations to fulfil their own”⁵.

Nowadays, in the twenty-first century, green projects are gaining popularity among the people. In this regard, green infrastructure (GI) practices serve as a driving force in the pursuit of sustainable urban development (SUD)⁶. The underlying concept of GI is to preserve and restore the natural environment by developing eco-friendly infrastructure, prioritizing green spaces within urban and suburban regions, and possessing a vital role in preserving natural ecosystems while delivering significant benefits to people¹. Some of the detrimental effects of urbanization on people and natural systems can be limited by the implementation of GI practices. It is regarded as an efficient approach in promoting urban sustainability that aids in the adaptation and mitigation of climate change, stormwater management, and heat mitigation. It has become more popular in urban areas because of its various benefits, such as reducing pollution and carbon emissions, enhancing the well-being of people, and improving the aesthetics of the environment. Although GI cannot completely replace natural landscapes, it is seen to be advantageous since it assists in protecting land- and water-dwelling organisms by providing habitats for various kinds of biota⁷. Furthermore, it facilitates water management by ensuring its effective utilization⁸.

Various GI practices are available to support SUD, providing practical solutions for handling environmental issues while enhancing urban resilience and liveability. Selecting an optimal choice among several GI practices can be difficult since their implementation requires systematic planning, financial sources, expert knowledge, and a comprehensive evaluation of all relevant parameters. This can be attained through the implementation of the multi-criteria decision-making (MCDM) technique. Among the several benefits of using MCDM techniques is the incorporation of varied criteria, which increases the dependability of the results. Numerous fields, including industrial, agricultural, biological, and energy systems, have made extensive usage of MCDM.

Aim of the study

      This study aims to provide an effective framework that can be utilized by a variety of beneficiaries, including those in the public, private, and community sectors, to assess the optimal GI practice for SUD. In this context, we present an advanced decision-making methodology to determine the most sustainable GI practice. It depends on the integration of the Distance Correlation-based Criteria Importance Through Inter-criteria Correlation (D-CRITIC) method and the Preference Ranking on the Basis of Ideal-average Distance (PROBID) method under the Spherical Bipolar Fuzzy Sets (SBFS) environment. The developed SBFS-D-CRITIC-PROBID model can be implemented to solve various challenging MCDM problems pertaining to sustainable development.

Literature and motivation

      Zadeh⁹ developed the notion of fuzzy sets to address the ambiguity and unpredictability that result from subjective opinions and data inconsistencies. Since then, several expansions and generalizations of fuzzy sets have been established by numerous researchers in the literature. Zhang¹⁰ initially presented bipolar-valued fuzzy sets (BFS) as a generalization of fuzzy sets with bipolarity (positive and negative), whose range of membership degree extends from [0,1] to [− 1,1]. Furthermore, Lee¹¹ discussed certain basic BFS operations, and Lee et al.¹² presented a comparison between the interval-valued fuzzy sets, IFS, and BFS. Recent applications of BFS decision-making include the assessment of high-risk coexisting tuberculosis disease in pregnant women using integrated COPRAS and TOPSIS approaches¹³ and the selection of unmanned aerial vehicle software using bipolar fuzzy aggregation operators¹⁴. The emergence of BFS gave rise to spherical fuzzy sets (SFS) presented by Kutlu Gündoğdu & Kahraman¹⁵, which combine the characteristics of PyFS and NS to offer a wider preference domain. One characteristic that makes SFS distinct is that each degree of membership, non-membership, and hesitancy is individually specified within the range [0, 1], along with its squared sum falling between 0 and 1. This allows investigators to express their hesitancies in greater depth. Recent applications of SFS decision-making include the assessment of environmental, social and governance performance of the global electronics industry employing SF-AHP and SF-WASPAS methodology¹⁶ and the selection of renewable energy sources in Turkey using integrated SF-DEMATEL, SF-ANP, and SF-VIKOR algorithms¹⁷. The concept of SBFS, which integrates the traits of SFS and BFS along with their properties, was first presented by Princy and Mohana¹⁸ and implemented in the MCDM application. The SBFS notion has been effectively implemented in the works of Çakır et al.¹⁹ and Deetae et al.²⁰.

The MCDM weighting techniques are split into two categories, which include the subjective and objective methods. Subjective techniques need the decision-makers to provide some preliminary information before determining the weight. This information is typically based on their experience or expertise. Subjective approaches provide the benefit of incorporating information obtained from skilled decision-makers. But, due to the decision-makers’ prior beliefs, this information may occasionally favour particular criteria, providing biased outcomes. Additionally, when there are several criteria involved in the MCDM problem, the procedure of providing such information might get complicated. Objective techniques, in contrast to subjective ones, are devoid of any kind of preliminary data or opinion from the decision-makers. Instead of that, they depend only on the decision matrix to obtain the criteria weighting. These techniques are renowned for enhancing impartiality by removing any possible bias related to subjective assessment.

One of the most popular objective weighting techniques in the literature is CRITIC²¹, which considers both the contrast intensity and the degree of conflict between the evaluation criteria. This method utilizes the Pearson correlation to capture the conflicting relationships between criteria which may not always represent their actual relationships. As an example, two criteria having a Pearson correlation coefficient of 0 couldn’t be totally independent, since the Pearson correlation determines only the linear relationship between them. To resolve this limitation, Krishnan et al.²² formulated the D-CRITIC approach, an enhanced version of the CRITIC technique that captures the conflicting relationships between criteria by taking into account the concept of distance correlation, thereby providing a more credible set of criterion weights than the former one. Zhang and Wei²³ applied the D-CRITIC approach under SFS to compute criteria weights in conjunction with the CoCoSo ranking technique for the location selection problem of electric vehicle charging stations. Maneengam²⁴ used the D-CRITIC technique to assign the weight of each objective function along with the modified TOPSIS approach in order to solve the multimodal routing problem. Liu and Shen²⁵ extended the D-CRITIC approach within the generalized hesitant fuzzy environment and combined it with the COPRAS approach to evaluate enterprise digital assets. Ghaemi-Zadeh and Eghbali-Zarch²⁶ utilized the D-CRITIC technique, in combination with the fuzzy MULTI-MOORA ranking approach, to assess business strategy based on corporate performance and investor behaviour. Liu et al.²⁷ investigated the location selection problem of emergency logistics center in Central China through the implementation of D-CRITIC-GRA methodology.

