Evaluation of the COVID-19 Pandemic Intervention Strategies with Hesitant F-AHP

In this study, a hesitant fuzzy AHP method is presented to help decision makers (DMs), especially policymakers, governors, and physicians, evaluate the importance of intervention strategy alternatives applied by various countries for the COVID-19 pandemic. In this research, a hesitant fuzzy multicriteria decision making (MCDM) method, hesitant fuzzy Analytic Hierarchy Process (hesitant F-AHP), is implemented to make pairwise comparison of COVID-19 country-level intervention strategies applied by various countries and determine relative importance scores. An illustrative study is presented where fifteen intervention strategies applied by various countries in the world during the COVID-19 pandemic are evaluated by seven physicians (a professor of infectious diseases and clinical microbiology, an infectious disease physician, a clinical microbiology physician, two internal medicine physicians, an anesthesiology and reanimation physician, and a family physician) in Turkey who act as DMs in the process.


Introduction
As was realized from the previous 2009 AH1N1 pandemic and the recent COVID-19 pandemic, countries need efficient mitigation planning to prevent mass infection and fatalities. An effective intervention plan may help flatten the epidemic curve and, with protective measures, there might be a delay and reduction in the peak of the outbreak. As a result, the number of cases at any time stays under the surge capacity of a country's healthcare system. If the surge capacity of a country's healthcare system is exceeded, the morbidity and mortality rates increase for all hospitalized patients, not just for COVID-19 cases. e basic reproduction number (R 0 ) is the key factor that shows the strength of the epidemic; it is, without any interventions, the mean number of secondary cases generated by a single infected case in a population with no immunity to infection [1]. When R 0 is greater than 1, the epidemic takes hold, and the overall fraction of population likely to be infected without interventions is the area under the epidemic curve which can be calculated roughly with 1-1/R 0 [2].
Effective intervention strategies, if followed properly, might reduce the R 0 below 1 and control the spread of COVID-19.
Countries need a systematic approach to determine which intervention strategies to apply during the COVID-19 pandemic and future potential epidemiological waves and pandemics. In this study, intervention strategies applied by countries during the COVID-19 pandemic are evaluated in terms of importance with the help of an MCDM method, hesitant F-AHP. Scenarios for the potential spread and impact of COVID-19 in the EU/EEA, with suggested actions for containment, were given in Johnson et al.'s article [3]. Also, Cheng et al. [4] presented an extensive dataset of government responses to the COVID-19 pandemic, and the interventions that are evaluated in this study are taken from their research. A list of these interventions is presented in Table 1 with detailed explanations and country examples.
In the literature, there is a limited number of studies that focus on the evaluation of intervention strategies. Aledort et al. [5] evaluated the evidence base for nonpharmaceutical public health interventions in an influenza pandemic with the help of literature review and expert opinions. Ciofi degli  Journal of Healthcare Engineering Atti et al. [6] evaluated the diffusion of pandemic influenza in Italy and the impact of various control measures with the help of SEIR (Susceptible-Exposed-Infected-Recovered) and individual-based models. Ajelli et al. [7] presented the realtime modeling analysis to estimate the impact of the pandemic and the mitigation measures during the 2009 A/H1N1v pandemic in Italy. Kohlhoff et al. [8] carried out an observational study and evaluated hospital mass screening and infection control practices with a pandemic influenza full-scale exercise in three acute care hospitals in Brooklyn, NY. Ventresca and Aleman [9] investigated the effects of six vaccination strategies in terms of the ability to contain disease spread by constructing a representative social network from the census of the Greater Toronto Area. Schiavo et al. [10] presented a review about evidence on interventions to communicate risk and promote disease mitigation measures in epidemics. Russell et al. [11] conducted a household survey in a school district of Kentucky to evaluate the effect of school closure mitigation on the transmission of influenza-like illness. Luca et al. [12] developed a stochastic spatial age-specific metapopulational model to investigate the impact of school closure on seasonal influenza epidemics in Belgium. Nicolaides [13] modified the SIR (Susceptible-Infected-Recovered) epidemic model to reflect the effects of hand washing in the infection process and investigated the effect of hand-hygiene mitigation strategy at airports for flu-type viruses. MCDM methods have been rarely utilized to evaluate interventions. Shin et al. [14] used AHP to decide if private clinics and hospitals or public health centers should offer free vaccination to children in Korea. Mourits et al. [15] implemented EVAMIX (evaluations with mixed data) to rank control strategies for classical swine fever epidemics in the EU. Aenishaenslin et al. [16] implemented D-Sight (PROMETHEE with GAIA) to evaluate prevention and control strategies for the Lyme disease in Quebec, Canada. Pooripussarakul et al. [17] applied best-worst scaling to evaluate vaccines in ailand. Previously, Samanlioglu [1] evaluated influenza intervention strategies in Turkey with fuzzy AHP-VIKOR.
In this study, various intervention strategies applied by countries in the world during the COVID-19 pandemic are evaluated by seven physicians with different expertise, acting as consultants and decision makers (DMs). For pairwise comparison of importance of strategies, as the MCDM method, hesitant F-AHP is applied. With (hesitant fuzzy) AHP, utilizing pairwise comparisons of alternatives and consistency check of these comparisons, dependable alternative scores can be determined. In this research, hesitant F-AHP is preferred over AHP or fuzzy AHP (F-AHP) since, different from AHP, with F-AHP, the uncertainty and vagueness on DMs' judgments can also be captured. Moreover, with the usage of multiple linguistic expressions and "hesitant" terminologies in hesitant F-AHP, more flexibility is attained in decision making than F-AHP since the degree of hesitation that DMs might have in reality can also be reflected.
In F-AHP, for pairwise comparisons, DMs give a single linguistic expression; and this does not reflect the hesitations DMs might have in reality. However, in hesitant F-AHP, DM might utilize hesitant fuzzy set (HFS) concepts [44,45], hesitant fuzzy linguistic term sets (HFLTS) [44,46], and multiple linguistic expressions and "hesitant" terminologies in their evaluations, which increase the flexibility and accuracy of the decision making process [47]. For example, while comparing interventions 1 and 8 pairwise, DM might give the following assessment: "intervention 1 is between absolutely strong and very strong in comparison to criterion 8".
Hesitant F-AHP was implemented in several MCDM problems in the literature. Some of these applications are assessment of suppliers [48], cargo company performance [49], woodwork manufacturing CNC routers [50], sustainability of hydrogen production methods [51], summer sport schools [52], power generation enterprises [47], and innovation projects [53].
Until now, to the best of the authors' knowledge, hesitant F-AHP has never been studied for the evaluation of intervention strategies. With the proposed hesitant F-AHP, importance of countries' COVID-19 intervention strategies is systematically evaluated. Application steps of hesitant F-AHP are explained in Section 3. An illustrative study is given in Section 4 to demonstrate the implementation, along with the conclusion and discussion in Section 5.

