Positioning of aerial ambulances to improve health care access: A framework using fuzzy DEMATEL and fuzzy ANP

ABSTRACT Air ambulances are a crucial enabler of emergency health care because of their high speed, ability to reach impassable areas, relocate more patients, provide better treatment while carrying patients, and ease of access to the hospital without traffic or sudden accidents. The right location must be selected according to scientific principles that address relevant factors to increase air ambulance efficiency in an emergency. A descriptive-analytical approach was adopted to solve the problem of identifying the best locations for aerial ambulances, combining three distinct methods. The first step was to identify criteria affecting the location of air ambulances. Then, the location was determined using a fuzzy analytical network process model coupled with a fuzzy decision-making trial and evaluation laboratory (DEMATEL) technique and a geographic information system. To examine the method, a case study was conducted in a province in southeast Iran. Case study results showed insufficient aerial ambulance stations and roads to meet the need. This study provides helpful information for city planners and health policymakers to determine the optimal location of air ambulances by analyzing geographical conditions and barriers to delivering high-quality care to remote area. The study can contribute to more sustainable cities through better health services for communities.


Introduction
About 86% of trauma-related deaths and 64% of cardiac arrest-related deaths occur before hospital arrival [1].This might be due to (a) the distance between the accident scene and the location of emergency services, (b) the inaccessibility of the area, or (c) the requirement for secondary transfer from the primary care center to a specialist hospital and advanced trauma centers [2].In critical times, an air ambulance can be immensely beneficial in both providing swift access to individuals involved in an incident and taking them from the occurrence to somewhere safe for treatment, thus increasing their chances of survival [3].
As a component of the emergency medical system, an air ambulance is one of the quickest and most effective means of delivering the injured and ill in emergencies, natural disasters, and automobile accidents [4].Air ambulances deliver a rapid and high-quality service by decreasing response and transfer times and maximizing population health management in accidents and emergencies by providing good local coverage and response to demand [5].In addition, it may overcome geographical obstacles such as mountains, woods, and great distances to save patients' lives in unreachable places [4].Thus, the proper location of air ambulance facilities is crucial, as improper decisions regarding the facility's location severely affect the outcomes.
Covering the largest region is one of the most significant aspects of creating or expanding emergency facilities to give patients the best care [6].Emergencies are unpredictable regarding time and location.Establishing facilities in an appropriate location decreases response time and services to the injured and medical centers, which is one of the primary objectives of the emergency medical service system [7].The optimal location for emergency medical services is a strategy for providing medical services by accomplishing the goal of the greatest coverage and decreasing the route's time, distance, and infrastructure costs [8].The proper establishment of air ambulance bases has decreased response time, increased the number of populations served, and decreased mortality [6].Countries are constantly striving to improve healthcare in remote regions, and one way of doing so is by increasing the number of air ambulances.In 2018, according to the Atlas & Database of Air Medical Services (ADAMS), there were 1,114 air ambulance bases in the United States, while Germany had 71.Developing nations are unfortunately lagging behind in this regard: India has just 49 air ambulances, and Iran only 50.
This research is important because ensuring an efficient location of the air ambulances supports society to access the health care system on time, particularly in remote areas where people have insufficient expertise or resources to treat emergency cases.Identifying effective locations for air ambulances allows countries to become more socially sustainable by using golden hour and providing the proper service during a period when an injured person still has a chance to survive.It also benefits communities in the surrounding region by providing the capability to operate everywhere, irrespective of the location, with faster speed.Despite rarely being examined by researchers, spatial data analysis and Geographic Information System (GIS) can be used to determine the optimal location, including proximity to routes, the slope of the area, proximity to crowded centers, proximity to high-risk passages, and distance from emergency departments.Most previous studies focus on optimization modeling to find the optimum location for the air ambulance.However, they ignore the importance of the geographical condition and the barriers (e.g.[7][8][9][10]).When selecting the location for an air ambulances, many factors must be considered.These can include the distance from the EMS center, proximity to routes, and nearby natural impediments such as mountains or forests.However, it is also essential to recognize the potential challenges posed by wind speed and vast distancesissues often neglected in past optimization models.To tackle this, a combined approach must be implemented to integrate different techniques and datasets with Geographic Information Systems (GIS).
To address this issue, this paper conducts a multilevel solution framework including documentary analysis, a multi-criteria decision-making (MCDM) technique, and Geographic Information Systems (GIS) to determine the best location for the air ambulances (a) reduce the risk of uncertainties and errors in expert opinions; (b) reduce time and cost spending the selection area by adopting a rich database from the GIS; (c) increase the accuracy of the location selection by providing a comprehensive assessment.Providing ontime service for seriousinjured and acute patients is one of the main criteria for enhancing social sustainability, including health, safety, and social welfare in cities [11].Air ambulance locations must be selected to ensure service availability in the entire region.
This essay aims to aid the healthcare system and empower policy-makers to elevate social welfare and healthcare standards.The findings of this inquiry will facilitate the government in stationing the air ambulance in an optimal location, supplying swifter and more effective aid to people in all parts of the country, particularly in rustic regions.
This paper is structured as follows.Section 2 outlines the material and method.Section 3 outlines the results and is followed by a discussion and conclusion in Section 4.

