Using the flexible analytic hierarchy process method to solve the emergency decision making of public health for COVID-19

doi:10.21203/rs.3.rs-1306380/v1

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Using the flexible analytic hierarchy process method to solve the emergency decision making of public health for COVID-19

https://doi.org/10.21203/rs.3.rs-1306380/v1

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The novel coronavirus COVID-19 was initially found in December 2019 in Wuhan, China. Since then, the COVID-19 virus has rapidly spread throughout the world, causing the collapse of medical systems and economic depression. In addition to providing various relief programs, many countries have implemented various anti-epidemic measures to stop the continuous deterioration of the epidemic and maintain the stability of their economies. Especially during the COVID-19 pandemic, emergency decision making and risk assessment is an important issue for guaranteeing the stable life of the people are considered emergency multicriteria decision making (MCDM) problems. The assessment information of the criteria simultaneously includes complete, incomplete and hesitant fuzzy linguistic information in emergency MCDM problems. The analytic hierarchy process (AHP) approach can effectively process MCDM problems; however, the traditional AHP approach cannot handle the incomplete and hesitant fuzzy linguistic information of emergency MCDM problems. In order to overcome these issues, this paper proposed a novel flexible AHP method to solve emergency MCDM problems under the COVID-19 pandemic, and adopted a numerical case about public health emergency decision making and risk assessment under the COVID-19 pandemic to verify the effectiveness and correctness of the proposed flexible AHP method.

Analytic hierarchy process

Soft set

COVID-19

Multicriteria decision making

Hesitant fuzzy linguistic

Since late December 2019, when the first case of COVID-19 was discovered, the COVID-19 coronavirus has rapidly spread throughout the world. On January 10, 2020, the World Health Organization (WHO) defined the new coronavirus as COVID-19, with ‘CO’ meaning corona, ‘VI’ meaning virus, ‘D’ meaning disease, and ‘19’ meaning the year it was discovered (Chen et al. 2021). The COVID-19 coronavirus spreads among people with frightening speed, posing a serious threat to life and causing a global pandemic (Hong et al. 2020). As of September 2021, 230 million people worldwide have been infected with COVID-19, and 4.77 million of them have died (WHO publication, 2021). In order to effectively reduce the spread of COVID-19, many scholars in various fields have conducted analysis and research on the epidemic situations related to COVID-19. For example, Chen et al. (2020) used news reports of COVID-19 as a simulation example and applied big textual data to demonstrate the effectiveness of the machine optimization process. The improved data analysis of Chen et al.’s (2020) method can remove functional and meaningless words quickly through machine processing and provide corpus data for decision makers in specific fields for further use. Wang et al. (2021) used the AHP method, brainstorming and literature research to establish a risk evaluation model for COVID-19 infection and provide management strategies to reduce COVID-19 infections. COVID-19 is no longer limited to medical issues, and various fields have taken great efforts to handle issues that are related to COVID-19, such as emergency logistics systems, supply chain risk management, travel, and tourism industry issues, medical issues, waste management, and so on (e.g., Baryannis et al. 2019; Bazan et al. 2021; Jiang et al. 2020; Skare et al. 2021; Van Fan et al. 2021). With the COVID-19 pandemic expanding rapidly while medical resources are limited and scattered across the country, how to collect opinions and suggestions from experts from various fields, as well as effectively integrate, allocate, and utilize existing medical resources, are truly complex and difficult issues which can be categorized as emergency multicriteria decision making (MCDM) problems. On the other hand, due to the rapid spread of COVID-19, the collection of emergency data is an enormous challenge due to the lack of sufficient information about the disease and statistics on the number of infected people and medical resources, etc. There are many unknown, partially known, missing, or non-existent data in the process of collecting information, which leads to increased uncertainty and complexity in emergency support decision-making.

Saaty (1980) developed a mathematical tool composed of a hierarchical structure called the analytic hierarchy process (AHP) method, which based on the judgment of knowledgeable experts to conduct pairwise comparison for each criterion, rank criteria and evaluate alternatives from the total weighted score to obtain the solution characteristics of multi-level and hierarchical structures and to systematically solve problems that contain qualitative and quantitative elements. The AHP method is considered an effective approach for handling complex decisions and can help decision makers prioritize various attributes and make correct decisions. For example, Das et al. (2021) combined the decision-making experiment and evaluation laboratory (DEMATEL) and AHP methods to evaluate the factors affecting supply chain networks under the environment of COVID-19. The results showed that the most important element is the optimization of cost. This research finding could help policy makers improve their operational capabilities and performance by developing a risk-resilient supply chain framework, as well as effectively eliminate the problems plaguing the supply chain during the epidemic. Hussain et al. (2021) used the AHP method to deal with group decision-making problems during the COVID-19 pandemic and emphasized energy management performance as a critical issue. The results showed that government measures and personal factors are the biggest influencing factors. The survey results also provided insights for government agencies as a reference for prioritizing workforce health and safety. In the case of the COVID-19 pandemic, Ortiz-Barrios et al. (2021) combined the technique for order preference by similarity to ideal solution (TOPSIS) and AHP methods to improve the preparation level of sales departments and applied it to the electrical appliance sector. The results showed that this is a flexible methodology that can identify weaknesses that should be resolved to improve effectiveness under current market conditions. The AHP method has also been used extensively in other applications, such as driver safety (Moslem et al. 2020), group decision making (Lin et al. 2020), risk management (Lyu et al. 2020), supplier selection (Chang et al. 2016), and so on.

