Start-up failures due to Quality Failures

: Software start-ups are fundamentally different from traditional software development firms and boutique software services enterprises of all sizes. They develop software products with strict time and resource constraints and are focused on beating competitors to the market. They fail fast and often pivot their business models several times in their lifetimes. Their approach to designing, developing, testing, and shipping software products differs vastly from the established software engineering principles that emerged during the field‟s earlier decades. One such principle is Software Quality Assurance. Start-ups tend to do away with procedures that ensure that their products are of the utmost quality. Instead, they focus on shipping their products to market as fast as possible, testing these products vis-a-vis real-life customers and use-cases, and eventually improving these products, repeating the process several times over. We hypothesize that this reluctance to adhere to software quality assurance principles can have adverse effects on the health of start-ups or their products. This paper investigates this hypothesis through over 20 questions presented to CEOs, CTOs, Technical Leads, and Product Managers of several start-ups. These questions focus on start-ups‟ motivations, their levels of understanding and appreciation of software quality assurance principles, and the limitations they face due to time and resource constraints. Our research‟s results indicate the surveyed start-ups‟ problems are partially due to the absence of robust software quality assurance practices within their processes.

Introduction
The start-up industry has shown significant growth in the last two decades. Pakistani start-ups alone raised 18 Million Dollars during the nation-wide Coronavirus lockdown [1].
As compared to the high-profile organizations and software development companies, the new start-ups face more problems in integration and ensuring the software"s quality. Those problems are the lack of human resources, investment constraints, time issues, and others [4]. Traditional software engineering and quality assurance practices are deemed unfit for fast-changing requirements, which have resulted in their evolution [6]. Software start-ups work under immense uncertainty and pivot their product frequently and as needed [7].
Furthermore, start-up founders tend to focus on more important factors, which result in Software Quality Assurance practices" deliberate disregard. IBM has published a whitepaper comparing the costs of discovering an error at different development lifecycle stages. The multipliers are 5x for the implementation phase, 10x for integration testing, and 30x after the product"s release to the market [5].
We found very rare research has been conducted on Software Quality Assurance (SQA) related issues for start-ups in the software industry, the software been a fastly growing industry specifically in Pakistan, which opens up a variety of topics to be researched. Our research investigates the role of Software Quality Assurance best practices within the fast-growing tech start-up ecosystem. Our research also focused on the impact of poor software quality practices on product and software failure. Our research paper analyses the SQA practices in the startup industry and helps in determining the reasons that result in software testing practices being overlooked by start-ups [3].

Background
The growth of start-ups has been motivated by many reasons, with job-security being the most important one. It has become evident during the COVID-19 pandemic due to downsizings.
Internet start-ups deliver technological (software) products to businesses and individuals. Being a newly launched firm, a start-up goes through multiple development phases to gain trust and name in the market, having limited personnel and resources.
During their development phases, the internet and software start-ups have to go through multiple challenges. The two most common are the software"s quality and the extremely short time-to-market, which is in weeks or months [2].
In the pressure of getting the products to the market ahead of the competitors, the start-ups consider quality assurance a less essential component of software development, which leads to frequent mishaps because of software failure or errors [18,19].
Our research analyzes the problems faced by the software start-ups that are caused by the lack of adherence to the software quality assurance practices. The research aims to achieve this goal by the literature and a survey conducted from the people having crucial roles in the software start-ups having a limitation of a small population belonging to this category. Similarly, it is perceived that most start-up lack standard practices and frameworks [22].
This study investigates the extent to which start-ups" failures can be attributed to failure to adhere to software quality assurance principles. Addressing these gaps can be significant as it could help start-up founders and leaders understand quality failures and work towards building more robust software products.
Moreover, we intend to validate the hypothesis that start-ups tend to mutate -often to disastrous effects -SQA tools and procedures to fit them into their inconstant software development goals.

Literature Review
There is little literature solely focused on software quality assurance practices in software start-ups. Most researchers tend to focus on the subject of software engineering when researching software start-ups and their operations.
Software quality assurance can become expensive in calendar time [10,11] and is mostly absent in software startups. Other reasons include a lack of experience amongst the start-up personnel [8] and weak methodological management [9]. Start-ups usually rely on usability tests to achieve product-market-fit [12,13,14]. Mater and Subramanian suggest focusing on a relatively smaller group of early adopters to drive their product"s quality assurance aspect [2]. Thus, removing bugs and adding more tests can be done if the early adopters run into issues with the software. This approach is different from traditional quality assurance practices [11].
Start-ups also outsource their testing work to software testing experts on an as-needed basis, often due to the lack of resources, as mentioned earlier. This outsourcing helps in focusing their resources on the development of core functionalities of their product. Communcation problems can exist between distributed teams [20].
Start-ups often ignore standard software quality assurance methodologies because they are mostly incompatible with lean start-up methodologies that most software start-ups practice for SQA in developing countries [17,21].
Technical debt management is universally harder for software start-ups than it is for traditional software firms. The software market changes rapidly. Thus, start-ups have to pivot multiple times in their lifetimes and often make snap decisions during smaller sprints and development life-cycles [8]. Failure to successfully manage technical debt contributes significantly to start-up failure.
The absence of standard quality assurance practices and established software engineering practices, in general, can also lead to inadequate software quality and, ultimately, start-up failure [15] The development of software in start-ups is product-oriented. The earlier success becomes irrelevant in the later stages of the product development of a start-up"s because the software becomes increasingly complex, resulting in deterioration of performance [15,16] In summary, the following table illustrates start-up failure reasons and causes behind them.

Research Methodology
Our research tactic is developed and directed using qualitative research methodologies. The qualitative research method is popular to derive and explore start-ups' social, cultural, and economic aspects. The qualitative research approaches play a vital role in comprehending a field's insights and the diversities among that field's contents. This research is a survey-oriented study that includes answers given to the questionnaire and face-to-face interviews where participants answer various questions.
Our research survey aims to determine the software quality assurance practices in Pakistani software start-ups. It seeks to understand the software testing methodologies used, the criteria for selecting an appropriate method based on time and personnel constraints, and the development and testing teams' relations. Additionally, this survey can suggest future research directions for the software quality assurance field vis-a-vis start-ups. The questionnaire of the study is segmented and defined based on hypotheses derived from the literature review.
The survey"s participants were individuals working at different positions in different departments of the software start-ups as they contribute to the software development, quality assurance, and overall performance of the enterprise. Due to a small number of software start-ups in Pakistan, we could only perform the study is on a limited number of participants. The participant rate is low, but it covers diverse roles of the software development ventures. As noticeable through figure 1, around half of the survey participants have their functions as Technical leads/senior software engineer, whose perspectives are critical as they directly contribute and stake in the software development process. The other four important roles of the research contributors are Chief Technical Officers, Product Designers, SQA/Test Engineers, and Product Managers /Owners. Looking at the roles of the participants of the study, it can be implied that the sample signifies the study"s targeted population.