Method
This research adopted a descriptive-analytical study in applied research.Three different but connected methods are used in this study to address the issue (See Figure 1).First, document analysis is used to determine the criteria of the air ambulance location.Second, an MCDM approach (Hybrid fuzzy analytic network process (ANP) and fuzzy decision-making trial and evaluation laboratory (DEMATEL)) is adopted to examine the relationship and interrelationship of the selected criteria from the first step and rank them.Finally, a geographic information system (GIS) is used to match the selected criteria from the previous step with geographic layers and identify the best location for air ambulances.
This section starts with a documentary analysis in section 2.1, followed by an explanation of the MCDM approach in section 2.2.Finally, section 3.3 discusses the combination of Geographic information systems (GIS) with the MCDM approach to find the most appropriate location.

Documentary analysis
Document analysis is a qualitative research technique that evaluates electronic and physical documents to interpret them, understand their meaning, and develop upon the information they provide [12][13][14].Based on the documentary method, the theoretical foundations and literature on establishing aerial ambulances and applying geographic information systems (GIS) in systems have been studied [12].

Fuzzy ANP and fuzzy dematel
The combination of fuzzy ANP with a fuzzy DEMA-TEL as an MCDM approach is applied in this research to determine the magnitude, direction, and relation of the criteria for air ambulance location.
Two questionnaires were developed (Appendix 1) to obtain experts' opinions and identify the relationships between criteria and their pairwise comparisons.The experts questioned in this study include 24 managers and deputies, Emergency Operations Center (EOC), pre-hospital emergency station officials, planning and development managers, and education and research managers for medical emergencies.Discussing the design with experts enabled us to improve the questionnaire's validity.
Since the standard DEMATEL and ANP methods require exporting explicit opinions using crisp numbers for pairwise comparisons and ratings, it seems that the standard DEMATEL and ANP have difficulty of overlooking uncertainties and errors in expert opinions, and in some way, uncertainties arising from human judgments should be affected in input data problem [15,16].To resolve this problem, fuzzy logic is proposed to consider the uncertainty in solving the location problem [15,16].

Fuzzy ANP
Analytic network processes (ANP) are more generalized forms of analytic hierarchy processes (AHP) used for multi-criteria decision analysis.AHP's decision problem is structured into a hierarchy with a goal, decision criteria, and alternatives, while in ANP, it is structured as a network [17].ANP is a problem-solving structure that organizes the perceptions, feelings, judgments, and information of the decisionmaker's mind; ANP examines the factors affecting decision-making results in a hierarchical form [17,18].The ANP provides measurements to assess the distribution of influence priorities between agents and groups of agents in the decision-making [19].The ANP method consists of four main steps [17,20,21].These steps include establishing the problem structure, pairwise comparison matrices, and priority vectors, forming a super-matrix, and choosing the best alternative.In the ANP, the pairwise comparison matrix is used to weigh and rank the priorities.However, this matrix cannot be used in the fuzzy ANP where input data is ambiguous [17,20,21].To solve this problem, the ANP in a fuzzy mode was introduced [22].The only difference between the proposed model and ANP is the method of extracting the rating weights from the pairwise comparison matrix [22].In this study, given the advantages mentioned, the fuzzy ANP is used to weigh the selected criteria and determine each criterion's influence on the problem's objective.The ANP method is encoded in MATLAB software to avoid complexity and waste of time.

Fuzzy dematel
The DEMATEL method is used to construct a causal diagram and visualize the structure of the complex causality relationships between a set of components in a system.The DEMATEL method is combined with fuzzy logic to resolve the ambiguity of experts' judgments.Respondents offer uncertainties in the form of a linguistic diagnosis based on experience rather than judging based on crisp values.Hence, the uncertainty of the input parameters of the decision-making system should be sufficiently considered to ensure that the results are improved.
To obtain the importance degree of criteria and understand the causal relationship between criteria, the fuzzy DEMATEL consists of five steps.These steps include computing the initial direct-relation matrix, calculating the normalized initial directrelation matrix, determining the fuzzy total-relation matrix, and calculating fuzzy values and defuzzification of fuzzy values [15,23,24].The fuzzy DEMATEL was encoded in MATLAB software.
In this study, a hybrid fuzzy DEMATEL and fuzzy ANP method have been used for rating the key criteria affecting the location of air ambulances.The output data of this method is used as input of GIS software to weigh the layers generated in this software.GIS is generally a coherent set of hardware, software, professional tools, and spatial data referrals that allows users to merge, store, edit, analyze, share and display geographic information [25,26].