In general, decision makers may not have sufficient confidence in their preferences, leading to an increased degree of uncertainty associated with their decisions. People also often make many ambiguous answers due to incomplete information. In order to represent uncertain evaluation information clearly, Zadeh (1965) presented the fuzzy set theory to solve these situations. However, human cognition not only has fuzzy uncertainty but may also contain hesitation uncertainty. Rodriguez et al. (2012) proposed the hesitant fuzzy linguistic term set (HFLTS), which uses different terms to estimate a linguistic variable instead of a single term to solve the hesitant information of experts. Later, Liao et al. (2015) redefined HFLTS in mathematics and introduced elements of hesitation and fuzzy linguistic. In addition, numerous other researchers have used HFLTS to deal with MCDM problems. For example, Samanlioglu and Kaya (2020) used country-level intervention strategies for COVID-19 to make pairwise comparisons using the hesitant fuzzy AHP method, determine the relative importance scores between intervention strategies, and assess the importance of alternative intervention strategies. The result showed that their method can provide flexibility in decision making for decision makers (policymakers, governors, and physicians). Sir and Sir (2021) combined the Vlsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method and the hesitant AHP method to determine the ranking of various alternatives for the treatment of pain, so as to select the best alternative to alleviate the pain of COVID-19 patients. According to the results, paracetamol and interventional therapy are the first two preferred treatment options, which implied that high accurate methods are used to eliminate errors that caused by experts’ subjective evaluation during the pain treatment process. HFLTS can deal with hesitant linguistic information effectively; therefore, it has been applied in various researches by many scholars, such as supplier selection (Chang 2015), strategic management (Liao et al. 2020), investments (Liao et al. 2019), and so on.

To carry out uncertainties or nonexistent information that traditional method can not to handle, Molodtsov (1999) initialed the soft set, which was a new concept of generic mathematical tool that could be used to deal with undefined or uncertain objects and reduce bias in the process of solving decision-making problems. Today, it can be seen that this mathematical model continues to be developed with each passing day, and it has been successfully applied to several areas, such as operational research, game theory, and probability (Baskaran and Eswari 2021). In addition, many researchers have used soft sets to deal with different decision-making problems, such as supplier selection (Chang 2015), cloud datacenter selection strategies (Baskaran and Eswari 2021), decision making (Dalkilic 2021), COVID-19 vaccine preferences (Narayanamoorthy et al. 2021), and other various fields.

Recently, Ashraf and Abdullah (2020) proposed the AHP method to handle the public health emergency decision making (PHEDM) of COVID-19. However, their method cannot deal with the incomplete and hesitant information provided by experts. In order to solve the above problem, this study developed a novel technique that integrated HFTLS, the soft set, and the AHP method to not only handle hesitant information but also handle nonexistent information under the COVID-19 environment.

The remainder of this study is organized as follows. In Section 2, this study reviews COVID-19 and related works on the AHP method, soft sets, and HFTLS. Section 3 proposes a flexible AHP method that integrates the AHP method, soft sets, and HFTLS to deal with emergency decision-making issues about COVID-19 under an incomplete information environment. Section 4 applies an illustrative example of the PHEDM for COVID-19 to demonstrate its effectiveness. Finally, this study represents conclusions and future works in section 5.

This section introduces an overview of COVID-19 and presents some basic concepts and procedures related to the AHP method, HFLTS, and soft sets.

2.1 COVID-19

Since the novel coronavirus COVID-19 was first found in Wuhan, China in 2019, it has caused severe economic losses worldwide, endangered people’s lives, caused social disorder, and affected people’s living standards seriously. There are many claims about the origin of COVID-19, including that it was caused by the consumption of wild animals. When investigating the initial COVID-19 infectious disease case, scientists discovered that many patients had been to a wholesale seafood market in Huanan, where many carcasses of wild animals were sold (Singhal 2020; Yuan et al. 2020). Furthermore, experts believe that the Wuhan biosafety level 4 laboratory did not take protective measures during the experiment, which caused the virus to leak.

COVID-19 symptoms include fever, cough, physical fatigue, dyspnea, and soreness. Compared with SARS-CoV in 2002, the similarity of its gene structure is more than 70% (Lu et al. 2020, Sun et al. 2020). At present, the number of patients infected with COVID-19 is still continuously increasing. Based on the above situation, the novel coronavirus is severely and continuously affecting global political and economic systems. Many countries hope to control the COVID-19 epidemic effectively by adopting the method of blocking cities and closing borders, resulting in the cancellation of a large number of flights and travel itineraries and having a huge impact on aviation, transportation, tourism, and other industries. Most countries have banned public gatherings, suspended classes (moving to at-home classes or online learning), prohibiting eating out, forced people to wear masks, and required companies to allow their employees to work at home to reduce gatherings. This has caused a change in lifestyle and increased the use of cloud operations. Many companies have also stopped production lines while for the epidemic to ease. Therefore, COVID-19 is considered to be the greatest crisis facing humanity since World War II (Lippi et al. 2020).

Over the past year, due to the successful development of vaccines, the situation in various countries has gradually stabilized. However, as the virus have mutated to the Alpha, Beta, and Delta virus, in addition to causing a large number of deaths in India, the number of people infected with the epidemic in Europe and the United States has risen again, and countries around the world are still struggling with the virus.

2.2 AHP method

In 1980, Saaty developed the AHP method, which decomposes complex MCDM problems into a hierarchical structure with criteria and alternatives and uses the pairwise comparison of factors to solve multi-dimensional MCDM problems. The AHP method can consider both qualitative and quantitative aspects, define unstructured issues, and clearly state goals and results. It is considered a powerful and flexible tool for solving complex MCDM problems that can help decision makers to make accurate decisions. The basic procedure of the AHP method for solving MCDM problems is as follows (Lee 2009):

Step 1: Identify critical factors and subfactors through a hierarchal structure

It deconstructs a problem through a hierarchical relationship from high to low, and then systematically determines the level, structure, and quantification of the problem.

Step 2: Make a pairwise comparison between the identified factors based on a scale of 1-9

The rating scale (Table 1) is used to perform pairwise comparisons between the identified factors.

Table 1

Rating scale of pairwise comparison
Importance intensity	Definition of preference judgments
1	Equally importance
3	Weakly importance
5	Strongly importance
7	Very strongly importance
9	Absolutely more importance
2,4,6,8	Slight differences existed between adjacent scale values

Step 3: Calculate the consistency ratio (CR)

The consistency ratio (CR) and consistency index (CI) are used to check the consistency of the expert assessment opinions, as shown in Eq. (2) and Eq. (3).

$Aw={\lambda }_{max}w$ , and $\sum _{i=1}^{n}{w}_{i}=1$ (1)

$$CI=\frac{{\lambda }_{max}-n}{n-1}$$

$$CR=\frac{CI}{RI}$$

where ${\lambda }_{max}$ is the maximum eigenvector of the pairwise comparison matrix A, and n is the size of the pairwise matrix. The random index (RI) value is based on the different matrix sizes, as shown in Table 2.