The ranking method selection is crucial in the assessment of the decision-making model. Various MCDM techniques exist in the literature, each having its unique calculation algorithm. Mufazzal and Muzakkir²⁸ acknowledged the rank reversal behaviour, which is defined as the addition or removal of an alternative from the original dataset causing the ranking order to shift or reverse, as a drawback in several MCDM techniques. In order to overcome these issues, Wang et al.²⁹ developed a new ranking algorithm called PROBID, which includes both the average and all possible ideal solutions, making it far more consistent than other well-known MCDM techniques. In this respect, Biswas et al.³⁰ implemented the PROBID technique in combination with the FUCOM weight method under the picture fuzzy environment to rank the video conferencing platforms. Chatterjee et al.³¹ applied the PROBID approach and its simplified version, the sPROBID method, along with the SPC weighting technique in the problem of selecting a delivery drone. Hua et al.³² assessed companies according to their new quality productive forces using the IDOCRIW-PROBID methodology. Furthermore, the study carried out by Stević et al.³³ examined the sensitivity assessments of seven distinct normalisation types in order to choose the small electric van using the PROBID, CODAS and SAW methodologies. Darko et al.³⁴ employed the TODIM-based PROBID technique to assess electronic mental health platforms under probabilistic reliable linguistic term sets. The criterion weights were measured using the CRTITC approach.

Recent studies have demonstrated the growing applicability of advanced fuzzy MCDM methods across diverse decision-making domains. For instance, the CRITIC–TOPSIS methodology has been employed for sustainable medical waste management under an f, g, h - fractional fuzzy set environment³⁵. Similarly, the CRITIC–WASPAS approach has been applied to sustainable energy planning using f, g, h - fractional fuzzy sets³⁶. In another innovative direction, a TOPSIS-based framework has been developed for optimal gate security system selection by integrating quantum mechanics principles into spherical fuzzy sets³⁷. Additionally, the BWM–CoCoSo methodology has been utilized in supply chain management by incorporating Z-number theory³⁸. Likewise, the SWARA–WASPAS approach using fuzzy numbers³⁹ and the SWARA–MARCOS technique using grey numbers⁴⁰ have both been applied in the domain of supply chain.

Alongside MCDM-driven assessments, certain studies conceptualize urban agriculture as a form of GI, highlighting the benefits pertinent to stormwater management, carbon mitigation, food security, and environmental and social sustainability^41,42. By emphasizing land-use planning and ecologically friendly strategies, these studies broaden the conceptual scope of GI beyond engineered solutions. Furthermore, planning-focused research highlights the integration of GI within spatial planning, land-use management, and transportation systems to improve urban resilience and sustainability^43,44. These studies indicate that the implementation of GI is influenced not just by environmental performance but also by planning policies and governance frameworks.

State of the art in GI decision-making

There are very few studies in the literature that incorporate MCDM in the evaluation of GI. For instance, Lin et al.¹ employed a modified VIKOR approach to evaluate six typical GIs for environmental sustainability, in which the DEMATEL-based ANP technique was utilized to figure out the relative importance of the ten considered criteria, which were grouped under four dimensions. Arya and Kumar⁴⁵ assessed five distinct GIs for sustainable stormwater management, both independently and in combination, based on five criteria encompassing fourteen sub-criteria. The criterion weights were generated using the AHP approach, and the alternatives were ranked employing the TOPSIS technique. Additionally, using the DEMATEL-based ANP approach, Khoshnava et al.⁶ evaluated six GI criteria in relation to the use of the green economy in the framework of sustainable development.

However, there is yet no expansion of the D-CRITIC technique into the SBFS environment. Decision-makers might find this expansion beneficial in assessing the significance of assessment criteria. The PROBID method has not been integrated yet into the D-CRITIC approach under the SBFS environment, which allows the decision-makers to evaluate the alternatives and identify the most effective solution. Nevertheless, there is still no literature on the application of GI in the context of SUD using an enhanced fuzzy decision model. This requirement serves as the driving force behind the development of this study.

Research gaps and contributions

      The following are the highlighted research gaps: The D-CRITIC approach has not been developed in the SBFS environment in any prior study. The PROBID technique’s implementation in the SBFS setting has not yet been examined. No prior research has integrated the D-CRITIC and PROBID approaches into a single framework for the assessment of GI selection.

The following are the study’s contributions:

• This study proposes an enhanced MCDM framework based on the combination of the D-CRITIC and PROBID techniques to select the appropriate GI practice in the context of SUD. In the combined D-CRITIC-PROBID methodology, expert assessment information is represented utilizing SBFS to eliminate imprecision and ambiguity. To our best knowledge, this appears to be the first study to integrate the D-CRITIC and PROBID methods under the SBFS environment.

• It provides an evaluation framework with fourteen criteria categorized into environmental, economic and social dimensions. The SBFS-based D-CRITIC approach was developed to establish the objective weights of the decision-making criteria for sustainable GI selection, which provides a reliable criterion weighting system for decision-makers.

• Then, the SBFS-based PROBID method was formulated to evaluate six GI practices and determine the most optimal solution. This presents a dependable evaluation of GI practices, which is essential for examining its effectiveness.

• The proposed SBFS-based D-CRITIC-PROBID model shall facilitate the researchers in solving various complex problems. It is anticipated to make a substantial contribution to the field of MCDM as a unique research on GI evaluation.

The following sections structure the remainder of the article: Section 2 provides the fundamental definitions related to SBFS. Section 3 details the D-CRITIC and PROBID methodologies. The case study of GI selection is provided in Section 4. Section 5 discusses the results of the proposed model along with comparative and sensitivity analyses, and the concluding comments are given in Section 6.

Preliminaries

Definition 1

²⁰ A bipolar fuzzy set (BFS) on the universe is described as:

1

where indicates the degree of positive membership and indicates the degree of negative membership of . To keep it simple, a BFS is expressed as , which is referred to as the bipolar fuzzy number.