Proposed Hesitant F-AHP Approach
In the proposed hesitant F-AHP, triangular fuzzy numbers (TFNs) are implemented due to their uncomplicatedness. A fuzzy number is a special fuzzy set Arithmetic operations between two positive TFNs if C and D are two TFNs (not necessarily positive TFNs).
For defuzzification of TFNs, "the graded mean integration approach" [56] is applied as In Triangular Fuzzy Hesitant Fuzzy Sets (TFHFS), the membership degree of an element to a given set is expressed by several possible TFNs. Several aggregation operators for TFHFS were introduced by Yu [57] for assessment of teaching quality.
If X is a fixed set, the HFS on X returns a subset of [0, 1] by where h G (x) is the possible membership degrees of element x ∈ X to set G with values in [0, 1]. e lower and upper bounds are calculated as Basic operations for 3 HFS, h, h1, h2, are given as "Ordered Weighting Averaging (OWA)" operator that can be employed is OWA a 1 , a 2 , . . . , a n � n j�1 w j b j , where b j is the jth largest of a 1 , a 2 , . . . , a n , w j ∈ [0, 1]∀j, and n j�1 w j � 1 [53,58].
Here, l depends on the number of terms in DM's evaluation scale (in Table 2), j is the rank of the highest, and i is the rank of the lowest evaluation value. i and j can take ranks starting from 0 to l and n � j − i [53,58].
In the proposed hesitant F-AHP approach, the DMs make pairwise comparisons of importance of intervention strategy alternatives using the linguistic terms given in Table 2.
Steps of the proposed hesitant F-AHP are as follows: Step 1. Identify K DMs, n alternatives (intervention strategies), and linguistic terms and scale for the pairwise comparison of alternatives. Each DM makes pairwise comparison of alternatives (intervention strategies) with respect to the importance criterion. Based on the scale used in Table 2 and utilizing equations (8)- (12), DM's assessments are combined with fuzzy envelope approach, and TFNs corresponding to the assessment of each DM are obtained. Calculate where x K ij � (a K ij , b K ij , c K ij )∀i, j, k is the TFN corresponding to the evaluation of the Kth DM.
with elements x ij � (a ij , b ij , c ij ) being then defuzzified with equation (4) and approximate alternative scores w � (w 1 , w 2 , ..., w n ) being determined by averaging the entries on each row of normalized X. erefore, the normalized principal eigenvector is w. e largest eigenvalue (principal eigenvalue, λ max ) is determined with e consistency index (CI) is e consistency ratio (CR) is then used to assess the consistency of pairwise comparisons: RI is the random index, and if CR < 0.10, the comparisons are consistent and acceptable; otherwise, they are not [18].
Step 3. If comparisons are acceptable, rank the alternatives (intervention strategies) from the best to the worst based on approximate alternative scores w � (w 1 , w 2 , · · · , w n ) in decreasing order. Note that higher w shows better alternative.