Table 2

RI value for different matrix sizes (Saaty 1980)
Size of Matrix (n)	1	2	3	4	5	6	7	8	9	10
RI	0.00	0.00	0.58	0.90	1.12	1.24	1.32	1.41	1.45	1.49

Step 4: Rank factors based on their optimal weight calculation

The calculation results in step 3 are used to obtain the weight of each evaluation attribute, then, the relative weights of the evaluation attributes are aggregated to get the total rating of the alternatives.

2.3 HFLTS

Rodriguez et al. (2012) first proposed the concept of HFLTS, which can process ambiguous conditions. The basic properties and operations of HFLTS are described below.

Definition 1

(Rodriguez et al. 2012): Let S = be a linguistic term set (LTS) and be an HELTS. is an ordered finite subset of the continuous language terms of S. For example, if S = is an LTS, then is an LTS of S.

Definition 2

(Rodriguez et al. 2012): Let S = be an LTS and be an arbitrary HFLTS of S. The lower and upper bounds of the HFLTS are defined as follows:

${H}_{{s}^{-}}=min\left({s}_{i}\right)={s}_{j}$ , ${s}_{j}\in {H}_{s}$ and ${s}_{i}\ge {s}_{j}, \forall i.$ (4)

${H}_{{s}^{+}}=max\left({s}_{i}\right)={s}_{j}$ , ${s}_{j}\in {H}_{s}$ and ${s}_{i}{\le s}_{j}, \forall i.$ (5)

Definition 3

(Rodriguez et al. 2012): The envelope of an HFLTS, env, is a linguistic interval between the lower and upper bounds :

env $\left({H}_{s}\right)$=$\left[{H}_{{s}^{-}}, {H}_{{s}^{+}}\right]$. (6)

2.4 Soft set

Molodtsov (1999) proposed the concept of soft sets as a mathematical approach for handling uncertainties that traditional methods cannot handle, and defined the principles of soft sets in the following way:

Definition 4

(Molodtsov 1999): Assume that the pair (F, A) is a soft set over U, where F is a mapping given by:

$$F:A\to P\left(U\right)$$

In other words, the soft set U is a family of parameterized subsets of the universe U. For $\epsilon \in A$, $F\left(\epsilon \right)$ may be considered as the set of $\epsilon$-approximate elements of the soft set (F, A).

Definition 5

(Maji et al. 2003; Ali et al. 2009): Let (F, A) and (G, B) be two soft sets on the common universal set U. The intersection set of (F, A) and (G, B) is represented by (H, C), which should meet the following conditions:

$$C=A\cap B$$

$\forall e\in C, H\left(e\right)=F\left(e\right) or G\left(e\right)$ (as both are the same set)

Definition 6

(Maji et al. 2003; Ali et al. 2009): Let (F, A) and (G, B) be two soft sets on the common universal set U. If (F, A) and (G, B) meet the conditions below, then (F, A) is a subset of (G, B), denoted as :

$$A\subseteq B$$

$$\forall e\in A, F\left(e\right)\subseteq G\left(e\right)$$

Definition 7

(Maji et al. 2003; Ali et al. 2009): Let (F, A) and (G, B) be two soft sets on the common universal set U. The union set of (F, A) and (G, B) is represented by (H, C), which should meet the following conditions:

(i)$C=A\cup B$

(ii)$\forall e\in C$

$$H\left(e\right)=\left\{\begin{array}{c}F\left(e\right) if e\in A-B\\ G\left(e\right) if e\in B-A\\ F\left(e\right)\cup G\left(e\right) if e\in A\cap B\end{array}\right.$$

3.1 The planning of proposed method

COVID-19 broke out at the end of 2019, raged across the world in 2020 and 2021, and continues to cause a large number of casualties and serious economic problems in various countries. It has caused nearly five million deaths worldwide. The economies of all countries have been severely tested, and most countries are still at the stage of fighting the virus. When a major emergency occurs in a country, although the government can invite experts from various fields to hold discussions within a short time period, due to the different backgrounds and expertise of the experts, they may not be able to clearly express the assessment information; moreover, the process of data collection often contains large amounts of qualitative and quantitative information. Emergency situations are characterized by limited time, limited information, and uncertainty. Therefore, PHEDM is considered a complex MCDM problem. The AHP method can adopt a hierarchical structure and consider qualitative and quantitative information, and can effectively handle complex decision-making problems.

Fundamentally speaking, the information of emergencies is incomplete and uncertain. Experts are severely bound by such uncertainty, yet they must respond immediately and provide emergency solutions to effectively control the situation. At the beginning of the outbreak, there was insufficient data on the variants, which caused results in clinical trials and other medical technologies remaining in the critical stage of exploration, moreover, these responses given by experts in the emergency decision may be include hesitant, and incomplete information, which made the traditional AHP method cannot be completely solved. In order to adapt appropriate and accurate measures to respond to emergency decision-making situations and solve the aforementioned issue, this paper integrated the typical AHP method, the soft set approach, and HFLTS to deal with a numerical case about PHEDM. The results demonstrated the effectiveness and correctness of the proposed method, showed that it would not lose any professional knowledge in providing useful information, and revealed that it could better reflect the practical feasibility of emergency decision making in the real world.

3.2 The procedure of the proposed method

The basic procedure for implementing the proposed method consists of the following steps:

Step 1. Organize an emergency decision making committee

Recruit experts and scholars in various fields related to emergency decision making and form a committee to hold discussions, determine decision-making problems, and seek solutions.

Step 2. Construct and determine emergency decision-making evaluation criteria

Define criteria or important influence factors related to decision-making as a key consideration in developing appropriate and accurate measures for analyzing and judging solutions, and ask experts to score each evaluation criterion.

Step 3. Defuzzify the hesitant fuzzy information

Use Eqs. (4) to (6) to deal with evaluation criteria scores containing hesitant fuzzy linguistic information, and calculations that use the arithmetic mean to defuzzify hesitant fuzzy information.

Step 4. Fill in incomplete information

Use the soft set concept to handle evaluation criteria scores containing incomplete or nonexistent information, and average the known information, then to supplement in incomplete information.