Geographic information systems (GIS)
The GIS is used in this study to improve the accuracy and reduce the time and cost spent on selecting the appropriate air ambulances location.The GIS method provides a rich and efficient database for better monitoring and reviewing the study area [27].For GIS application, you must first create a database that includes these three steps: (1) data collection to assess effective factors; (2) establish a database to create layers associated with identified criteria (This information was collected from the sources including Emergency Medical Service Centers of Province A, the Statistics Center of Iran, Bureau of Toll and Road Transportation, Office of Statistics and Information, Governor's Deputy of Planning), and (3) digitizing point, line and polygon effects; point effects include EMS and county and district centers; line effects include highway roads and high-risk passages in the province, and polygon effects include Province A that are considered as separate layers in the GIS environment.The hybrid uses of GIS and MCDM analysis integrate GIS maps, and the priorities and uncertainties of expert opinions on decision-making alternatives provide a comprehensive assessment [28].Therefore, the fuzzy maps of criteria affecting the location of air ambulances are generated in the GIS software environment.Then, the importance coefficient obtained from the fuzzy ANP and fuzzy DEMATEL encoded in MATLAB software is affected for each criterion in its information layer.Finally, the best locations to deploy air ambulances are prioritized.The detailed steps of the solution framework are presented in Figure 2.

Results
This section presents the case study used to examine the model (section 3.1), and sections 3.2-3.4show the results of the multi-level solution framework.

The study area
Sistan and Balouchestan (Province A) is the largest province in the southeastern region of Iran, accounting for 11.5 percent of the country's territory, with 19 counties, 37 cities, 48 districts, 112 rural districts, and 9285 villages and roads [29].This province has an area of 187,502 sq.Km, 200 Km of highways, 888 Km of main roads, 2256 Km of secondary roads, and 7540 Km of rural roads [29].
The main roads of the province are often two-way and narrow without adequate lighting, and cross-sectional repairs and the secondary roads are also slender and inappropriate.Thus, the region is one of the riskiest areas of the country in road accidents, while it is also one of the most deprived areas in addressing these road problems The map of the geographic area of the study area is shown in Figure 3.

Documentary analysis
In this step, a documentary analysis has been conducted to identify the most important criteria for the air ambulance location.According to the literature and the information provided from three provinces located in the south of Iran, including Sistan and Baluchestan (province A), Kerman (province B), and South Khorasan (province C), the most important criteria for air ambulance locations are: (a) proximity to the routes, (b) the proper slope of the area, (c) proximity to crowded centers, (d) proximity to high-risk passages, and (e) the appropriate distance from the emergency medical service centers.

Hybrid fuzzy ANP and fuzzy dematel
To understand the relation of the provided criteria in the previous section, a hybrid fuzzy ANP and DEMA-TEL fuzzy method was conducted.Following the document analysis, the retrieved criteria has been screened and validated by expert panel and the criteria were adjusted.The completed list is converted into a DEMATEL questionnaire and 24 experts weighted the inter-relation between criteria.Follwing the DEMATEL method, a fuzzy ANP approach were conducted to address the decision-making issues.The hierarchical questionnaire with the same criteria of the DEMATEL questionnaire were filled with the same 24 experts to provide a pairwise comparison of criteria.The output of each questionnaire is a directrelation matrix for each expert's judgment; ultimately, there are 24 matrices.The corresponding entries are averaged to obtain the comprehensive matrix (Table 1).
Fuzzy DEMATEL was implemented by coding in MATLAB software.Therefore, the final fuzzy directrelation matrix was entered as input to the coding, and all stages of the DEMATEL method were implemented.Given the fuzzy matrix entries and triangular fuzzy numbers of the initial direct-relation matrix, this matrix is divided into three matrices; the first matrix is the lower bounds, the second matrix is the middle bounds, and the third matrix is the upper bounds of the triangular numbers contained in the direct-relation matrix.Each time the coding of the DEMATEL method is executed for each of the matrices, the defuzzied total-relation matrix is obtained (Table 2).
The hierarchical questionnaire was provided to 24 experts based on this question, which one of the two factors, A and B, is more important for obtaining the appropriate space for air ambulances in Province A. In the fuzzy pairwise matrix, the original diameter is always numbered one, and the comparisons of one side of the original diameter are opposed to its other side.The final pairwise comparison matrix from the aggregation of the entire population is shown in Table 3.The output of each questionnaire is a pairwise comparison matrix, which ultimately, there are 24 matrices.The corresponding entries are averaged to obtain the final matrix.
Fuzzy ANP was encoded in MATLAB software.Therefore, the final pairwise comparison matrix aggregating all experts' judgments is coded into vectors, and the output is the criteria weights.The weights given to the criteria using fuzzy ANP are shown in Table 4.
Finally, the final total-relation matrix obtained in the DEMATEL method, which is 5 × 5 matrices, is multiplied by the output matrix of the fuzzy ANP, which is a 1 × 5 matrix.Therefore, hybrid DEMATEL and ANP methods are implemented, and the weights obtained in the GIS layers are affected.The results of this method are shown in Table 5.