Definition 2

²⁰ A spherical fuzzy set (SFS) on the universe is given by the expression:

2

where and corresponds to the degree of membership, non-membership, and hesitancy, respectively, of with the condition for all . For convenience in utilization, a SFS is represented as , which is referred to as the spherical fuzzy number.

Definition 3

¹⁸ A spherical bipolar fuzzy set (SBFS) on the universe is described as:

3

where , , , , , and , for all . For each p the numbers , and represents the positive membership, non-membership and hesitancy degrees, respectively, of p to and , and represents the negative membership, non-membership and hesitancy degrees, respectively, of p to . A SBFS can be denoted as for ease in utilization. This term is referred to as the spherical bipolar fuzzy number (SBFN).

Definition 4

¹⁸ Spherical bipolar weighted geometric mean (SBWGM) with regard to and , SBWGM is determined as:

4

Definition 5

¹⁸ The score function of a SBFS, is determined by:

5

Methodology

      The proposed methodology commences with a decision matrix which denotes the performance of different alternatives based on predetermined criteria, as shown in Eq. 6. The set of alternatives to be ranked is represented as , while the set of criteria that are employed to rank the alternatives is represented as . is the performance of the alternative on the basis of the criterion.

6

Each alternative’s performance was gathered using SBFS, after which the D-CRITIC technique was utilized to evaluate the relative importance of the criteria, and the PROBID approach was utilized to establish the optimal choice. A BFS captures the dual nature of human perception and cognition. It is appropriate to handle information containing a property, as well as its counter-property. SFS has the freedom in uncertainty representation, allowing membership, non-membership, and hesitancy to coexist with greater flexibility⁴⁶. Combining these two sets serves as an efficient measure for eliminating ambiguity in experts’ recommendations for making decisions and enhancing the identification of information uncertainties. It better articulates the vagueness and uncertainty of the evaluation system. The added value of bipolarity in the selection of GI practice encompasses both the benefits and drawbacks of a GI alternative simultaneously. The negative membership is essential since the GI alternatives often exhibit explicit drawbacks that cannot be captured as a mere absence of benefit.

D-CRITIC method

      The D-CRITIC technique incorporates the concept of distance correlation into the conventional CRITIC approach, capturing both linear and nonlinear relations between criteria. Compared to the original CRITIC technique, it can provide more efficient standard weights and more accurately replicate the conflict connection between criteria. The existence of both beneficial (BF) and non-beneficial (NBF) criteria, as well as negative elements in the decision matrix, constitutes the basis for using this approach. In Step 3, the D-CRITIC technique employs distance correlation, whereas the original CRITIC method utilizes Pearson correlation, which is the main difference between the two approaches. The following describes the computing process for the D-CRITIC approach:

• Step 1: Normalize the decision matrix by applying Eq. (7), as the process involves converting the scores into standardized scales with a 0–1 range.

  7

  where is the normalized score value of the alternative in connection with the criterion, is the actual score value of the alternative with regard to the criterion, is criterion best and worst outcomes for BF and NBF criteria, respectively, and is criterion worst and best outcomes for BF and NBF criteria, respectively.
• Step 2: Establish the standard deviation for each of the criteria utilizing Eq. (8).

  8

  where denotes the average score value of criterion v, and g signifies the total number of alternatives.
• Step 3: Compute the distance correlation between each pair of criteria. The computation of the pairwise distance correlation for each criterion is summed up as follows: Step 3.1: Create the Euclidean distance matrix for each of the criteria based on all the alternatives using Eq. (9).

  9

  Step 3.2: Using Eq. (10), determine the double-centred matrix for criteria .

  10

  where indicates the Euclidean distance matrix, and indicate the average of the row and column of , respectively, and indicates the total average of . Step 3.3: Calculate the distance covariance of criteria and using Eq. (11).

  11

  Step 3.4: Finally, determine the distance correlation between criteria using Eq. (12).

  12

  where denotes the distance covariance between and , and and are the distance variance of and , respectively.
• Step 4: Obtain the information content for each criterion using Eq. (13).

  13
• Step 5: Compute the objective weights for each criterion employing Eq. (14).

  14

PROBID method

      The fundamental concept behind the PROBID approach is to comprehensively evaluate both the average and all possible ideal solutions. It typically combines the benefits of the EDAS and TOPSIS approaches and is not prone to rank reversal. Compared to other well-known MCDM techniques, PROBID appears to be consistent due to its comprehensive covering of ideal solutions. It can provide more reliable solutions for MCDM problems, especially those with larger datasets and high dimensions.

• Step 1 Compute the normalized decision matrix by means of vector normalization using Eq. (15).

  15

  where is the normalized element of the actual element .
• Step 2 Establish the weighted normalized decision matrix utilizing Eq. (16).

  16

  where is the normalized value. Here, denotes the objective weight of the criteria acquired from the D-CRITIC approach.
• Step 3 Obtain the most positive ideal solution (PIS) , PIS , PIS , , and PIS [i.e., the most negative ideal solution (NIS)] by Eq. (17).

  17

  where V corresponds to the set of BF criteria and corresponds to the set of NBF criteria. and indicate the highest and lowest values in the weighted normalized criterion column (i.e., ), respectively, and indicates the best solution (i.e., worst for NBF criteria) in the criteria column. Subsequently, the average value for each of the criteria columns is calculated using Eq. (18).

  18

  Then, the average solution is given by,

  19
• Step 4 Determine the Euclidean distance between each solution and each of the g ideal solutions along with the average solution. The distance of the ideal solutions is calculated using Eq. (20).

  20

  In the same way, the distance of the average solution is computed utilizing Eq. (21).

  21
• Step 5 Calculate the overall positive-ideal distance (PID) by Eq. (22), which basically represents the weighted sum distance of one solution to the half of the ideal solutions.

  22

  In this case, weight decreases with the ideal solution number (i.e., ). Likewise, calculate the overall negative-ideal distance (NID) by Eq. (23), which represents the weighted sum distance of one solution to the half of the ideal solutions.