Characterization
This section represents the numeric and quantitative details of the software start-ups in Pakistan. Firstly, the research participants were asked about the time their start-up firms have been in service. Figure 2 shows that all the participants" firms have ages of up to 5 years; the majority of the start-ups have been established around 2-5 years ago while 23% have been present in the industry for less than a year. It shows the growth of the start-ups in the Pakistani technology industry in the last few years, particularly during the Covid-19 pandemic. Secondly, the participants were asked about the development phase that their start-up firm is in. It was found that 77% of firms are independently offering their services in the market. Around 15% of those start-ups are in their initial development phase, approximately 7% of the start-ups have ceased operation, while none of them has been acquired by another company as apparent in figure 3. The third question"s purpose was to get an insight into the employee size and resources that the start-ups possess. As visualized in figure 4, the study found that around one-fourth of the participants" are working in start-ups having less than ten employees. The percentage remains the same at around 30% for the number of start-ups having 10-25 employees and 25-50 employees, while around 15% of the start-ups have more than 50 employees in their firms. The number of employees in these firms has been increasing with time.

Documentation
This section of the study aimed to determine whether the start-ups documented their business processes, codes, and several software development steps. Figure 5 tells us that 37% of start-ups have either not documented any part of their codebase, or have documented one-fourth part of it. There were 30% of participants working in a start-up that had documented less than or half of their codebase. The percentage remains the same for those having three-fourth part of their code written. In the second question related to the documentation, participants were asked about their start-ups" software components. We found that 15% of start-ups did not have any of the three, System Architecture, Test plans, and Software Requirement specifications. On the other hand, most of the start-ups performed the System Architecture Copyright © 2021 MECS I.J. Engineering and Manufacturing, 2021, 2, 1-13 documentation, and the documentation for the test plans and software requirements specification was done by half of them. Fig. 6. Types of testing performed in the start-up

Software Quality Assurance Practices
Software quality assurance is a vital part of the software development life-cycle. This statement was supported and accepted by all the participants when they were asked whether they considered Software Quality assurance a critical aspect of Software development. They unanimously answered a yes, as visualized in figure 7. This section of the questionnaire aimed to identify the measures and steps taken by the start-ups to maintain the quality of the software products they develop. At first, we asked a question to get the number of start-ups who have a dedicated Software quality assurance department. The Yes to No ratio was 54% to 46%, as evident in figure 7. We further noticed that all the start-ups with a dedicated Software Quality Assurance department have been functioning for a longer time and have a higher human resource than those not having it. The next question was related to the step at which the start-up"s software quality assurance team comes on board for testing, troubleshooting, and other quality assurance purposes. As mentioned earlier, a major portion of the respondents said that they don"t have a Software Quality Assurance department at their workplaces. Among the respondents having a Software Quality Assurance team, 33% take the Software Quality Assurance team on board Copyright © 2021 MECS I.J. Engineering and Manufacturing, 2021, 2, 1-13 during the testing phase. In comparison, the number is 16% for the start-ups, which involve the software quality assurance team during the initial phase of Requirements Gathering and Analysis. The percentage remains the same at 8% for the start-ups applying the Software Quality Assurance at the Design, Implementation, and for every phase of the software development life cycle. Fig. 9.
Step at which the SQA team gets on board The third question of this section aimed to determine the testing types performed to ensure the software"s quality by checking multiple factors. According to the research results as represented in figure 9, 7-8 out of 10 start-ups perform unit tests on their software products. The results show a similar number for the start-ups performing Integration and Functional Tests. 5-6 out of 10 start-ups run the Smoke tests on their software programs. The number is very low for the Automated UI tests performed by only 38% of the start-ups. The question results also confirm that there was no start-up, which did not perform any software testing. We can further observe that the testing methodology depends on the start-up and its software products" types. The fourth question aimed to get an idea of how many start-ups in Pakistan maintain bugs databases for tracking the issues in their developed software products. Figure 11 shows a 6:4 ratio of the start-ups maintaining bugs database to those not maintaining it. It must be mentioned that the start-ups not maintaining bugs databases will need to repeat through th/e whole process of searching till solving the problems in the softwares. In the next question, the study focused on the bugs that arise after developing the applications. Those bugs" cost is usually higher than pre-release bugs" costs due to the multitudinous installations and other time-consuming efforts. The study found out that around 46% of the start-ups have 25% post-release bugs, while the number of start-ups having 25-50% was 38% and 50-75% post-release bugs was around 15%. It infers that around half of the Pakistani software ventures track the bugs after deploying their software products, which may result in consuming more time and human effort. The results of figure 12 can be related to the results of figure 13. The visualization of the results of the question in which the survey respondents were asked the critical aspect of their ventures. out of 10 respondents chose the option "Releasing with fewer bugs" while 4 out of 10 selected "Releasing the software fast." These numbers can be referred to as the hurry and launch of the products in the fast-paced industry with newly arriving businesses every day. We further note from figure 14 that 9 out of 10 participants belong to the start-ups which perform their software quality assurance tasks themselves. In comparison, only 1 out of 10 participants belonged to the start-up, which gets their softwares tested through third-party firms.

Challenges due to ignorance of Software Quality Assurance Practices
The study contains this section to identify the challenges the start-ups face due to the lack of adherence to Software Quality Assurance practices. At first, this section finds out the technical debt caused by the lack of commitment to the Software Quality Assurance principles and practices. This question recognizes the importance of software quality Copyright © 2021 MECS I.J. Engineering and Manufacturing, 2021, 2, 1-13 assurance in start-ups and the efforts required to redo the tasks appearing faulty in the testings. As figure 15 represents, only 37% of start-ups don"t have about or less than 25% technical debt due to the lack of software quality assurance practices. On the other hand, the number for those having a high technical debt is more elevated. 23% of start-ups have 25-50% technical debt due to not implementing the software quality assurance concepts. Lack of these applications causes 50-75% technical debt to around 38% of Pakistan"s start-ups. In the second question, it was found that there has been no financial penalty to the 75% of participants" start-ups because of the software failures, while 25% of them have faced it. In the third question of this section, the survey respondents were asked if their start-ups scraped any software product because of not meeting the requirements of the product. As shown in figure 17, it didn"t occur in 73% of cases, while 27% of start-ups destroyed their products because they did not meet the requirements. 27% is a large percentage considering the human effort, cost, and resources consumed for developing the software. These facts and figures strengthen the concept and importance of the Software quality assurance practices that ensure the products having the required performance, maximum functionalities, and the least number of errors and bugs. Fig.17. Start-ups that scraped any product because of not meeting the requirements?
The participants themselves further strengthen this statement. There was a 92% positive response from them when they were asked if they think that whether strictly following the software quality assurance practices will improve their products" life and capability, revenues, and the overall performance and market standing of their ventures. The survey results highlight the importance of the software quality assurance practices and support the hypothesis of the study that the lack of adherence to the Software Quality Assurance practices leads to several problems that cause a great loss to the image, reputation, and standing of a venture.

Future Work
Start-ups are an emerging area for research work. As noted in the Literature survey section of the paper, the present literature about software practices in start-ups focuses on the broader aspect of Software Engineering in start-ups. Its focus on Software Quality Assurance is limited. Based upon our findings, future research work could look further into the SQA personnel"s role within start-ups and the relationship between technical debt and SQA. Furthermore, it could investigate how certain established Software Quality Assurance principles are mutated and molded to serve Software Start-ups" requirements.
Our research focused mainly on a limited number of Pakistani internet start-ups in which we identified the situations, requirements, industry pace, and other important factors. In the future, this research agenda could be expanded to include a broader array of software start-ups from around the country or the world as operating in different markets could result in various challenges. It can be further detailed to identify the testing methodologies, types of practices, and other SQA options relevant to specific tech-related start-ups. Investigating such difficulties and their impact on Software Quality Assurance could open different research paths.
Due to the nature of the research and the absence of relevant literature, there is still much needed to establish Software Quality Assurance in Software startups as a research area. Abstract concepts in the field require concrete definitions, and further research needs to be conducted to validate our original findings.