Step 5. Calculate the relative weights of the criteria

Use Eqs. (1) to (3) to calculate the pairwise comparison matrix, and then obtain the relative weights of each criterion.

Step 6. Calculate the aggregated value of the emergency decision making and rank the alternative solutions

Once the relative weights of the criteria are confirmed in step 5, calculate the relative weights and the alternatives to gain the aggregate value of the PHEDM. Then, use the results to rank the alternatives and select the best alternative solution.

Step 7. Provide suggestions from the project team

According to the result of ranking the PHEDM, execute the most suitable plan, evaluate the effectiveness of the decision making, and review the implementation results.

4.1 Overview

During the COVID-19 pandemic, emergency decision making and risk assessment have become important issues for guaranteeing the stable life of the people. However, the decision-making process often contains qualitative and quantitative information, as well as limited time. The assessment information of the criteria simultaneously includes complete, incomplete and hesitant fuzzy linguistic information, so it is regarded as an emergency MCDM problem. In order to verify the effectiveness of the proposed method, this section gives an illustrative case of the PHEDM for COVID-19 (adapted from Ashraf and Abdullah 2020). The case of public health emergency decision making for COVID-19 was composed of seven criteria and five alternatives. The basic criteria included clinical management (CM), first-aid training (FT), technician training (TT), banning intra-city transportation (BT), global uncertainty (GU), country-level coordination and planning (CP), and monitoring (MO), as shown in Table 3. The five alternatives included risk communication (A1), blocking borders and cities (A2), medical system (A3), research needs (A4), and asking the experts (A5).

The consultant committee was comprised of five experts who provided scores for the preventive emergency criteria of COVID-19, as shown in Table 4. The importance scores of the seven evaluation criteria for the five alternatives are shown in Table 5.

Table 3

Preventive emergency criteria of COVID-19
Emergency criteria	Definition
CM	Vaccination is a massively effective preventive method for reducing COVID-19 in many countries. It is rarely seen to have severe side effects, and it is an effective disease prevention and control measure.
FT	Due to the rapid spread of COVID-19, representatives need to undergo relevant first aid training.
TT	The rapid sharing of viral genetic information among countries in the world will help countries develop potential vaccines.
BT	To prevent the virus from spreading and to protect the safety of the people, the government has taken measures to ban flights, cancel various celebrations, and maintain social distancing between people.
GU	COVID-19 has changed people's lifestyles, affected the transportation and tourism industries, caused factory closures, delayed deliveries, and harmed international trade and economic development.
CP	The government needs to work closely with all local administrative agencies to deal with the uncertainty of COVID-19.
MO	Government public health experts should continuously monitor the state of COVID-19 and provide suggestions to improve the situation.

Table 4

Pairwise comparison matrix of the preventive emergency criteria
		CM	FT	TT	BT	GU	CP	MO
CM	Expert1	1	1	1/2	7	7	1/2	6
	Expert2	1	2	1/3	4	6	1/3	4-5
	Expert3	1	1	1/5	4	7	1/4	5
	Expert4	1	1	1/3	5	7	*	6
	Expert5	1	1/2	1/3	7	8	1/3	6
FT	Expert1	1	1	1/2	8	7	1/2	6
	Expert2	1/2	1	1/4	4	6	1/3	5
	Expert3	1	1	1/4	4-5	5-6	1/4	5
	Expert4	1	1	1/3	5	7	*	6
	Expert5	2	1	1/2	7	6	1/2	5
TT	Expert1	2	2	1	7	4	2	6
	Expert2	3	4	1	4	5-6	1	6
	Expert3	5	4	1	5	6	1	7
	Expert4	3	3	1	4	7	*	5
	Expert5	3	2	1	6	4	2	5
BT	Expert1	1/7	1/6	1/7	1	1/2	1/5	1/3
	Expert2	1/4	1/4	1/4	1	2	1/5	1
	Expert3	1/4	1/5-1/4	1/5	1	2	1/4	1/2
	Expert4	1/5	1/4	1/4	1	3	*	2
	Expert5	1/7	1/5	1/6	1	1/2	1/5	1/2
GU	Expert1	1/7	1/8	1/4	2	1	1/6	2
	Expert2	1/6	1/4	1/6-1/5	1/2	1	1/6	2
	Expert3	1/7	1/6-1/5	1/6	1/2	1	1/7	2
	Expert4	1/7	1/5	1/7	1/3	1	*	1
	Expert5	1/8	1/7	1/4	3	1	1/6	2
CP	Expert1	2	2	1/2	5	6	1	7
	Expert2	3	3	1	5	6	1	7
	Expert3	4	4	1	4	7	1	8
	Expert4	*	*	*	*	*	*	*
	Expert5	3	2	1/2	5	6	1	5
MO	Expert1	1/6	1/6	1/6	3	1/2	1/7	1
	Expert2	1/7-1/6	1/5	1/6	1/2	1/2	1/7	1
	Expert3	1/5	1/5	1/7	1	1/2	1/8	1
	Expert4	1/6	1/6	1/5	1/2	1	*	1
	Expert5	1/6	1/5	1/5	2	1/2	1/5	1
Note: * indicates missing/non-existent data

Table 5

The importance of criteria for alternative of emergency public health decision
Alternative	CM	FT	TT	BT	GU	CP	MO
A1	0.8	0.8	0.9	0.4	0.2	0.9	0.2
A2	0.9	0.4	0.9	0.8	0.9	0.6	0.4
A3	0.4	0.9	0.9	0.4	0.8	0.6	0.9
A4	0.1	0.9	0.8	0.9	0.3	0.4	0.7
A5	0.9	0.2	0.4	0.6	0.1	0.8	0.9

4.2 Application of the typical AHP method

The AHP method has the advantages of providing solutions with a multi-level and hierarchical structure, and it can systematically solve problems that contain both qualitative and quantitative elements, making it an effective tool for handling complex decisions. During information processing, the AHP method can only deal with complete information. According to Table 4, Experts 2 and 3 provided partially hesitant information, and Expert 4 provided partially incomplete information. However, the typical AHP method could only deal with complete information about the evaluation criteria for the emergency public health decisions given by the experts. Thus, only Experts 1 and 5 provided complete information that could be used to calculate the criteria weight, whereas, the information from the Expert 2-4 should be eliminated. The solution procedure was as follows:

Step 1. Calculate the criteria weights

Experts 2, 3, and 4 lacked professional knowledge of the criteria and could not give them appropriate ratings. As these limitations would lead to an invalid questionnaire, only the rating results of Experts 1 and 5 could be used to perform arithmetic average calculations for the calculation weights.