  23

  In this case, weight increases with the ideal solution number (i.e., k increasing to m).
• Step 6 Using Eq. (24), calculate the ratio () of the overall PID to the overall NID.

  24
• Step 7 Determine the performance score () of each solution using Eq. (25).

  25

  It is seen from Eq. (24) that a smaller value of indicates that the solution is nearer to PIS, which results in a greater value of . On the other hand, a greater value indicates that the solution is nearer to NIS, which results in a smaller value. The alternative that has a higher value turns out to be the ideal choice.

An outline of the proposed research framework is depicted in Fig. 1.

Fig. 1.

Overall framework of the proposed work.

Case study

      Urban regions need to adapt to the intricacies brought about by economic expansion and climate change, in addition to various other challenges. The necessity of adapting to these changes is widely acknowledged across global levels. However, most of the existing adaptation strategies fail to be sustainable, making sustainable development a significant task. GI practices have gained popularity recently as an advantageous and adapted approach to sustainable development. Effective planning of GI might improve a region’s resilience and long-term sustainability. In order to promote SUD, this study examines six potential GI practices, namely green roofs , rain gardens , urban forests , permeable pavements , grass swales , and green walls , as alternatives. The following is a description of each of these alternatives.

• (i)Green roofs Green roofs, commonly referred to as vegetated or living roofs, are rooftops that are covered entirely or in part by vegetation, which might include grasses, herbs, shrubs, plants, and even tiny trees integrated with the growing medium and planted over a waterproof layer. Other layers, like irrigation and drainage networks, and even a root barrier, could also be included.
• (ii)Rain gardens : Rain gardens are landscaped with different kinds of vegetation in the appropriate soil, such as shrubs, grass, and floral perennials, in a shallow depression that collects rainwater from rooftops, sidewalks, roadways, and streets and lets it seep into the ground, reducing the risk of flood and water pollution. It may also incorporate filtration media, mulching layers, and possibly underdrains.
• (iii)Urban forests Urban forests comprise groups of trees and other types of woody vegetation that grow in and around residential areas located within the urban and suburban regions, which may include trees in recreational spaces, along streets, and in neglected or unused areas. Both private and public entities may possess urban forests.
• (iv)Permeable pavements Permeable pavements are surfaces composed of either a porous substance that allows water to pass through it or of nonporous blocks separated by spaces that enable water to pass between those openings, permitting the percolation and infiltration of the rainwater into the aggregate layers or soil beneath the pavement. It is widely employed on roadways, sidewalks and parking lots.
• (v)Grass swales Grass swales, a form of vegetated swales, are graded and designed landscape structures that are lined with grass possessing a trapezoidal or parabolic cross-section. They are typically linear, shallow, and slightly sloped open channels. They are commonly utilised to reduce runoff in residential areas, around buildings, and along roadways and parking lots.
• (vi)Green walls Green walls, also referred to as vertical gardens, are structures having the whole or portions of their walls coated with vegetation on a growing medium that is placed vertically. They usually incorporate a range of plant species with an arrangement that enables vertical plant growth. Both the interior and exterior of the structures may have green walls installed in different sizes.

The three fundamental aspects of sustainability, viz., environmental, economic and social, serve as the foundation of sustainable development. Therefore, the GI practice for SUD can also be evaluated using these three factors. Despite the fact that GI may be beneficial in numerous situations, it is typically employed for certain purposes, involving flood prevention, water and air treatment, or enhancing local attractiveness. Thus, the criteria need to consider these factors to better comprehend the relationships between social, economic, and environmental aspects. Following a literary survey, fourteen evaluation criteria were selected for this study, which were grouped under three dimensions utilized to assess the six alternatives considered. The featured GI practices are widely known and well suited for the implementation of the local urban environment. Table 1 provides a description of these criteria. The + and − signs stand for the BF and NBF criteria, respectively. The alternatives and criteria are illustrated graphically in Fig. 2.

Table 1.

List of the evaluation criteria.

Dimension	Criteria	Description
Environmental ()	Stormwater management ()	Ability to decrease the overall water runoff brought on by heavy rainstorms or hurricanes and minimize flooding risks
	Heat mitigation ()	Capacity to reduce the urban heat island effect and enhance human thermal comfort
	Biodiversity enhancement ()	Capacity to support the survival of native species (flora and fauna) by providing habitats
	Air purification ()	Ability to remove airborne pollutants (such as carbon dioxide, sulphur dioxide, etc.) from the atmosphere
	Water purification ()	Ability to trap and filter contaminants (such as sediments and chemicals) from runoff before they reach groundwater or water bodies
	Energy efficiency ()	Capacity to lower the dependence on heating and cooling systems in order to reduce energy usage
Economic ()	Cost ()	Cost required for implementing the GI system
	Space efficiency ()	Spatial requirements for setting up the structure
	Lifespan ()	Durability period of the GI
	Ease of installation ()	Intricacy and effort level required to build the GI system
Social ()	Aesthetic value ()	Ability to enhance and beautify urban landscapes
	Health and wellness ()	Capacity to improve human health by lowering pollution and creating green areas for recreation
	Risk to society ()	Possibility of GI negatively impacting the public in one way or another during the period of its existence
	Public recognition ()	Willingness of the public to accept and implement GI

Fig. 2.

Graphical illustration of alternatives and criteria.

Furthermore, the implementation of GI practice in an urban setting cannot be determined by a single individual. Hence, forming a panel of experts is essential to guarantee a sustainable GI practice. Therefore, this study gathered insights from an environmental engineer (), a landscape architect (), and an urban planner (), who provided independent evaluations on the performance of GI practices based on the criteria under consideration, which were subsequently synthesized into a single decision matrix using the SBFS aggregation operator to handle conflicting opinions. Environmental engineers ensure that a GI is technically efficient. Landscape architects assist in presenting them in an eco-friendly and aesthetic manner, while urban planners focus on the strategic positioning of the GI. Their contributions are essential to the planning, designing, and implementation of GI in order to ensure its sustainability and functionality. SBFS are adaptive to these circumstances by offering a more subtle and flexible representation useful for decision-making purposes. At this point, the PROBID methodology can be effectively utilized to assess alternatives based on a number of criteria represented by SBFS, enabling a systematic approach. Consequently, SBF-PROBID is suggested to order the alternatives in accordance with expert’s recommendations.