Conclusion
Our research paper highlights the problem faced by software start-ups during their early development phases. The problems were meant to be judged on the hypothesis that the lack of software quality assurance practices is the reason for several hurdles in the way to the progress of the start-ups with limited sources, rush to the market, and other subjective circumstances.
Our analysis"s key points indicate the Software Startups understand the importance of traditional Software Quality Assurance principles and the benefits that rigorous adherence to them could bring to Software products. However, the consensus among start-ups is that a stricter commitment to these practices restricts the pace at which these companies operate. The Start-up ecosystem rewards those who are first to the market and fail fast. Unlike a traditional client"s business requirements, the requirements of a start-up are not set in stone. For a start-up, involving SQA personnel in the designing, planning, or requirements gathering phase of product development is redundant. Our research found out that the tech-related ventures have been growing significantly specifically during the Covid-19 pandemic. Acceptability of the products of the start-ups which follow the SQA practices and technical debt of the start-ups not adhering to them is the evidence to the hypothesis.
Our findings are significant as they would open new research paths in the developing research area of Software Quality Assurance within start-ups. They can help expand the ways to look at the presented problem by asking subsequent questions based on our research. Software start-ups are diverse both in terms of the people involved and the issues that they focus on solving. The type of solutions being developed and the testing needs of these solutions need to be further investigated.
It should be noted that this research work was not meant to be exhaustive. It hypothesized a problem through anecdotal evidence and performed the necessary investigation on a subset of software start-ups. To develop into a promising significant research area, further contributions are required from researchers of varied backgrounds.


Collaborative governance in solving problem air pollution in Indonesia: a systematic literature review

This research is explaining a problem in environmental management that need more attention because the impact of environmental problems involves all elements of the government, private sector, and society. The purpose of this paper is to review which one is the best practice for environmental problems related to air pollution in the government’s efforts. This research focuses on the issue of environmental pollution on air pollution in Indonesia. The theory used is the Collaborative Governance model of Ansell and Gash and De Seve. The research uses a qualitative approach with Systematic Literature Review and secondary data. Perspective in Collaborative Governance. The Literature approach is applied to scientific journals published in the database. The author found that several policies related to environmental problems have been implemented. But not running optimally. The government needs to use its authority to solve existing problems, including the problem of poor air quality.

Introduction
Greenpeace encourages governments in all sectors to invest in renewable energy sources, namely wind, solar energy, and public transportation that have clean energy quality that serves to protect the public from dirty air pollution. Data from WHO kills about seven million people worldwide every year. This shows that 9 out of 10 people breathe air that exceeds the WHO guideline limit that contains high level of pollutants such as low-and middle-income countries with the highest exposure. about 4.2 million deaths per year are caused by air pollution [1]. The results of the Greenpeace Southeast Asia report in February 2020, predicts air pollution as a source of fossil fuels can cost the world around US$8 billion every day or 3.3% of global GDP. In 2020, approximately 160 people lost their lives in the world's five most populous cities and the cost of this urban economy was US$85 billion [2].
The effects of air pollution not only threaten public health but also harm plants and ecosystems, leading to the climate crisis with the effects of greenhouse gases and air pollutants originating from the same source. Indonesia is one of the most polluted countries and is ranked 20th out of 243 countries in the Air Quality Index (AQLI) https://aqli.epic.uchicago.edu/the-index/. The development of the physical development of cities and industrial centers, as well as the development of transportation, causes air quality to change [3]. The level of urbanization and population density affect air emissions in Indonesia [4]. Forest fires such as in Riau and Kalimantan are a serious problem faced because forest fires include modern air pollution with CO (carbon monoxide) as the dominant pollutant resulting from forest fires [5]. Without realizing it, in urban areas such as big cities in Indonesia, air quality has reduced the quality of life of urban people, especially in the transportation and industrial areas. This is a real problem faced by the government. Various efforts have been made by many parties. About the implementation of air pollution control in the regions, the legal basis governing the Regulation of the State Minister of the Environment is in accordance with Number 12 of 2010. This Regulation of the state minister for the Environment was issued in the context of efforts to control air pollution in Indonesia. The control of this implementation is regulated in PP Number 38 Article 2007 concerning the division of government affairs between the provincial government and the city district government. This implementation is determined by the minister as the organizer of government affairs in the field of environmental management.
Collaborative governance is one way to respond to the wishes of the stakeholders involved in the implementation of development and to respond to the limited government budget where the development of demands from the community regarding performance the wishes of the actors of these interests. Support and encouragement from the government are needed in the application of technological developments related to industrial pollution sources. In 2015, the construction of a network of air quality monitoring systems or e-Quality Monitoring, or systems were built in 26 cities spread throughout Indonesia by The Ministry of Environment and Forestry. In addition, the ministry of environment and forestry, local governments, and the private sector have also been connected to 45 stations belonging to the Meteorology, Climatology, and Geophysics Agency (BMKG). Therefore, air quality monitoring stations can also be accessed directly through the website.
The previous research contained in this study was sourced from journals. The results of research from Achmad Raihan Hidayat on the Provision of Green Open Spaces in Bandung City through Collaborative Governance (Studies on Ganesha Park) are in the collaboration process carried out there are four stages including a) face-to-face dialogue; b) building trusts; c) commitment to processing; d) common understanding [6]. Research results from Masyhuri, Aziz about ''Collaborative Governance in the Implementation of the Healthy City Program (Study on the Batu City Government)'' The results show that the government, private sector and community have collaborated well with the Healthy City Program and have been running since 2016 until now [7].
The issue of air problems is a serious problem. Community activities are expanding, so support for the environment needs to be increased and is environmentally friendly, without excluding socioeconomic factors. Therefore, the handling and prevention of air pollution must be considered seriously, both by the community and the government. The government continues to try to monitor and overcome air pollution with various actions with several related parties. From the background of the problems above, the formulation of the problem in this study is how to control collaborative governance in efforts to solve air pollution problems in Indonesia. This paper aims to analyze the collaborative governance process in managing air pollution in Indonesia.

Theoretical
Collaboratively collaborate on the existence of an interest in finding solutions to issues or problems that will be faced. Collaborative Governance is governance that brings together public and private stakeholders in a collective forum with public institutions to engage in consensus-oriented decisionmaking [8]. In the dynamics of collaborative governance, the legal framework is an important variable as well as public value collaboration [9]. Collaborative governance is a response to the failure of the policies made. Citizens jointly develop and adopt a common understanding regardless of their identity, field, and motivation [10]. Ansell and Gash [8] defines collaborative governance as a government arrangement of one or more public institutions that directly involve non-state stakeholders in a formal, consensus-oriented, and deliberative collective decision-making process and has the goal of making / implementing public policies. or manage public programs or assets [8]. Collaborative governance is further defined by Emerson, Nabatchi and Balogh as a process, and structure in making public policy and management decisions that involve the community constructively with various levels of 3 government, public, private and civil to carry out public goals that cannot be achieved unless by shared forum [10]. Ansell and Gash [8] mention there are several important criteria in collaboration, namely: 1. Ideas in forums from public institutions or institutions, 2. Members in the forum are listed as non-permanent actors, 3. Members are involved in decision-making and are "consulted" by public agencies, 4. Formally the forum is organized collectively, 5. The purpose of this forum is to decide by consensus (including if the objectives are not achieved in the implementation of policies), and 6. Collaboration focuses on management or public policy.
Something that is an important thing in implementing collaborative governance is a problem-based approach to identify and address policy deficiencies. In decision making must integrate and prioritize flexibility and innovation.