The pairwise comparison matrix shown in Table 4 was used to calculate the weight of each standard. First, the AHP method was used to calculate the arithmetic mean from Expert 1 and 5’s given scores, and then the weight calculation was implemented. The CR value was calculated to examine the consistency of the test and ensure that the judgements of the decision makers were consistent. When the CR value < 0.1 the judgements were acceptable. Eqs. (1) to (3) were used to calculate the ${\lambda }_{max}$, CI, and CR values, as shown below:

$$CI=\frac{{\lambda }_{max}-n}{n-1}=\frac{7.621-7}{7-1}=0.104$$

$$CR=\frac{CI}{RI}=\frac{0.104}{1.32}=0.078$$

Step 2. Rank the alternatives

Through the weight calculation shown in Table 4, the priority vector results indicated that TT had the most important weight value at 0.282, following by the weights of CP, FT, FT, CM, MO, and GU at 0.241, 0.189, 0.172, 0.046, 0.043, and 0.027, respectively. After multiplying the weight values of the seven evaluation criteria with the scores shown in Table 6, the weighted scores of five alternatives were obtained, as shown in Table 7. In the ranking of the alternatives, from highest to lowest, A1 was the best alternative with a score of 0.788, followed by the weights of A3, A2, A4, and A5 at 0.720, 0.708, 0.579, and 0.560, respectively.

Table 6

Computation results of the preventive emergency criteria
Evaluation Criteria	Weight	Ranking
CM	0.172	4
FT	0.189	3
TT	0.282	1
BT	0.027	7
GU	0.043	6
CP	0.241	2
MO	0.046	5

Table 7

Computation results of the emergency public health decision alternatives
Alternative	Score	Ranking
A1	0.788	1
A2	0.708	3
A3	0.720	2
A4	0.579	4
A5	0.560	5

4.3 Application of the hesitant AHP method

In real life, people often provide ambiguous answers to problems due to incomplete information, and they can be severely bound by uncertainty and risk. When encountering harmful and uncertain situations, the typical AHP method can only deal with complete information. In this study, regarding the preventive emergency criteria given by the experts, as shown in Table 4, the typical AHP method would delete the partially hesitant information provided by Experts 2 and 3, causing some important information to be dismissed. However, the hesitant AHP method proposes a concept that uses a set of possible linguistic terms to represent the hesitation of the experts and uses different terms to estimate a linguistic variable instead of using single terms to solve hesitant information, and therefore it can effectively deal with the shortcomings of the typical AHP method. The solution procedure is shown as follows:

Step 1. Defuzzify the hesitant fuzzy information

According to Table 4, Expert 3 have a score to MO in CM is 4-5 which represented hesitant fuzzy information. This study used Eq. (6) and the arithmetic mean to defuzzify the hesitant fuzzy information. The average number was calculated to be 4.5 and was used in the next calculations. Other hesitant values are also used with the same method to obtain the exact value.

Step 2. Determine the evaluation criteria weight

After defuzzifying the hesitant fuzzy information, based on Table 4, Eqs. (1) to (3) were used to calculate ${\lambda }_{max}$=7.603 and then calculate the CI value. The calculation results showed that the CR value was 0.077, which met the consistency standard (CR <0.1). The priority vector results showed that TT had the most important weight value at 0.297, followed by the weights of CP, CM, FT, GU, BT, and MO at 0.275, 0.159, 0.149, 0.044, 0.040, and 0.036, respectively.

$$CI=\frac{{\lambda }_{max}-n}{n-1}=\frac{7.603-7}{7-1}=0.101$$

$$CR=\frac{CI}{RI}=\frac{0.101}{1.32}=0.077$$

Step 3. Confirm the rankings of the criteria and alternatives

After multiplying the weight values of the seven evaluation criteria with the scores in Table 8, the weighted scores of the five alternatives could be obtained, as shown in Table 9. In the ranking of the alternatives, from highest to lowest, A1 was the best alternative with a score of 0.793, followed by the weights of A2, A3, A5, and A4 at 0.721, 0.709, 0.573, and 0.572, respectively.

Table 8

Computation results of the preventive emergency criteria
Evaluation Criteria	Weight	Ranking
CM	0.159	3
FT	0.149	4
TT	0.297	1
BT	0.040	6
GU	0.044	5
CP	0.275	2
MO	0.036	7

Table 9

Computation results of the PHEDM alternatives
Alternative	Score	Ranking
A1	0.793	1
A2	0.721	2
A3	0.709	3
A4	0.572	5
A5	0.573	4

4.4 Application of the proposed method

In cases of emergencies or disasters, it is often necessary to carry out major disaster relief operations, and decision-making teams often have to be established. This requires the input of relevant experts from different backgrounds and various fields. When an emergency occurs, effective rescue methods must be provided to control and respond the emergency immediately. When asked to make a decision, experts in different fields may be unable to make quick and correct judgments or provide advice under unfamiliar situations, which usually results in nonexistent information. The traditional procedure of data collection will delete any incomplete information, which may result in biased assessment results. In order to overcome these issues, this study extended the AHP method and combined HFLTS and the soft set to solve PHEDM problems. The following steps describe the procedure:

Steps 1 and 2. Organize an emergency decision-making committee to construct and determine the emergency decision-making evaluation criteria

Gather domestic experts in various fields to form a decision-making team to respond to the epidemic, establish a structure for decision making, and define criteria or important influencing factors relevant to the decision-making as a key consideration for analyzing and judging the solutions, and ask the experts to give a score for each evaluation criteria.