Results and discussion

      According to the definition of SBFS, the linguistic scale is determined and displayed in Table 2. The panel of experts assessed the performance of each alternative in relation to every criterion, and the evaluation values are represented as linguistic terms in Table 3. Every expert must evaluate their recommendation on the basis of SBFS. The experts’ weight, = (0.4, 0.35, 0.25), is determined by their requirements for the particular problem. The experts’ respective competence and decision-making significance in GI planning are reflected in the weights assigned to them, with greater emphasis focused on technical and implementation-oriented experience. The SBWGM operator is employed, and the aggregated SBF decision matrix is developed using Eq. (4). Then, the SBF score matrix is determined by employing Eq. (5), which is presented in Table 4. This score matrix serves as the decision-making matrix for subsequent steps.

Table 2.

Linguistic scale for SBFS.

Linguistic term	Abbreviation	SBFN
Very extremely effective	VEE	(0.92, 0.08, 0.08, − 0.13, − 0.87, − 0.13)
Extremely effective	EE	(0.8, 0.2, 0.2, − 0.25, − 0.75, − 0.25)
Quite effective	QE	(0.68, 0.32, 0.32, − 0.37, − 0.63, − 0.37)
Moderately effective	ME	(0.5, 0.5, 0.5, − 0.48, − 0.52, − 0.48)
Somewhat effective	SE	(0.32, 0.68, 0.32, − 0.63, − 0.37, − 0.37)
Less effective	LE	(0.2, 0.8, 0.2, − 0.75, − 0.25, − 0.25)
Very less effective	VLE	(0.08, 0.92, 0.08, − 0.87, − 0.13, − 0.13)

Table 3.

Expert’s opinion on alternatives based on criteria in linguistic terms.

		QE	EE	ME	EE	QE	VEE	SE	EE	SE	LE	QE	EE	LE	EE
		VEE	ME	EE	ME	VEE	ME	EE	ME	ME	EE	SE	ME	ME	EE
		SE	VEE	QE	VEE	SE	QE	ME	QE	EE	ME	ME	VEE	QE	VEE
		EE	LE	VLE	LE	EE	LE	QE	SE	VEE	QE	VLE	LE	SE	ME
		ME	SE	LE	SE	ME	SE	VEE	LE	QE	VEE	LE	SE	EE	SE
		LE	QE	SE	EE	LE	EE	LE	VEE	LE	SE	EE	QE	VLE	LE
		QE	QE	QE	QE	ME	EE	SE	EE	LE	VLE	EE	ME	VLE	EE
		EE	SE	VEE	ME	EE	SE	QE	ME	QE	QE	ME	QE	QE	QE
		ME	EE	EE	VEE	ME	ME	QE	QE	VEE	ME	QE	EE	SE	EE
		QE	LE	LE	LE	VEE	VLE	ME	ME	EE	SE	LE	VLE	ME	SE
		LE	VLE	SE	SE	QE	LE	EE	LE	ME	EE	SE	LE	EE	LE
		VLE	ME	ME	EE	SE	QE	SE	EE	SE	LE	VEE	SE	LE	ME
		VEE	VEE	EE	QE	QE	VEE	LE	VEE	SE	LE	VEE	QE	SE	QE
		EE	ME	VEE	SE	EE	QE	EE	QE	ME	EE	EE	EE	EE	EE
		ME	VEE	EE	EE	ME	EE	QE	ME	EE	QE	ME	VEE	ME	EE
		QE	SE	VLE	VLE	QE	SE	ME	ME	QE	ME	SE	VLE	QE	ME
		SE	LE	LE	LE	SE	ME	VEE	VLE	ME	VEE	ME	LE	VEE	VLE
		LE	EE	QE	ME	VLE	VEE	SE	EE	VLE	SE	QE	ME	SE	SE

Table 4.

SBF score matrix.

	0.092	0.118	0.024	0.091	0.018	0.149	− 0.064	0.140	− 0.066	− 0.082	0.114	0.035	− 0.083	0.114
	0.144	− 0.030	0.148	− 0.027	0.144	− 0.020	0.108	− 0.011	− 0.005	0.108	− 0.015	0.024	0.024	0.108
	− 0.032	0.149	0.104	0.151	− 0.032	0.029	0.013	0.028	0.142	− 0.011	− 0.005	0.149	− 0.012	0.144
	0.091	− 0.071	− 0.086	− 0.080	0.127	− 0.083	− 0.002	− 0.032	0.129	− 0.012	− 0.084	− 0.085	− 0.022	− 0.030
	− 0.047	− 0.083	− 0.070	− 0.064	− 0.011	− 0.054	0.149	− 0.080	− 0.002	0.149	− 0.054	− 0.069	0.140	− 0.080
	− 0.082	0.029	− 0.022	0.062	− 0.080	0.118	− 0.067	0.144	− 0.080	− 0.066	0.127	− 0.012	− 0.084	− 0.050

The next stage is to obtain the criterion weights. By evaluating the considered criteria using the D-CRITIC approach, the normalized decision matrix is computed utilizing Eq. (7). Here, , , , , , , , , , , and are considered to be BF criteria, whereas , , and are considered to be NBF criteria. After that, Eq. (8) is used to compute the standard deviation for each normalized criterion. Their values are = 0.410, = 0.420, = 0.403, = 0.402, = 0.400, = 0.403, = 0.411, = 0.412, = 0.428, = 0.405, = 0.414, = 0.362, = 0.371, and = 0.438. Next, in order to obtain the distance correlation between each pair of criteria, the Euclidean distance matrix is created utilizing Eq. (9), and the double-centred matrix is then determined using Eq. (10). High distance correlation values reflect strong interdependence among criteria, implying that policy interventions affecting one criterion are likely to influence others simultaneously, which is valuable for integrated and coordinated decision-making. Following that, Eq. (11) is used to calculate the distance covariance of the criterion. Lastly, the distance correlation is determined using Eq. (12), and Table 5 shows their outcomes. Subsequently, the information content of each criterion is determined in Table 6 employing Eq. (13). Finally, the objective weights of each criterion, which were calculated using Eq. (14) have been presented graphically in Fig. 3. It is evident from the results that , viz., stormwater management, has the highest relative importance, indicating the effective control of flooding as the most indispensable factor, followed by public recognition () and lifespan (), emphasizing the significance of social acceptance and longevity. A strong emphasis is given to water purification () and biodiversity enhancement (), which highlights the importance of environmental benefits. Cost (), ease of installation (), heat mitigation (), and health and wellness () are fairly taken into consideration, ensuring economic viability, technical feasibility and social well-being. Space efficiency () and energy efficiency () obtain the least relative importance, making them essential for sustainability but not primary drivers. Overall, the D-CRITIC weighing technique reveals a significant focus on environmental performance (e.g., and ), project durability, and public support, demonstrating a balanced assessment of environmental, economic, and social dimensions.