Methods
In this study, the author uses a qualitative method using a literature review study method, which presents several references related to the research focus on accordance with the theme or topic. Then to search for journals, it is done online through the Google Scholar database. The author also limits the search through Google Scholar. With Boolean logic AND "Collaborative governance" AND "Environment" AND "Air pollution" AND "Indonesia". Where the time span in searching the database is accessed in the range of 2016-2021. Then, by combining these methods, the author uses an international database as a basis for searching, which the author only focuses on searching for scientific journals. The databases used are since direct, Taylor, and France. Both databases are very rational because the data sources used are selected journals from academic and international organizations. The author also limits the year the journal is published with a minimum year of publication for the last 5 years. To find more relevant and specific data, the author uses 4 keywords, namely collaborative governance, environment, air pollution, Indonesia.

Results and discussion
Some the research result conducted on the impact of environmental pollution in Indonesia are related to air pollution. The first research from Bachtiar et al. [11] related to research on air pollution, this research was conducted in the city of Padang, by taking ozone gas samples at 52 points in the city of Padang analyzed by the NBKI method using a spectrophotometer. The results concentration of ozone gas in the city of Padang varies between 6.32 and 87.06 g/Nm3 with a concentration average of 25.67 g/Nm3. Regarding these results, the air pollution conditions in Padang city are below the standards set in the Regulation of the Republic of Indonesia No. 41 of 235 g/Nm3 [11]. There are several factors that affect the concentration of ozone gas, namely meteorological and transportation factors. The influential air temperature is related to Meteorological Factors.
The impact of air pollution causes various kinds of diseases such as respiratory, cardiovascular, diseases that can attack other parts of the body. From the results of research related to air pollution from the transportation sector reaching around 60 percent, this can be obtained from the effects of air pollution in the transportation sector such as motor vehicles on human health in the city of Bandung, especially Acute Respiratory Infections or abbreviated as ISPA. According to the results of a study conducted [12] regarding environmental disasters in the socio-ecological system, due to industrial waste that causes environmental damage, an adaptive approach is urgently needed. Approach to public governance, collaborative and adaptive. Collaborative governance looks at various levels as balancing policies, integrating adjacent policies, encouraging innovation and social learning, and adapting solutions continuously. Then the results of research related to the collaborative role of governance in environmental pollution efforts, namely research conducted by Denny Irawan in Surabaya City, requires a good governance perspective where effective government actions in public affairs are carried out [13]. Regarding the good governance perspective, in implementing its policies, governance actors such as the government, the private sector, and the community are involved through a governance perspective to create a constructive and harmonious relationship between the three actors. Basically, the principle of good governance refers to shared responsibility related to the decision-making process and the implementation of the policy. An understanding of the principles of good governance will become a benchmark for performance in government. The assessment of the good and bad of government can be assessed according to the perspective of good governance.
A study by Nurwita et al. [14] conducted in Tangerang City on air pollution control related to efforts to prevent, restore air quality and countermeasures shows that the central government, local governments, and those in charge of a business, by making policies and managerial practices. Success in controlling air pollution can be seen from 4 criteria of organizational effectiveness such as adaptation, integration, motivation of members, and production. The government's role is seen in the process, socialization is carried out to the community such as through the eco-driving program or good driving procedures and the application of the use of manicure applications (monitoring air quality). One of the government's roles in air pollution efforts is by monitoring air quality which includes emissions and ambient, issuing regulations on air pollution control, implementing KIR vehicles, traffic engineering, vehicle restrictions, making Car Free Day (CFD) policies, developing green open spaces. (RTH) as well as providing education to the community, including school students [15].
Some of the results of the research above on the impact of environmental pollution on the first pattern related to the impact of air pollution can endanger human health. Respiratory disorders are one of the causes of air pollution in Indonesia. From the results of the study, it was stated that the transportation sector was the cause of dirty air. It is known that the State of Indonesia is a country with a dense population and most Indonesian citizens carry out various kinds of daily activities or activities outside the home. The second pattern is related to collaborative governance, from the research that has been done, the government makes various efforts such as issuing regulations on air pollution control, making policies and managerial practices, outreach to the public, and education to the public, according to what has been done by the city of Yogyakarta. DKI Jakarta, which is the capital city of Indonesia, issued Governor Regulation No. 66 of 2020 concerning Motor Vehicle Exhaust Emission Tests in July 2020.

Conclusion
Collaborative Governance in this study is very relevant to be applied to problems related to air pollution in Indonesia which relies on a stakeholder pattern, which involves the private sector and the government. Regarding air pollution efforts, the role of the private sector has been seen starting from responsibility, organizational effectiveness such as adaptation, integration, member motivation and production. Meanwhile, the Government as a stakeholder has issued several policies to minimize problems related to air pollution. One of the government's roles seen in DKI Jakarta is the Governor's Regulation Number 66 of 2020 concerning Motor Vehicle Exhaust Emission Tests in July 2020. The Indonesian government in developing Collaborative Governance is seen in the principle of good governance in carrying out its duties and responsibilities.


Comparison of GIS-based AHP and fuzzy AHP methods for hospital site selection: a case study for Prayagraj City, India

Identification of hospital sites and their ranking is important for the planning and development of any country's health infrastructure. The site selection problem is a typical multi-criteria decision making problem involving multiple stakeholders and their interests. Multi-Criteria Decision Analysis (MCDA) is a promising approach to solve a location-based problem due to the constitution of various criteria involved in decision making. In this research, eleven criterion are chosen which are classified under three main criteria; socio-economic, geographical and environmental. This research aims to identify the appropriate MCDA method for the selection of a new hospital sites. Here, two MCDA methods named Analytical Hierarchy Process (AHP) and Fuzzy AHP (FAHP) are used. Further, Geographical Information System (GIS) based MCDA methodology is proposed in this paper. The results obtained with both AHP and FAHP methods are compared. This comparison is based on criterion rankings, proposed hospital locations and sensitivity analysis. The main difference in results is shown in the result of sensitivity analysis in which constant variation in site ranking is obtained when weight change analysis is performed using AHP. The FAHP result shows only one variation in site ranking after a change in weight from +10 to +20%. The result suggests that FAHP may be a better approach to the hospital site selection problem.