Geographic information systems (GIS)
After determining the influence of each criterion, the detailed maps of information layers related to each criterion were prepared in the GIS software (ArcGIS) using field data from different institutions.The Reclassify operator first classified each of the layers to unify the classes, and then they were fuzzified using the Fuzzy Membership operator.Then, the weights obtained in Table 4 were applied to each of the fuzzy layers by the Raster Calculator operator, and the weighted fuzzy maps were obtained (Figures 3-7).Finally, all fuzzy layers were placed for overlapping using the Fuzzy Overly operator and gamma function at a rate of 0.9 (Figure 8 and 9).
In the current situation of Province, A, there are two air emergency bases in cities A1 and A4.Each base, like Figure 10, can cover its area with an operating range of 150 Km.The amount of coverage is small due to the vast area of the province.Given the final map of the effective factors on the location of air ambulances in Province A (Figure 9), it is observed that the optimal points for this location are placed in cities A2 and A3 (Figure 11).

Discussion and conclusion
A comprehensive research method was employed to determine the optimal locations for air emergency bases in Province A, incorporating field studies, similar investigations, prior experience, and library-based analysis.The criteria considered when assessing prospective sites consisted of proximity to transport routes, the area's slope, vicinity to highly populated areas, proximity to high-risk routes, and distance from EMS centers.The outputs of the hybrid MCDM method (fuzzy ANP and fuzzy DEMATEL) were the weights that must be assigned to each criterion in the GIS software: 0.224, 0.083, 0.0435, 0.182, and 0.057, respectively.
Previous investigations were chiefly focused on optimizing air ambulances' deployment considering limited resources and maximizing the number of fulfilled demands while diminishing service time.Nevertheless, in contrast to this current inquiry, they neglected their optimization models' geographic requirements and impediments.Consequently, this study employed GIS to ascertain the ideal location for air ambulances, considering geographical constraints.
Utilizing Geographic Information Systems (GIS), studies have been conducted for various purposes.For instance, evaluating the best sites for the extension of pre-hospital helicopter emergency services by determining population coverage in relation to service Table 1.The comprehensive fuzzy direct-relation matrix (the output of the DEMATEL questionnaire).

The appropriate distance from the EMS centers
Proximity to highrisk passages

Proximity to crowded centers
The proper slope of the area Proximity to the routes S D (0.5, 0.75, 1) (0.75, 1, 1) (0.75, 1, 1) (0.12, 0.37, 0.62) Proximity to the routes (0,0, 0.25) (0.25, 0.5, 0.75) (0, 0.25, 0.5) (0.25, 0.5, 0.75) The proper slope of the area (0.75, 1, 1) (0.75, 1, 1) (0.25, 0.5, 0.75) (0.62, 0.87, 1) Proximity to crowded centers (0.62, 0.87, 1) (0, 0.12, 0.37) (0,0, 0.25) (0.12, 0.37, 0.62) Proximity to high-risk passages (0.12, 0.37, 0.62) (0,0, 0.25) (0,0, 0.25) (0,0, 0.25) The appropriate distance from the EMS centers centers and the time frame for access [30], assessing and analyzing the variation in transfer times of injured individuals from accident sites via air or ground-based emergency services depending on the type, distance and infrastructure features of the roads [31], and determining the optimal locations for Helicopter Emergency Medical Services (HEMS) sites with the intention of providing maximum coverage while utilizing minimal facilities [32].Similarly, we can assess the best locations for air ambulances by using GIS and fuzzy ANP in this study.An in-depth analysis of the air ambulance dispersal map for Province A strongly suggests that the existing emergency service system is inadequate in terms of coverage and speed.It can be reasonably concluded that this system    requires significant improvement if it is to adequately meet regional healthcare needs.This research aims to maximize social sustainability; thus, response time stands as a critical factor for assessing the performance and quality of healthcare services.Moreover, medical emergency care directly impacts patient well-being and safety, rendering response time a decisive criterion for measurement [33].In this study, using effective criteria for establishing an air base and the proposed method and considering the road conditions and facilities of Province A, suitable points were identified for establishing air emergency bases (Figure 9).From these areas, both cities A2 and A3 were determined as the most desirable locations for establishing air emergency bases due to the selected criteria.According to Figure 11, by establishing an air emergency base in cities A2 and A3, besides providing relief to most densely populated cities, most highways and especially high-traffic areas of the province are also fully covered by air ambulances, leading to reduced relief times, improved medical services, and increased the survival of patients and accident injuries.