Table 5.

Distance correlation matrix.

	1.000	0.372	0.472	0.428	0.878	0.399	0.398	0.394	0.328	0.392	0.359	0.459	0.458	0.540
	0.372	1.000	0.680	0.975	0.613	0.818	0.658	0.769	0.480	0.680	0.712	0.868	0.655	0.728
	0.472	0.680	1.000	0.674	0.457	0.640	0.513	0.606	0.435	0.481	0.647	0.871	0.568	0.890
	0.428	0.975	0.674	1.000	0.680	0.880	0.710	0.835	0.559	0.718	0.791	0.859	0.694	0.636
	0.878	0.613	0.457	0.680	1.000	0.651	0.485	0.622	0.445	0.473	0.592	0.469	0.511	0.389
	0.399	0.818	0.640	0.880	0.651	1.000	0.822	0.981	0.725	0.797	0.981	0.683	0.826	0.478
	0.398	0.658	0.513	0.710	0.485	0.822	1.000	0.870	0.702	0.995	0.809	0.464	0.956	0.364
	0.394	0.769	0.606	0.835	0.622	0.981	0.870	1.000	0.732	0.839	0.980	0.630	0.899	0.447
	0.328	0.480	0.435	0.559	0.445	0.725	0.702	0.732	1.000	0.686	0.774	0.586	0.684	0.326
	0.392	0.680	0.481	0.718	0.473	0.797	0.995	0.839	0.686	1.000	0.764	0.452	0.942	0.363
	0.359	0.712	0.647	0.791	0.592	0.981	0.809	0.980	0.774	0.764	1.000	0.642	0.829	0.453
	0.459	0.868	0.871	0.859	0.469	0.683	0.464	0.630	0.586	0.452	0.642	1.000	0.539	0.873
	0.458	0.655	0.568	0.694	0.511	0.826	0.956	0.899	0.684	0.942	0.829	0.539	1.000	0.487
	0.540	0.728	0.890	0.636	0.389	0.478	0.364	0.447	0.326	0.363	0.453	0.873	0.487	1.000

Table 6.

The information content of each criterion.

	2.917	1.677	2.044	1.433	2.296	1.338	1.750	1.400	2.369	1.790	1.519	1.666	1.465	2.643

Fig. 3.

Graphical representation of criteria weights.

Following this, the PROBID approach is employed to evaluate the alternatives and determine the optimal GI practice. The initial procedure is to normalize the decision matrix by means of vector normalization using Eq. (15). To align with the distinct objectives of the considered approaches, different normalization techniques have been utilized. Linear normalization in D-CRITIC retains variability and inter-criteria relationships essential for reliable weight estimation, whereas vector normalization in PROBID assures impartial distance-based ranking. Without compromising the stability of the findings, this distinction preserves methodological consistency. Then, employing the weights obtained from the D-CRITIC approach, Eq. (16) yields the weighted normalized decision matrix. Next, Table 7 provides the ideal and average solutions derived from Eqs. (17) and (18). Eqs. (20) and (21) are used to calculate the Euclidean distances of each solution to the ideal solutions and average solutions which is presented in Table 8. Table 9 displays the overall PID , overall NID , their ratio , and performance score of each of the GI practices, obtained using Eqs. (22–25). The alternatives are sorted based on the value in decreasing order. Higher the value, the better is the alternative. The ranking results of the alternatives are shown graphically in Fig. 4. The findings show that rain gardens () rank first, followed by urban forests (), green roofs (), permeable pavements (), green walls () and grass swales (). Marginal score differences between closely ranked alternatives, such as between and (0.031) and and (0.039), indicate proximity to the same decision boundary and are unlikely to be practically meaningful for planners and policymakers. These options should therefore be considered using contextual factors (criteria) rather than rank alone. Sensitivity analysis further shows that excluding socially driven criteria leads only to marginal shifts among intermediate alternatives, while the optimal option remains unchanged.

Table 7.

Ideal and average solutions.

	0.073	0.043	0.054	0.038	0.059	0.035	− 0.021	− 0.019	0.059	0.048	0.037	0.050	− 0.025	0.061
	0.047	0.034	0.038	0.023	0.052	0.028	− 0.021	− 0.008	0.053	0.034	0.033	0.012	− 0.025	0.049
	0.046	0.008	0.009	0.016	0.007	0.007	− 0.001	− 0.003	− 0.001	− 0.003	− 0.002	0.008	− 0.007	0.046
	− 0.016	− 0.009	− 0.008	− 0.007	− 0.005	− 0.005	0.004	0.007	− 0.002	− 0.004	− 0.004	− 0.004	− 0.004	− 0.013
	− 0.024	− 0.020	− 0.025	− 0.016	− 0.013	− 0.013	0.035	0.034	− 0.027	− 0.021	− 0.016	− 0.023	0.007	− 0.021
	− 0.042	− 0.024	− 0.031	− 0.020	− 0.033	− 0.019	0.048	0.035	− 0.033	− 0.026	− 0.024	− 0.028	0.042	− 0.034
Average	0.014	0.005	0.006	0.006	0.011	0.005	0.007	0.008	0.008	0.005	0.004	0.002	− 0.002	0.015

Table 8.

Euclidean distances of each solution to the ideal solutions and average solutions.