Introduction
Over the period of time, the demand for healthcare facilities has increased exponentially all over the world (Pantzartzis et al., 2017;Velez et al., 2021). Healthcare services play an essential role in the socioeconomic development of any nation. The main aim of health services is to fulfill the need of healthcare facilities to all people at all times (Daskin & Dean, 2004;Murad, 2007;Tripathi et al., 2020a). The need for healthcare is more pronounced in urban areas where the population increases continuously due to the migration of people from rural areas that resulted in a disparity of access to such services (Dell'Ovo et al., 2018;Reath et al., 2019;Shahbod et al., 2020). However, healthcare is often ignored by the governments during budget allocation and infrastructure development. The recent outbreak of COVID-19 pandemic has realized several nations about the pathetic condition of their health infrastructure (Jabaris & Ananthalakshmi, 2021;Siddiqui et al., 2020). It has reflected the healthcare reality of nations (Caligiuri et al., 2020;Tripathi et al., 2019). For example, the German government was able to save its citizen more than other European Union countries from COVID-19 because of the larger number of hospitals (Zolfani et al., 2020). The mortality and morbidity of this pandemic have highlighted the importance of healthcare access.
More hospitals are needed to be established to improve the healthcare facility. The very first requirement for this is to select the locations of the opening of new hospitals. Site selection of hospitals is an ill structured problem. It has several stakeholders like doctors, medical staff, patients, pharmaceutical representatives and real estate developers. It requires proper coordination between the city planners, government and health-related policy makers (Ahmed et al., 2016;Kahraman et al., 2019;Miç & Antmen, 2019). Optimal hospital location will help to improve the effectiveness of hospitals' functionality in terms of service provision, delivery and optimization. The selection of undesired locations always leads to a decrease in customer satisfaction and an increase in expenses. Therefore, to meet the need for an adequate healthcare facility, there is a need to plan new optimal hospital sites.
The selection of optimal hospital location depends upon the various criteria. These criteria are heterogeneous in nature and require an optimization method to evaluate them and their effect on each other (Ç etinkaya et al., 2016;Erbaş et al., 2018). Therefore, a multidimensional approach to decision making is required that can be fulfilled by the Multi-Criteria Decision Analysis (MCDA) method (Ding et al., 2020;Longaray et al., 2018). Integration of GIS with MCDA can assist the site selection with its spatial extent analysis. This capability helps the planner to make an informative decision on the hospital site selection problem. It will be more appropriate in a situation where the planning instruments do not provide prescriptive guidelines for the decisions. Some studies have been carried out in the selection of optimal hospital locations. These studies have been carried out by different MCDA methods like AnalyticHierarchy Process (AHP), Fuzzy AHP (FAHP), Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), Fuzzy TOPSIS and Elimination and Choice Expressing Reality (ELECTRE) (Kumar et al., 2016;Rajak & Shaw, 2019;Senvar et al., 2016;Vahidnia et al., 2009).
In light of the above discussion, the establishment of new hospitals is undoubtedly the need of the hour. Site selection for the hospital is a complex decision that needs to be supported by advanced decision making techniques using GIS. Although some studies are found on this topic, there is a need for more elaborated evaluation of hospital site selection parameters and criteria by involving more stakeholders. Also, a comparative analysis between popular MCDA methods, viz, AHP and FAHP, is required to ascertain which method would be best for the hospital site selection. Many site selection researches have been carried out by fuzzy AHP methods without examining whether it will actually make a significant difference in outcome than traditional AHP. Few studies have done a comparative analysis of AHP and FAHP in site selection (Guler & Yomralioglu, 2020;Rajak & Shaw, 2019;Rajasekhar et al., 2019). But these studies are mainly focused on identifying differences in criterion weight, criterion ranking and suitability map, which need to be done extensively in the context of GIS based MCDA. This will help the decision-makers to analyze different perspectives such as criterion weight, criterion ranking, suitability map analysis and identifying the spatial extent of alternative locations. However, no research has found that includes a comparative analysis in hospital site selection. Therefore, it is mandatory to conduct a comparative analysis of the AHP and FAHP approaches for the hospital site selection. This research work is an attempt in this direction.
The main objective of this paper is to compare AHP and FAHP based identification of hospital sites. For this purpose, a four-step method is proposed in this paper. In the first phase, three main-criteria and eleven sub-criteria are determined based on the knowledge of experts and literature survey. The next step involves spatial mapping of criteria using GIS analysis. The third stage is the GIS-based MCDA approach, which involves the prioritization of main-criteria and sub-criteria using AHP and FAHP. In the final phase, a site suitability map is created to determine the optimal sites for the hospital. Finally, a critical comparison of the AHP and FAHP-based hospital site selection process is performed. This comparison is based on criteria ranking, location of hospital sites and sensitivity analysis.

Literature review
MCDA technique for site selection MCDA provides a set of procedures and techniques to solve complex decision-making problems in a hierarchical manner (Malczewski & Rinner, 2015). AHP is one of the most common MCDA methods used for site selection (Saaty, 1977(Saaty, , 1990. It analyzes decision making based on deterministic data values. However, sometimes the data are incomplete and complex. Therefore, experts built different opinions from it due to varying perceptions. This creates ambiguity and uncertainty in the decision space. To deal with such uncertainties, a combination of fuzzy set theory and AHP, known as FAHP, is being introduced (Aggarwal & Singh, 2013). In FAHP, attribute datasets are expressed using a fuzzy membership function that defines the degree of membership value for the interest of the particular attribute.
MCDA technique is frequently used in site selection as it is a multidimensional problem that involves several criteria in decision making. Facility location assessment problems are considered as a critical decision making problem. It is a crucial task for any government to resolve the issue of land acquisition, to avoid undesirable environmental load and to utilize the profitability of the land use Saha & Agrawal, 2020;Soltani et al., 2019). Site selection aided with GIS technology could play a significant role in the creation of a problem-solving environment for spatially referenced data (Maguire, 1991). Although, GIS and MCDA are two different area of research but their integration could benefit the site selection problem in analyzing the spatial decision and evaluating the ranking of different criteria (Feizizadeh et al., 2014;Tripathi et al., 2020b). Site selection studies like railway station (Mateus et al., 2008;Prasertsri & Sangpradid, 2020), fire station (Chaudhary et al., 2016;Nyimbili & Erden, 2020), solar photovoltaic plant (Garni & Awasthi, 2017;Shorabeh et al., 2019), landfill (Aksoy & San, 2019;Rahmat et al., 2017) and wastewater disposal (Aydi et al., 2016) proves that MCDA could be the best possible model to solve the location based problems.
Hospital site selection is one of the ill structured problem which is faced by the planners, especially for developing countries like India (Kumar et al., 2016;Mishra et al., 2019). A number of research papers focused on the hospital site selection have been found. These literatures offered different procedures for hospital site selection. For example; Kim et al. (2015), Murad (2007), Ramani et al. (2007) and Schuurman et al. (2008) proposed the GIS-based approach for hospital site selection. But, they do not consider the priority of the criterion affecting to the hospital sites and focus only on GIS-based analysis. Therefore, GIS-based MCDA approach is introduced for the hospital site selection that includes the prioritization of affected criterion along with their spatial distribution. This approach is capable of achieving a transparent and analytical decision making environment for hospital site selection. It can consider various factors which cannot be ignored to get a solution closer to reality. These criteria vary with the location of study area (Senvar et al., 2016;Vahidnia et al., 2009). Critical factors that affect the hospital sites are identified through literature review. These factors are population density, land cost, proximity to road, proximity to railway, pollution and distance to other hospital (Dehe & Bamford, 2015;Dell'Ovo et al., 2018;Oppio et al., 2016;Rahimi et al., 2017;Senvar et al., 2016;Vahidnia et al., 2009). In addition to the selection of influential criteria, there is a need to know their relation to each other as well as their impact on overall site suitability.
Recent studies adopted several MCDA techniques such as ELECTRE-TRI, ordered weighted averaging, compromise programming, goal programming and AHP for hospital site suitability. Among them, AHP method is used by several researchers (Ahmed et al., 2016;Dell'Ovo et al., 2018;Hariz et al., 2017;Mishra et al., 2019;Rahimi et al., 2017;Soltani et al., 2019). In AHP, numerical values are used to express expert judgment. Such precise comparisons of decisions may be impossible to determine and can therefore lead to ambiguity in many practical implementations. Therefore, many hospital site selection researches use the more advance FAHP approach (Kumar et al., 2016;Neisani Samani & Alesheikh, 2019;Rajak & Shaw, 2019;Soltani & Marandi, 2011;Vahidnia et al., 2009). AHP AHP is a multi-criteria decision-making approach in which the criteria are organized in a hierarchical structure. In this approach, the relative importance of the criterion is assumed to be based on the AHP scale. This scale is used to direct the decision-maker to construct the Pairwise Comparison Matrix (PCM). The PCM shows whether each element is equally strong, slightly strong, fairly strong, very strong, or absolutely strong than the other elements. These relative intensities are then converted into numerical values, as shown in Table 1.
The following steps are used to identify the criteria weight through the AHP process: 1. From the PCM m = (n*n) for n criteria. Let P ij is the value of the cell located at the ith row and jth column of PCM. Then, the scores entered in P ij and P ji should satisfy the constraint in Eq. (1).
2. Calculate the Consistency Ratio (CR) based on Eq.
(2). This defines whether the formed PCM is consistent or not. If CR is less than 0.1, then it is consistent.
Here, RI is the Random Index and CI is the Consistent Index, which is calculated using Eq. (3).
Here, k max is the biggest eigen value of PCM. 3. The normalized matrix is then formed using Eq. (4).
4. In this step, the average across row entries is calculated to obtain the final weights using Eq. (5).
FAHP Sometimes dissipation or ambiguity problems arise when creating a comparison matrix. It is not always possible to specify crisp values to compare different criteria. Therefore, FAHP is used so that fuzzy crisp values can be assigned. The following is the working procedure of FAHP.