Step 3. Defuzzify the hesitant fuzzy information

As shown in Table 4, Experts 2, 3, and 5 partially lacked professional knowledge of the criteria and could give them appropriate. In order to deal with the hesitant fuzzy information, the solution procedure was also completed in reference to section 4.3. According to that shown in Table 3, Expert 3 gave a score to GU in FT is 5-6, which represented hesitant fuzzy information. This study used Eq. 6 and the arithmetic mean to defuzzify the hesitant fuzzy information. The average number was calculated to 5.5 and used for further computations. The same method was then used for other information containing hesitant values to obtain the exact value.

Step 4. Fill in incomplete information

After completing the hesitant fuzzy information computation, based on Table 4, Expert 4 could not give a score to CP in CM, perhaps Expert 4 doesn’t understand the criteria mean, so the incomplete or nonexistent information has to be deleted directly in traditional data collection approach, which will lose some important information for other criteria. To overcome the challenge of incomplete or nonexistent information, this study used Eqs. (7) and (8) from section 2.3 to average the other known information and then fill in the incomplete information. The same way was used with other incomplete values to obtain the determined value and then proceed to the subsequent calculation process.

Step 5. Determine the evaluation criteria weight

The solution procedure was also completed in reference to section 4.2, after steps 3 and 4, according to Table 4, employs Eqs. (1), (2), and (3) to calculate ${\lambda }_{max}$=7.574 and then shows the calculation for the CI value. The calculation results showed that the CR value was 0.073, which met the consistency standard (CR <0.1).

$$CI=\frac{{\lambda }_{max}-n}{n-1}=\frac{7.574-7}{7-1}=0.096$$

$$CR=\frac{CI}{RI}=\frac{0.096}{1.25}=0.073$$

After confirming the consistency of the information provided by the experts, different weight values for the weight calculations were assigned according to their degree of importance. As shown in Table 10, the priority vector results showed that TT had the most important weight value at 0.299, followed by the weights of CP, CM, FT, GU, BT, and MO at 0.275, 0.158, 0.151, 0.042, 0.040, and 0.035, respectively.

Step 6. Calculate the aggregated value of the emergency decision making and rank the alternative solutions

After finishing the weight calculations of the criteria, the results of the scores of 7 evaluation preventive emergency criteria from step 5 will multiply with 5 alternatives that are obtained in Table 11, then rank the computation result for PHEDM. In the ranking of alternatives, from highest to lowest, A1 was found to be the best alternative with a score of 0.796, followed by the weights of A2, A3, A4, and A5 at 0.720, 0.710, 0.575, and 0.573, respectively.

Step 7. Provide project team with suggestions

The results of the PHEDM ranking were used to provide the most suitable alternative anti-epidemic policy. The implementation results of the most suitable alternative were continuously reviewed to evaluate the effectiveness of the decision and confirm the problem had been solved effectively to achieve the expected goal.

Table 10

Computation results of the preventive emergency criteria
Evaluation Criteria	Weight	Ranking
CM	0.158	3
FT	0.151	4
TT	0.299	1
BT	0.042	5
GU	0.040	6
CP	0.275	2
MO	0.035	7

Table 11

Computation results of the PHEDM alternatives
Alternative	Score	Ranking
A1	0.796	1
A2	0.720	2
A3	0.710	3
A4	0.575	4
A5	0.573	5

4.5 Comparison and discussion

This study used an illustrative case in Section 4.1 to compare the different computation results between the proposed method, the typical AHP method, and the hesitant AHP method. The experimental results of the three methods for the weights of the evaluation criteria and the scores for the most effective alternatives are shown in Tables 12 and 13, respectively.

Table 12

Evaluation criteria weights
Evaluation Criteria	Weight			Ranking
Evaluation Criteria	Typical AHP method	Hesitant AHP method	Proposed method	Typical AHP method	Hesitant AHP method	Proposed method
CM	0.172	0.159	0.158	4	3	3
FT	0.189	0.149	0.151	3	4	4
TT	0.282	0.297	0.299	1	1	1
BT	0.027	0.040	0.042	7	6	5
GU	0.043	0.044	0.040	6	5	6
CP	0.241	0.275	0.275	2	2	2
MO	0.046	0.036	0.036	5	7	7

Table 13

Ranking of the alternatives
Alternative	Score			Ranking
Alternative	Typical AHP method	Hesitant AHP method	Proposed method	Typical AHP method	Hesitant AHP method	Proposed method
A1	0.788	0.793	0.796	1	1	1
A2	0.708	0.721	0.721	3	2	2
A3	0.724	0.714	0.714	2	3	3
A4	0.579	0.572	0.576	4	5	4
A5	0.560	0.573	0.574	5	4	5

The typical AHP method can only handle exact information, moreover, the hesitant AHP method addressed only hesitant fuzzy information. If the experts provided information containing partially nonexistent information, the typical AHP method and hesitant AHP method would dismiss some available information, causing bias in the decision procedure. The proposed method was verified by numerical examples and found to be useful when encounter information containing unknown, partially known, missing, or non-existent information during the collection of COVID-19 data. The advantages of the proposed method are presented below.

First, when collecting information to solve group MCDM problems, experts in various fields such as economics, medicine, and public health may be unfamiliar or unaware of certain professional knowledge and be unable to answer certain questions, causing certain information to be unavailable. Traditionally, due to research method limitations, the typical AHP method and hesitant AHP method have been unable to handle partially nonexistent information; therefore, the typical AHP method and hesitant AHP method will often neglect important information. In order to deal with incomplete information, this study used the concept of the soft set to deal with this situation and retain crucial questionnaire information. The proposed method could calculate all possible selection values for each object and supplement missing information by means of numerical averaging to overcome the aforementioned problem of partially nonexistent information. Therefore, all the questionnaire information could be presented authentically, considered fully, and applied widely.

Second, in practice, the typical AHP method can only handle exact values; when encountering hesitant fuzzy information, the available information will be ambiguous. Therefore, questionnaires containing hesitant fuzzy information will be considered invalid and deleted, causing valuable information to go missing and easily resulting in biased assessment results. The hesitant AHP method and the proposed flexible AHP method can deal with hesitant fuzzy information by applying a defuzzification method to determine the interval value of the evaluation data set and replacing this information with the mean value. According to Table 13, after considering the hesitant fuzzy information, the A2 and A3 for ranking of alternative is2nd and3rd in the hesitant AHP method and proposed flexible AHP method, different from the typical AHP method with 3rd and 2nd, in addition, the result of typical AHP method may have significant errors in emergency medical resource allocation.