							Average
	0.152	0.122	0.077	0.131	0.161	0.201	0.097
	0.135	0.115	0.096	0.149	0.179	0.213	0.107
	0.142	0.121	0.112	0.138	0.182	0.209	0.110
	0.193	0.151	0.121	0.112	0.139	0.173	0.105
	0.244	0.204	0.155	0.095	0.099	0.104	0.118
	0.231	0.189	0.141	0.091	0.109	0.138	0.113

Table 9.

Ranking of the alternatives.

					Rank
	0.238	0.325	0.734	0.747	3
	0.225	0.352	0.640	0.817	1
	0.240	0.346	0.693	0.786	2
	0.309	0.280	1.101	0.557	4
	0.397	0.185	2.146	0.297	6
	0.372	0.222	1.673	0.376	5

Fig. 4.

Graphical representation of ranking results of the alternatives.

Interpretation of the results

      Rain gardens are effective in managing stormwater by absorbing runoff, minimizing the risk of floods and erosion. This helps in replenishing groundwater and mitigating heat to enhance climate resilience. They also improve the quality of the water by filtering the contaminants from the runoff before it reaches the groundwater or nearby water bodies. By providing habitat for a range of native plants, birds, and other species, they raise the likelihood of urban biodiversity. Rain gardens are relatively easy to install in a variety of urban locations, such as parking lots, roadways, and residential areas. They utilize colourful and low-maintenance plants that enhance the aesthetics of the landscapes while also offering the advantage of low installation and maintenance costs. It is one of the widely accepted GI practices and poses a minimal level of risk to society. Thus, with their significant beneficial impacts on the environment, economy and society, rain gardens lead the list, making them an ideal GI practice. Urban forests come next due to their broader environmental and social benefits, followed by green roofs for their multifunctional use of space. Permeable pavements provide good infiltration but less ecological benefits, while green walls and grass swales are more limited by maintenance needs and space constraints, placing them lower in the ranking. By identifying effectively functioning alternatives, the proposed model promotes targeted investments in GI to resolve regionally relevant concerns such as urban floods, heat reduction, and land utilization. From the viewpoint of policy, these findings can help planning authorities and local governments in integrating GI projects with sustainability objectives, plans for adapting to climate change, and urban development regulations. The study enhances the fuzzy MCDM framework by integrating uncertainty, diverse criteria, and expert judgement into a cohesive structure for GI evaluation. The findings support real-world urban sustainability policies by offering a structured, decision-support prioritization of GI practices that balances environmental, economic and social objectives. By explicitly incorporating trade-offs and expert uncertainty, the paradigm assists policymakers in identifying viable and efficient GI options.

Spatial, land-use, and transportation dimensions of GI

The proposed fuzzy MCDM model positions GI selection within the broader context of spatial planning, land-use management, and transportation systems by serving as an adaptable decision-making tool for integrated urban development. Building-integrated GI like green roofs and green walls enable compact development in alignment with spatial planning goals, while surface-based GI like rain gardens, urban forests, and grass swales are associated with land-use zoning and public spaces. Transportation-orientated GI, such as permeable pavements and grass swales, highlights the integration of GI within transport corridors. GI is strongly related to transportation planning, since these practices are commonly implemented into roadways, sidewalks and parking lots to improve walkability and reduce runoff, heat waves, air pollution, and noise. Environmental performance, land-use viability, and societal balance factors are also reflected in the evaluation criteria. By accommodating expert-based fuzzy evaluation, the framework enables these planning elements to be methodically represented in the assessment and selection of GI, promoting more cohesive and SUD strategies.

Leapfrogging towards GI entails the direct adoption of nature-based solutions, unlike incremental initiatives that integrate GI into pre-existing urban systems. The evaluated GI practices are ideal for leapfrogging situations, as they can be incorporated into buildings, streets, and open areas at early phases of urban development. By enabling criterion weights and expert judgements to be modified in accordance with various planning priorities, the suggested fuzzy MCDM framework supports transformative planning scenarios alongside incremental urban development strategies. The expert-based fuzzy assessment can be enhanced by spatially grounded case studies, which provide actual geographical information to enable more robust weighting and improve criterion selection. Expert opinions can be supported by observed differences in GI performance among various urban designs, land-use patterns, and transportation systems. Such insights can guide future extensions of the model towards GIS-integrated decision-making for context-sensitive GI planning.

Comparative analysis

      To illustrate the consistency and efficacy of the proposed method, a comparative assessment was carried out based on the same dataset utilized by the proposed method. The analysis compared the results of the PROBID method with those of the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution), VIKOR (VIsekriterijumska optimizacija i KOmpromisno Resenje in Serbian), sPROBID, and MOORA (Multi-Objective Optimization based on Ratio Analysis) techniques. TOPSIS is a renowned distance-based MCDM technique which incorporates both the ideal and anti-ideal solution through a utility value to identify the optimum alternative that is nearest to the ideal solution. VIKOR provides a compromise solution, which is closest to the ideal. It ranks the alternatives in ascending order, where the option with the lowest value is considered optimal. The sPROBID technique is a simplified variant of the PROBID approach that employs only the upper and lower quarters of the ideal solutions rather than the and halves to calculate the overall PID and NID. The rankings obtained from the TOPSIS, VIKOR and sPROBID techniques are identical to that of our proposed method. MOORA is a compensatory approach which ranks the alternatives based on their appraisal score, estimated as the difference between the total performance scores of the BF and NBF criteria. The results from the MOORA technique show a considerable difference with our proposed method, in which the first-ranked alternative is placed second and the second-ranked alternative is placed first, while the remaining alternatives retain the same rankings. This might be due to minor methodological variations between the two approaches. To sum up, the comparison study’s findings closely align with our proposed PROBID method, demonstrating its efficiency and consistency. The comparative study findings are provided in Table 10, and Fig. 5 displays the graphical depiction.

Table 10.

Comparative analysis results.