Generation of comparison matrix
In FAHP, a linguistic statement is used to compare the two criteria. These linguistic statements are expressed by the Fuzzy Comparison Ratio Scale, as shown in Table 2. This ratio scale is defined as TFN, namely, a triple with the smallest, most probable and largest possible fuzzy values (Ayag, 2014). These TFNs are  Absolutely important (8,9,10) (1/10, 1/9, 1/8) used to produce fuzzy PCMs in FAHP (Chan et al., 2013). The fuzzy PCMC for n criteria or alternatives is defined by Eq. (6) (Chang, 1996;Demirel et al., 2008).
where l, m, u represents the lower, medium and upper bound of the TFN respectively.

Generation of fuzzy weight matrix
Several approaches are available to generate FAHP weights from pairwise comparison matrix. It produces output as a set of fuzzy weights or crisp weights. Geometric mean method (Buckley, 1985), fuzzy logarithmic least-squares method (Wang et al., 2006), and linear goal programming method (Wang & Chin, 2008) are some approaches to produce fuzzy weights from PCM. Extent analysis (Chang, 1996) and fuzzy preference programming based nonlinear method (Mikhailov, 2003) are approaches to produce crisp weights. Chang (1996) proposed an extend analysis method which computes the synthetic extend values of the pairwise comparison (Murat et al., 2015). These synthetic extend values, known as weighted values of all parameters, are also available in the form of TFNs. Fuzzy synthetic extent value for the ith criterion is calculated by the Eq. (7) (Chang, 1996).
where denotes the extended multiplication of two fuzzy numbers, j and k are row and column of the corresponding matrix, respectively.

Generation of crisp weight for each criterion
In this step, the approximation of fuzzy priorities is performed. For this purpose, the degree of possibility between two fuzzy synthetic extent values is calculated. The given equation computes the degree of possibilityS i !S j .
Finally, the estimation of the priority vector W ¼ w 1 ; :::; w n ð Þ T of a comparison matrix is calculated by using Eq. (9).

Study area
Prayagraj city, formerly known as Allahabad city, is one the biggest cities in the State of Uttar Pradesh (U.P.) of India. It has been selected as Smart City by Ministry of Housing and Urban Affairs (MoHUA), Government of India (GoI) in 2015. The Smart Cities Mission is an innovative and new initiative by the GoI to drive economic growth and improve the quality of life of people by providing core infrastructure and harnessing technology to enable the local area development and create smart outcomes for the citizens. Prayagraj city has rapidly evolved in the last three decades due to the urbanization process and there is a need to provide a clean, inclusive and sustainable environment for the development in the city with technological intervention. Due to this, Prayagraj city is selected as the study area for the present work. Prayagraj city is located in the north-central region of the state of U.P., India and falls in the administrative boundary of Prayagraj district (Fig. 1). The area of Prayagraj city is about 76.29 km 2 . The total population of the city is 1,112,544. Prayagraj city has 20% of the district population and 80% of the total urban population. The population density of city is 157 person per hectare. According to Prayagraj Municipal Corporation, the city is divided into 80 wards. Ward 76 has the highest population of 25,256 person and ward 78 has the highest population density of 1115 person per hectare.
As per the Ministry of Urban Development (MoUD) report, Prayagraj city has 37 dispensaries (1 for every 15,000 person), 15 small hospitals (1 for every 45,000-1 lakh person) and 12 multi-specialty hospitals (1 for every 1 lakh person). As per norms, there should be 162 dispensaries, 54 small hospitals and 24 multi-specialty hospitals. As per GoI's latest National Family Health Survey (2015-16) just 7.1% of district households are covered by health insurance or related schemes. There are some key health b Fig. 1  indicators in this survey that can highlight the need of the hospitals in the study area. In the urban area, just 37.9% of children whose age is 12-23 months got fully immunized. This immunization includes BCG, measles, three doses of polio vaccine and three doses of DPT vaccine. The anemia condition of children and women is also alarming. In the urban region, 60.7% children and 55.5% of women are anemic. Lifestyle diseases are also getting rampant in the urban population. Among the adults of age 15-49 years, 9.5% are suffering from a higher level of blood sugar while 16.7 are having hypertension. Therefore, new hospitals must be established around the city to fulfill the healthcare requirement of people. website. This multispectral image has a spatial resolution of 10 m for band 2 (blue), band 3 (green), band 4 (red) and band 8 (near infrared). Image preprocessing and layer stacking is performed to obtain a composite image. The LULC map is then generated by applying the supervised classification technique. The ASTER DEM data, acquired on October 17 th , 2011 with 30 m resolution, is downloaded from the USGS website. It helps to generate the slope map of the study area.

Methodology
The flowchart of the proposed methodology is given in Fig. 2. It is a four-step process, which includes: (1) criterion analysis, (2) GIS analysis, (3) MCDA methods, and (4) GIS-based MCDA analysis. A detailed description of this method is given below.