Third, based on Table 4, it contained hesitant fuzzy information (Expert 3 and 4) and partially nonexistent information (Expert 5). Due to the hesitant AHP method being unable to handle partially nonexistent information, as shown in Table 13, the calculation result of the hesitant AHP method indicated that A4 (0.572) was ranked fifth and that A5 (0.573) was ranked fourth. The closeness of these values could cause errors in ranking. However, because of the proposed flexible AHP method being able to deal with unknown, partly-known, missing, inexistent, or hesitant fuzzy linguistic data, it could fully consider the available information and distinguish small numerical differences. The calculation result showed that A4 (0.576) was ranked fourth and A5 (0.574) was ranked fifth, which was the correct ranking. This result showed that the proposed method could allow decision makers to fully consider the available information.

Table 14

Differences between the three calculation methods
Method selection	Solving characteristic
Method selection	Hesitant information	Missing or nonexistence information	Full consideration of all available information
Typical AHP method	X	X	X
Hesitant AHP method	O	X	X
Proposed method	O	O	O

The outbreak and rapid spread of COVID-19 since December 2019 have severely affected the world’s economic development and people’s lives and survival. From the past experience of epidemic prevention in various countries, it can be understood that if correct epidemic prevention measures and medical planning are adopted in the early stage of an epidemic, the severity of the epidemic can be greatly reduced. How to properly allocate medical resources is a crucial issue for emergency MCDM problems related to COVID-19. Emergency MCDM problems involve many levels and factors and usually contain both qualitative and quantitative information and factors. Moreover, when giving assessment criteria scores for emergency MCDM problems, the experts may encounter problems due to time constraints or insufficient information, including incomplete and hesitant fuzzy information. These conditions will make it difficult for group decision makers to make correct decisions. In order to deal with the above situation, this study extended the AHP method to propose a flexible AHP method that was proved through a numerical analysis of PHEDM. It did not lose any expertise in providing important and useful information, and it could overcome the challenges of emergency MCDM problems under uncertain and ambiguous environments.

The advantages of the flexible AHP method are summarized as follows:

(1) The proposed flexible AHP method can deal with partially nonexistent information in PHEDM for COVID-19.

(2) The proposed flexible AHP method can address hesitant fuzzy linguistic information in PHEDM for COVID-19.

(3) The proposed flexible AHP method can fully consider the available information.

(4) The traditional AHP method (Ashraf and Abdullah 2020) is a special case of the proposed flexible AHP method.

Due to the traditional AHP method usually supposed to be independent during criteria assessment, in the future, this article may be able to study in the direction of the correlation among criteria, and preferable to reflect the practical feasibility in the real world.

Funding

The authors would like to thank the Ministry of Science and Technology, Taiwan, for financially supporting this research under Contract No. MOST 109-2410-H-145-002 and MOST 110-2410-H-145-001.

Competing Interests

The authors have no relevant financial or non-financial interests to disclose.

Author Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Hsiang-Yu Chung and Kuei-Hu Chang. The first draft of the manuscript was written by Hsiang-Yu Chung and Kuei-Hu Chang, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Data Availability

All data generated or analysed during this study are included in this published article.