Alternatives	Proposed method	Rank	TOPSIS	Rank	VIKOR	Rank	sPROBID	Rank	MOORA	Rank
	0.747	3	0.569	3	0.291	3	1.322	3	0.206	3
	0.817	1	0.611	1	0.046	1	1.572	1	0.208	2
	0.786	2	0.595	2	0.259	2	1.471	2	0.253	1
	0.557	4	0.473	4	0.446	4	0.898	4	0.006	4
	0.297	6	0.299	6	0.898	6	0.426	6	-0.203	6
	0.376	5	0.374	5	0.857	5	0.597	5	-0.063	5

Fig. 5.

Graphical representation of comparative analysis.

Sensitivity analysis

      Sensitivity study is performed to assess the robustness of the decision model by examining how changes in input variables impact its outcome. This work involved three distinct cases of sensitivity analysis to ascertain how variations in the experts’ weighting of the decision matrix affect the ranking of the alternatives.

Case I In this case, the experts’ weighting is determined as = (1, 0, 0), where ranks first, followed by , , , , and . Here, there is a slight shift in the ranking where moves to the second position and to the third, while all other alternatives retain their original positions.

Case II Here the experts’ weighting is established as = (0, 1, 0), where holds the first position, followed by , , , , and . This shows that despite changes to the experts’ weights, the ranking remained the same.

Case III The experts’ weighting in this case is = (0, 0, 1), and again holds the first position, followed by , , , , and , which is similar to Case I.

In each of the cases discussed above, the alternative , i.e., rain gardens, takes the first position, indicating the robustness of the proposed methodology. The sensitivity analysis demonstrates that moderate variations in criterion weights do not alter the overall ranking structure, indicating strong model robustness under realistic uncertainty conditions. Environmental aspects, especially stormwater management and heat mitigation, exert the greatest influence on ranking adjustments, underscoring their crucial significance in policy-driven GI selection. From a decision-making standpoint, this suggests that policies prioritizing environmental resilience will constantly favour the same GI practice, even when stakeholder preferences vary. The observed stability of the foremost alternative confirms that the proposed framework provides reliable and feasible guidance for real-world GI planning. Table 11 provides the sensitivity ranking of the alternatives, and it is represented graphically in Fig. 6.

Table 11.

Sensitivity analysis results.

Cases	Ranking values						Ranking order
Case I	0.728	0.793	0.683	0.621	0.306	0.406
Case II	0.703	0.818	0.792	0.538	0.308	0.361
Case III	0.821	0.835	0.821	0.469	0.267	0.335

Fig. 6.

Graphical representation of sensitivity analysis.

Conclusion

      This study addresses the problem of selecting an appropriate GI practice for SUD, which is an MCDM problem often involving multiple and conflicting criteria. In this regard, we develop an advanced MCDM model which integrates the D-CRITIC and PROBID approaches. SBFS is employed to represent the experts’ evaluation information in order to eliminate imprecision and uncertainty from the data. The case study’s process featured six kinds of GI practices as alternatives with fourteen evaluation criteria categorized under environmental, economic and social dimensions. The relative significance of each criterion is established utilizing the D-CRITIC weighting approach, and the alternatives are ranked using the PROBID technique, where the rain gardens turned out to be the optimal solution. In addition, the findings of the proposed method were compared to those of other MCDM approaches such as TOPSIS, VIKOR, sPROBID, and MOORA, and a sensitivity analysis was performed by modifying the experts’ weighting of the decision matrix. Overall, this study provides a reliable and efficient approach for communities and stakeholders to evaluate the performance of GI, which may greatly help in developing focused improvement plans for SUD.

Limitations

The proposed work possesses methodological constraints due to its dependence on predefined criteria and fixed aggregation operators, which may limit adaptability to different contexts. Although the expert opinions are systematically aggregated and transformed into fuzzy values, outcomes may be impacted by differences in expert interpretation. Since the current study does not provide a direct real-world application or validation, practical implementation of the suggested work may be constrained. The computational load of the D-CRITIC technique is a potential limitation of this work. Since GI performance and prioritization might vary among locations with various climate, geographic, or governance settings, the reliance on a particular set of GI practices and criteria poses a contextual issue. Furthermore, as the framework reflects a static planning environment and is best suited to local contexts, scaling it to the national level may be challenging.

Implementation solutions

The framework can be strengthened by incorporating the design dimension¹ alongside environmental, economic, and social dimensions to better capture practical planning considerations. In addition, applying the model to a real-world case study within a specific study area enhances contextual relevance and supports actionable decision-making⁴⁵.

Future Work

Future work could involve conducting a real-world, GIS-based case study to support GI selection for SUD. Integrating machine learning technology with the approaches discussed in this study may be a useful strategy for solving crucial decision-making problems. Furthermore, Real-time object detection using deep learning, as demonstrated in the Forklift Automated guided vehicle study⁴⁷ illustrates how intelligent automation can process dynamic data for contextual decision-making. Integrating such methods could make the proposed framework adaptive, updating priorities in real time to support responsive and sustainable green infrastructure planning⁴⁸.

Author contributions

Kannusamy Aarthi: Writing – review & editing, Writing – original draft, Visualization, Validation, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Samayan Narayanamoorthy: Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Methodology, Investigation, Formal analysis, Conceptualization. Navaneethakrishnan Suganthi Keerthana Devi: Writing – review & editing, Visualization, Validation, Methodology. Krishnan Suvitha: Writing – review & editing, Visualization, Validation, Methodology. Naif Almakayeel: Writing – review & editing, Visualization, Validation, Funding acquisition. Hasan Dincer: Writing – review & editing, Visualization, Software, Resources, Funding acquisition. Serhat Yuksel: Writing – review & editing, Visualization, Validation, Funding acquisition. Daekook Kang: Writing – review & editing, Visualization, Validation, Software, Resources, Funding acquisition.

Funding

Not applicable.

Data Availability

The study utilizes secondary data, which are publicly available and anonymized. The datasets analyzed during the current study are available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

The study involved a panel of domain experts who provided professional evaluations. All participating experts were fully informed about the purpose of the study, the procedures involved, and the voluntary nature of their participation. Informed consent was obtained from all experts prior to their inclusion, and their responses were used exclusively for academic research purposes. All methods were conducted in accordance with relevant guidelines and regulations.

Declaration of competing interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Competing interests

The authors declare no competing interests.