Criteria analysis
The first phase involves the analysis and evaluation of criteria that affect the location of the hospital. For this, a board of experts and academicians is created. Experts are local administrators working in various hospitals in the Prayagraj city while academicians are the researchers working in the health service domain. In this research, hospital site selection criteria are evaluated based on the expert's and academician's knowledge and from literature survey. From the relevant literature, it is founded that the criteria used   Table 3 lists all the criteria along with their brief descriptions and the authors who evaluate them in their studies. A total of eleven criteria have been identified for this research. Population density, land cost, accessibility (proximity to road and railway), and possibility of extension have been selected by several researchers. However, air pollution, green area and unhealthy industry norms have also been pointed out as important criteria by some researchers. In very few researches, slope and urban slum population are considered for hospital site selection. These are included in this research as the role of these criteria was found to be very important for the selected study area.
All these criteria are aggregated hierarchically at two levels: main-criteria and sub-criteria. The hierarchical structure of all eleven criteria is shown in Fig. 3. All eleven criteria are grouped into three main criteria viz., socio-economic, geographical and environmental. The socio-economic criterion considers the social and economic factors that are related to human health. Geographical criterion examines access to health facilities. The environmental criterion helps in locating the places where less pollution and more vegetation is around the hospital.

Generation of thematic layers
Spatially referenced criterion provides more detail and visual information that helps decision-makers to make decisions effectively and quickly. This step analyzes the spatial extent of each criterion. It aggregates different geospatial layers to create suitability maps. As different forms of criterion data such as satellite images, topographic maps and field data are collected, different GIS operations such as euclidean distance, slope, interpolation, etc., are needed to create the thematic layer of each criterion. Table 4 presents all the criteria for creating thematic layers with their sources and spatial operations performed on them.
Since most of the data used in this study are in vector format, they need to be converted to raster format. The Raster Calculator and Reclassify GIS tools are used to perform this conversion. This process helps in extracting useful information from the converted file. Here, to maintain the integrity of the measurement, the ranges defined in the thematic layer are normalized in a scale from 0 to 1. Pixel value 1 denotes the most suitable area for hospital sites and is indicated by white color on the map. The pixel value 0 depicts an area unsuitable for hospital sites and is shown by black color on the map. This helps experts to make critical comparisons among each criterion and to rank the identified alternative sites. The construction of normalized thematic layer maps of each criterion corresponding to all sub-criteria is described below.

Thematic layer map of socio-economic criteria
The thematic map of socio-economic criteria is shown in Fig. 4.
Population density Population density should be examined to determine population distribution around the city. Hospitals should be located in such a way that more and more population gets the benefit of health services at the nearest possible location. Figure 4a shows the population density criteria map. In this map, higher population density wards are given a higher score than the wards with lower population density.
Proximity to slum area The slum area is recognized as a highly populated area located in deteriorating infrastructure. There is a high need for health services in the slum and fringe areas as health and sanitation conditions in these areas are generally poor. Figure 4b represents the slum area map where higher scores are given to the slum areas.
Land cost The value of land is an essential parameter in deciding the location of hospital sites. It somehow directly reflected the cost of health care services. The land cost map is shown in Fig. 4c. Higher score is given to the land with lower cost as it is economical to build new hospitals over there.

Thematic layer map of geographical criteria
The thematic map of geographical criteria is shown in Fig. 5.
Proximity to road Effective transport facilities in terms of access positively affect hospital sites. It benefits those who were in need of health services. It is important to build a new hospital near the streets. In view of this, a high priority has been given to nearby road areas. Figure 5a shows the proximity to road map where higher priority is given to the pixels near to the roads.
Distance to other hospital It is important to assess the availability of existing hospitals. New hospitals should be constructed from existing hospitals so that health services are well distributed around the city. Distance to other hospital map is shown in Fig. 5b in which higher priority is assigned to the area away from the existing hospitals.
Proximity to railway This is another important criterion for the selection of a hospital site. People living away from urban areas sometimes travel via railways. Due to this, the area near the railway is given more priority than the area away from the railway. The proximity to railway map is shown in Fig. 5c.

Possibility of extension
Since most of the land within the city is already occupied, it is difficult to acquire land within the city to build a new hospital or to expand an existing one. Keeping this criterion in mind, the open area is given a higher priority than the built-up area. Figure 5d shows the possibility of extension map.
Slope The slope of the land may contribute to checking the site of the hospital. Flat or low slope areas are better for building a hospital. Figure 5e shows the slope map, where higher scores are given to the lower slope areas. The thematic map of environmental criteria is shown in Fig. 6.
Air pollution It is very important to consider air pollution for the selection of a hospital site because it exerts extreme influence around the place in which people live and the hospital is located. If the air pollution around the hospital is high, it will affect the health of patients. Therefore, a lower priority level is  given to the area where the air quality index is higher. Figure 6a represents the air pollution map of the study area.
Green area Surrounding of the hospital plays a crucial role in providing effective healthcare services to the patients. Green area must be present at the hospital sites. Due to this, a higher priority is given to the location near to the green area. Figure 6b represents the green area map of the study area.
Unhealthy industry The industrial sector negatively affects hospital patients due to various types of pollutants, such as wastewater, disposals and hazardous waste. To minimize its impact, the new hospital should be located away from the industrial area. Figure 6c represents the unhealthy industry map of the study area.

Criteria weights using AHP & FAHP
In this step, criteria weights are calculated based on the above definition of AHP and FAHP. For this purpose, expert opinions are considered to assign the weight using the scale given in Tables 1 and 2. To determine the relative importance of each criterion, the opinions of experts are obtained in linguistic terms. It is further transformed and evaluated on a nine-point scale for both AHP and FAHP (Tables 1, 2). In this study, experts from hospital planning authority are taken for their judgment for the site selection of the hospital. The final score of the relative weight is calculated by applying the geometric mean to the expert judgments. The geometric mean method was given by Saaty (1990) and Dyer and Forman (1992) to integrate individual judgments. This will help to generate the PCM for criteria and sub-criteria. After this, the weight is calculated by AHP and FAHP methods. Finally, the overall normalized weight of each subcriterion is calculated by multiplying the individual weight of sub-criteria with the weight of the corresponding criteria (Chang, 1996). Table 5 shows the calculated priority weights and ranking of each subcriteria in AHP and FAHP.

GIS-based MCDA approach
This step involves GIS-based MCDA analysis to obtain the final suitability map. This is done by implementing a weighted linear combination (WLC) operation. In this operation, more than one attributes or criteria along with its weight are taken into consideration. Each criterion is transformed into a GIS layer and described by its pixel values. The overall suitability map is generated by using Eq. 12. This formula evaluates the suitability of each pixel based on standardized score and normalized weight. where A j represents the alternatives score of jth pixel in the final suitability map, X i represents the standardized score of ith criterion, and W i represents the normalized weight of ith criterion. The resulting hospital site suitability maps generated via WLC method are shown in Fig. 7. Here, each criterion GIS layer is multiplied by AHP and FAHP weight separately to generate the corresponding hospital site suitability maps. Raster calculator is used to generate the final hospital site suitability maps for the study area. Figure 7a and b shows the normalized suitability map generated from AHP and FAHP, respectively.
To analyze the spatial pattern and distribution of the most appropriate location for the hospital, the normalized maps are classified into five suitability classes: very suitable, suitable, moderately suitable, unsuitable and very unsuitable. This is achieved by applying the natural break (Jenks) classification method to the normalized suitability map. The classified suitability map for AHP and FAHP is shown in Fig. 8a and b, respectively.
Hospital suitability maps generated from AHP and FAHP show some differences in results. It can be seen from Fig. 8a and b that there is a significant difference in a very suitable class. This is due to ranking and weight differences in AHP and FAHP. A quantitative comparison of the differences in the suitability area is also performed, which is summarized in Table 6. This is done by converting all five suitability classes into polygon layers. The results show that 18.78% of the area in AHP and 14.33% of area in FAHP are identified as suitable locations for setting up the new hospitals. Higher suitability values are envisioned primarily in an area that is far from the city center as most existing hospitals are located in this area. The total unsuitable and very unsuitable area is about 19.44% and 24.62% of the total area in AHP and FAHP respectively.