Ali MI, Feng F, Liu XY, Min WK, Shabir M (2009) On some new operations in soft set theory. Comput Math Appl 57(9):1547-155.
Ashraf S, Abdullah S (2020) Emergency decision support modeling for COVID-19 based on spherical fuzzy information. Int J Int Sys 35(11): 1601-1645.
Baryannis G, Validi S, Dani S, Antoniou G (2019) Supply chain risk management and artificial intelligence: state of the art and future research directions. Int J Prod Res 57(7): 2179-2202.
Baskaran N, Eswari R (2021) Efficient VM selection strategies in cloud datacenter using fuzzy soft set. J Organ End User Com 33(5): 153-179.
Bazan D, Nowicki M, Rzymski P (2021) Medical students as the volunteer workforce during the COVID-19 pandemic: Polish experience. Int J Disast Risk Re 55: 102109.
Chang KH (2015) Enhanced assessment of a supplier selection problem by integration of soft sets and hesitant fuzzy linguistic term set. P I Mech Eng B-J Eng 229(9): 1635-1644.
Chang KH, Chain K, Wen TC, Yang GK (2016) A novel general approach for solving a supplier selection problem. J Test Eval 44(5): 1911-1924.
Chen LC, Chang KH, Chung HY (2021) A novel statistic-based corpus machine processing approach to refine a big textual data: an ESP case of covid-19 news reports. Appl Sci 10(16): 5505.
Dalkilic O (2021) A novel approach to soft set theory in decision making under uncertainty. Int J Comput Math 98(10): 1930-1945.
Das D, Datta A, Kumar P, Kazancoglu Y, Ram M (2021) Building supply chain resilience in the era of COVID‑19: An AHP‑DEMATEL approach. Oper Manage Res (Early Access).
Hong KH, Lee SW, Kim TS, Huh HJ, Lee J, Kim SY, Park JS, Kim GJ, Sung H, Roh KH, et al. (2020) Guidelines for laboratory diagnosis of coronavirus disease 2019 (COVID-19) in Korea. Ann Lab Med 40(5): 351-360.
Hussain S, Wang XT, Hussain T, Khoja AH, Zia MZ (2021) Assessing the impact of COVID-19 and safety parameters on energy project performance with an analytical hierarchy process. Util Policy 70: 101210.
Jiang P, Wang YX, Liu C, Hu YC, Xie JC (2020) Evaluating critical factors influencing the reliability of emergency logistics systems using multiple-attribute decision making. Symmetry-Basel 12(7): 1115.
Lee AHI (2009) A fuzzy AHP evaluation model for buyer-supplier relationships with the consideration of benefits, opportunities, costs and risks. Int J Prod Res 47(15): 4255-4280.
Liao HC, Gou XJ, Xu ZS (2020) Hesitancy degree-based correlation measures for hesitant fuzzy linguistic term sets and their applications in multiple criteria decision making. Inform Sciences 508: 275-292.
Liao HC, Qin R, Gao CY, Wu XL, Hafezalkotob A, Herrera F (2019) Score-HeDLiSF: A score function of hesitant fuzzy linguistic term set based on hesitant degrees and linguistic scale functions: An application to unbalanced hesitant fuzzy linguistic MULTIMOORA. Inform Fusion 48: 39-54.
Liao HC, Xu ZS, Zeng XJ, Merigo JM (2015) Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets. Knowl-Based Syst 76: 127-138.
Lin CS, Kou G, Peng Y, Alsaadi FE (2020) Aggregation of the nearest consistency matrices with the acceptable consensus in AHP-GDM. Ann Oper Res (Early Access).
Lippi G, Sanchis-Gomar F, Henry BM (2020) Coronavirus disease 2019 (COVID-19): The portrait of a perfect storm. Ann Transl Med 8(7): 497.
Lu RJ, Zhao X, Li J, Niu PH, Yang B, Wu HL, Wang W, Song H, Huang B, Zhu N, et al. (2020) Genomic characterisation and epidemiology of 2019 novel coronavirus: Implications for virus origins and receptor binding. Lancet 395(10224): 565-574.
Lyu HM, Zhou WH, Shen SL, Zhou AN (2020) Inundation risk assessment of metro system using AHP and TFN-AHP in Shenzhen. Sustain Cities Soc 56: 102103.
Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45(4-5): 555-562.
Molodtsov D (1999) Soft set theory-first results. Comput Math Appl 37(4-5): 19-31.
Moslem S, Gul M, Farooq D, Celik E, Ghorbanzadeh O, Blaschke T (2020) An integrated approach of best-worst method (BWM) and triangular fuzzy sets for evaluating driver behavior factors related to road safety. Mathematics, 8(3): math8030414.
Narayanamoorthy S, Pragathi S, Parthasarathy TN, Kalaiselvan S, Kureethara JV, Saraswathy R, Nithya P, Kang D (2021) The COVID-19 vaccine preference for youngsters using PROMETHEE-II in the IFSS environment. Symmetry-Basel 13(6): 1030.
Ortiz-Barrios M, Borrego-Areyanes AA, Gomez-Villar ID, De Felice F, Petrillo A, Gul M, Yucesan M (2021) A multiple criteria decision-making approach for increasing the preparedness level of sales departments against COVID-19 and future pandemics: A real-world case. Int J Disast Risk Re 62: 102411.
Rodriguez RM, Martinez L, Herrera F (2012) Hesitant fuzzy linguistic term sets for decision making. IEEE T Fuzzy Syst 20(1): 109-119.
Saaty TL (1980) Analytic hierarchy process. McGraw-Hill, New York, NY, USA.
Samanlioglu F, Kaya BE (2020) Evaluation of the COVID-19 pandemic intervention strategies with hesitant F-AHP. J Healthc Eng 8835258.
Singhal T (2020) A review of coronavirus disease-2019 (COVID-19). Indian J Pediatr 87(4): 281-286.
Sir GDB, Sir E (2021) Pain treatment evaluation in COVID-19 patients with hesitant fuzzy linguistic multicriteria decision-making. J Healthc Eng 8831114.
Skare M, Riberio SD, Porada-Rochon M (2021) Impact of COVID-19 on the travel and tourism industry. Technol Forecast Soc 163: 120469.
Sun PF, Lu XH, Xu C, Sun WJ, Pan B (2020) Understanding of COVID-19 based on current evidence. J Med Virol 92(6): 548-551.
Van Fan Y, Jiang P, Hemzal M, Klemes JJ (2021) An update of COVID-19 influence on waste management. Science of the Total Environment 754: 142014.
Wang YC, Wang LH, Zhao X, Zhang JL, Ma WH, Zhao HJ, Han X (2021) A semi-quantitative risk assessment and management strategies on COVID-19 infection to outpatient health care workers in the post-pandemic period. Risk Manag Hlthc Pol 14: 815-825.
WHO publication: https://www.who.int/publications/m/item/weekly-operational-update-on-covid-19---20-september-2021 (published on 20 September 2021).
Yuan JJ, Lu YL, Cao XH, Cui HT (2020) Regulating wildlife conservation and food safety to prevent human exposure to novel virus. Ecosystem Health and Sustainability, 6(1): 1741325.
Zadeh LA (1965) Fuzzy sets. Inform Control 8(3): 338-353.

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Using the flexible analytic hierarchy process method to solve the emergency decision making of public health for COVID-19

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Abstract

1 Introduction

2 Literature review

2.1 COVID-19

2.2 AHP method

2.3 HFLTS

2.4 Soft set

3 The Proposed Approach

3.1 The planning of proposed method

3.2 The procedure of the proposed method

4 Case Study

4.1 Overview

4.2 Application of the typical AHP method

4.3 Application of the hesitant AHP method

4.4 Application of the proposed method

4.5 Comparison and discussion

5 Conclusion And Future Works

Declarations

References

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Alternative	CM	FT	TT	BT	GU	CP	MO
A1	0.8	0.8	0.9	0.4	0.2	0.9	0.2
A2	0.9	0.4	0.9	0.8	0.9	0.6	0.4
A3	0.4	0.9	0.9	0.4	0.8	0.6	0.9
A4	0.1	0.9	0.8	0.9	0.3	0.4	0.7
A5	0.9	0.2	0.4	0.6	0.1	0.8	0.9

Alternative	CM	FT	TT	BT	GU	CP	MO
A1	0.8	0.8	0.9	0.4	0.2	0.9	0.2
A2	0.9	0.4	0.9	0.8	0.9	0.6	0.4
A3	0.4	0.9	0.9	0.4	0.8	0.6	0.9
A4	0.1	0.9	0.8	0.9	0.3	0.4	0.7
A5	0.9	0.2	0.4	0.6	0.1	0.8	0.9

Alternative	CM	FT	TT	BT	GU	CP	MO
A1	0.8	0.8	0.9	0.4	0.2	0.9	0.2
A2	0.9	0.4	0.9	0.8	0.9	0.6	0.4
A3	0.4	0.9	0.9	0.4	0.8	0.6	0.9
A4	0.1	0.9	0.8	0.9	0.3	0.4	0.7
A5	0.9	0.2	0.4	0.6	0.1	0.8	0.9