Implications for practice
The findings of this study offer insight to decisionmakers for enhancing social sustenance and wellbeing by ensuring timely and effective healthcare for emergency patients.Without sufficient dispersal of helicopter medical rescue sites, the 'golden time' period will be jeopardized, causing a climb in mortality [34].Consequently, strategically placed air ambulances afford cities equal accessibility to medical attention, including in distant areas.This service can significantly boost life expectancy by furnishing quick treatment to seriously injured persons, thereby rescuing them from imminent risk.

Limitation and future research
This study's primary objective was to increase social sustainability by deploying air ambulances in the most accessible place; however, environmental sustainability must also be considered while determining the ideal position.
For future research, we should include environmental circumstances such as suitable distance from faults and natural calamities such as Sistan's 120-day winds and Baluchistan's monsoon rains.This investigation was undertaken for one of Iran's most populous provinces.This province's geographical circumstances differ from those of a province in northern Iran that is more humid and forested.It is suggested that this research be applied to other Iranian areas.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Funding
The author(s) reported there is no funding associated with the work featured in this article.Farzad Firouzi Jahantigh is an Associate Professor, researcher and academic member in the Department of Industrial Engineering at the University of Sistan and Baluchistan.He possesses specialized expertise in the fields of optimization, health systems engineering, data mining, and artificial intelligence, and his research pursuits are dedicated to furthering the knowledge and advancements in these areas.

Notes on contributors
Dr. Mona Koushan is an academic scholar with a focus on operations research, operations management, health care management.Her research aims to understand how operations management and operations research can assist healthcare policymakers in enhancing the quality of services and making more efficient use of healthcare resources.Key areas of her expertise include projects management and scheduling, system analytics and sustainable operations.
Lincoln C. Wood is an Associate Professor, researcher and academic with a focus on operations management, logistics, sustainability, healthcare management, rural studies, and information systems.His research aims to enhance decision-making processes and performance across various industries using analytical tools and sustainability practices.
Prof. Wood's work examines the relationships between global events, technology adoption, and organizational strategies.Key areas of his expertise include systems thinking, strategic decision-making, data-driven insights, and socioeconomic awareness.His projects often address decisionmaking under uncertainty, employing tools such as Fuzzy DEMATEL and machine learning to manage risk in uncertain contexts.Prof. Wood's research emphasizes the importance of sustainability and the circular economy in various industries and highlights the role of advanced technologies like Industry 4.0 in enhancing efficiency, productivity, and sustainability.

Figure 2 .
Figure 2. Detail steps in our novel, multi-level solution framework.

Figure 3 .
Figure 3. Geographic area of the study area (Province A).

Figure 4 .
Figure 4.The fuzzy rated map of 'the proper slope of the area'.

Figure 5 .
Figure 5.The fuzzy rated map of 'the appropriate distance from the EMS centers'.

Figure 6 .
Figure 6.The fuzzy rated map of ' proximity to the routes'.

Figure 7 .
Figure 7.The fuzzy rated map of 'proximity to high-risk passages'.

Figure 8 .
Figure 8.The fuzzy rated map of 'proximity to crowded centers'.

Figure 9 .
Figure 9.The final rated map of Province A for the location of air emergency centers.

Mojtaba
Ghaderi is Master of Industrial engineering from Univeristy of Sistan & Balouchestan.

Figure 10 .
Figure 10.The current status of air emergency stations.

Figure 11 .
Figure 11.The status map proposed by the study for the location of air emergency bases.

Table 2 .
The defuzzied total-relation matrix of the DEMATEL output.

Table 4 .
Output weights of fuzzy ANP.

Table 5 .
The output weights of the hybrid fuzzy ANP and fuzzy DEMATEL method.

Table 3 .
The final pairwise comparison matrix of criteria.