Comparative analysis
A comparison between AHP and FHAP results is made in this section on the basis of three parameters, which are (1) divergence in criteria ranking (2) extent and location of hospital sites and (3) weight change influence on sites ranking in different scenario based on sensitivity analysis.

Criteria ranking
The one of the critical input in GIS-based MCDA analysis is the ranking of criteria based on the relative importance of each criterion. Here from Table 5, it can be seen that the criteria ranking and weighting results derived by AHP and FAHP are quite different. By criterion weighting, it appears that the relative local weights of each criterion and sub-criterion are the same in AHP and FAHP. However, the global weight ranking differs in both methods. For example, in AHP, population density (C11) is ranked as the most important criterion, whereas in FAHP, distance to other hospital (C22) is assigned as the most important criterion. The Possibility of extension (C24) and slope (C25) are given the lowest priority for both AHP and FAHP.
The biggest differences in global weight can be seen for proximity to railway (C23) and unhealthy industry (C33), as they have almost the same impact in AHP while in FAHP method proximity to the railway (C23) has a greater impact than unhealthy industry (C33). This happens because in the AHP method, an exact numerical number is given as a weight by the Although this comparison shows differences in AHP and FAHP weights and rankings, it does not recognize the true impact of this difference on the final result. Therefore, the next section is done to see the difference between the outcomes of both methods.

Extent and location of hospital sites
This comparison is done on the basis of alternative sites identified by APH and FAHP method where new hospitals are to be established. Here, the area that falls under the very suitable class is considered for further selection. Along with this, another consideration has also been taken that new hospital sites should be in only those wards which do not have any hospital. The location for the new hospital is identified based on the         Fig. 9. Here, it can be seen that three of those sites are identified at the same location by both methods. Next, the spatial distribution and ranking order of these identified alternative sites is calculated and then compared in both methods. For this purpose, weight order of each site with respect to each criterion is calculated by AHP and FAHP methods. Here, criteria weights and PCM of each alternative site in regard to each criterion are taken part to calculate the final weight and ranking of each site. The overall weight and ranking of each criterion by both methods are shown in Tables 7 and 8, respectively. This analysis shows that the ranking order of sites differed slightly in both methods. For example, Site 1, Site 2, Site 3 and Site 7 are located in the same ward, but the ranking order differs in both methods. However, Site 5 and Site 6 are not only located in one place, but they ranked in the same order by both methods. Although Site 4 option from the AHP and FAHP is located in separate  wards, this analysis ranked it as the most appropriate location for the hospital site.

Sensitivity analysis
Sensitivity analysis is used to test the reliability and robustness of alternative sites in various models. In other words, it identifies the sensitivity of alternatives to the criteria weight changes. To examine this analysis, the weight of one criterion is changed while keeping the others to the same. In this way different combinations of weights are prepared. Experiments are then conducted to evaluate the impact of the weight variation on the output. High degree of change shows high sensitivity in output.
To perform the sensitivity analysis, weight (w i ) of each criterion is altered at a certain percentage change (PC). Weight is calculated by the following equations: where w i0 is the weight of the main affecting criterion. w i and w j is the new weight value assigned to the ith and jth criterion. w i0 and w j0 are the weights of criterion i and j, which are used as an input at base run. To apply criteria weight change analysis, weight deviation range from ?50 to -50% with the percent change of 10% is applied in this study. To do the fair comparison between AHP and FAHP results, the sensitivity analysis is done separately for both methods. Due to having highest weight among other criteria, population density and distance to other hospital criterion is selected as the main affecting criterion for AHP and FAHP, respectively. Criteria weight change according to AHP and FAHP is shown in Tables 9 and 10, respectively.
After generating the criteria weight changes, their impact in the overall ranking is analyzed. For this, overall weight of sites with respect to each criteria weight change is calculated using the weighted operation. The results of ranking order of sites in AHP and FAHP are shown in Figs. 10 and 11, respectively. The AHP result shows a continuous variation in the order of site ranking in respect to criteria weight change. In FAHP, the order of site ranking varies only between ?10 and ?20% criterion weight while other weight deviations have no effect on site ranking. From the results, it can be seen that Site 4 is identified as the most suitable location for hospital siting both ways. Thus the impact of criteria weight change in the FAHP sites is nearly negligible. The sensitivity analysis results suggest that the FAHP site ranking is more tolerant for the criteria weight change than the AHP ranking.

Conclusions
The site selection like problems that have multiple conflicting criteria requires MCDA based decision making. AHP can be used for this purpose as it can handle both qualitative and quantitative parameters. It integrates expert opinion, specialist experience and public feedback to assign the weights to these criteria. Sometimes, FAHP is used instead of AHP to incorporate the vagueness of human thinking. FAHP use the fuzzy number instead of the crisp number in the weight assignment. In this research work, a four-step methodology is proposed for hospital site selection along with the comparative analysis of AHP and FAHP. In the first step, the parameters are picked under three broad categories, viz, socio-economic criteria, geographical criteria and environmental criteria. Eleven sub-criteria are subsequently identified under them: population density, proximity to slum, land cost, proximity to road, distance to other hospitals, proximity to railway, possibility of extension, slope, air pollution, green area and unhealthy industry. After the screening and selecting of criteria and sub-criteria, thematic layers are generated and weight is assigned to them on a ninepoint scale. In FAHP, the extend analysis method is used to calculate the crisp weights. Finally, suitability maps are generated using both methods. Total of nine sites are identified in each of the methods where hospitals can be established.
The AHP and FAHP are compared based on the criterion ranking, location of sites and sensitivity analysis. It shows that these methods' difference in the criterion weight assignment is ultimately reflected in the respective criterion ranking. The criterion weight change has an impact on the final suitability map which varies between these two methods. For example, in AHP, the population density criterion greatly impacts the final suitability map, whereas in FAHP, it is the distance to other hospitals. The results of both methods on final suitability indicate high variance in the ranking of their respective alternative locations.
The result of sensitivity analysis shows high differences in the outcomes of both methods. This difference is not only due to distinct sets of alternative sites from AHP and FAHP but also due to the spatial extent of site location. The sensitivity analysis results show that the FAHP site ranking is more tolerant of the criteria weight change than the AHP ranking.
This study has shown the use of AHP and FAHP in the complex decision making of hospital site selection. It could help the local administrators in the handling of the emerging health threats in a more efficient manner. The solution can reduce the widening gap between the patients and the availability of health infrastructure in present COVID-19 like situations. In the future, this study can be further enhanced by including more demographic parameters of that location like age, medical insurance, education and employment.
Funding No funding received for this study.

Declarations
Conflict of interest The authors declare that they have no conflict of interest.
Human or animal rights The research does not involve human participants or animals.