Illustrative Study
In this study, 15 intervention strategies (A1, · · ·, A15) applied by countries worldwide during the COVID-19 pandemic are evaluated and compared in terms of the importance criterion by 7 physicians who act as DMs. In this study, DMs are a professor of infectious diseases and clinical microbiology (DM1), an infectious disease physician (DM2), a clinical microbiology physician (DM3), two internal medicine physicians (DM4 and DM5), a family physician (DM6), and an anesthesiology and reanimation physician (DM7) in Turkey.
In the proposed hesitant F-AHP, 7 DMs compare intervention strategy alternatives pairwise with the help of linguistic terms in Table 2, and the comparison is given in Table 3. After the combination of each DM's assessments with "fuzzy envelope approach" and aggregation of the corresponding TFNs of 7 DMs assessments, the fuzzy evaluation matrix for the alternative scores (X) in Table 4 is obtained.
Based on the w � (w 1 , w 2 , ..., w n ) obtained with hesitant F-AHP, intervention strategy alternatives are ranked in terms of importance criterion from the best to the worst as follows: declaration of emergency (A15), quarantine/lockdown of patients and those suspected of infection (A1), curfew (A13), common health testing (independent of suspected infection) (A12), social distancing (A3), closure of schools (A9), external border restrictions reducing the ability to exit or enter a country (A8), internal border restrictions reducing the ability to move freely (transportation) within a country (A2), restrictions of mass gatherings (A7), health monitoring (A4), restriction of nonessential government services (A14), government policies that affect the country's health resources (materials and health worker) (A10), formation of new task units/bureaus   Journal of Healthcare Engineering Table 3: Continued.   A1 A2  A3  A4  A5  A6  A7  A8  A9  A10  A11  A12  A13  A14  A15   A8   E  FW  SW  FW  AW  AW  VW  AW  E  E  SS  SS  VW  VW  E  VW  E  E  SW  SW  FW  FW-VW SW  VW  E  SS  FS  SS

Conclusion and Discussion
In this paper, a hesitant F-AHP approach is presented to help DMs such as policymakers, governors, and physicians evaluate and rank intervention strategy alternatives applied by various countries during the COVID-19 pandemic. At present, there does not appear to be a study in the literature that evaluates countries' COVID-19 intervention strategies. Moreover, in the literature a systematic MCDM approach such as hesitant F-AHP has never been utilized to evaluate and rank COVID-19 intervention strategies. Adoption of hesitant fuzzy linguistic terms in the process captures the fuzziness and hesitations and provides flexibility in decision making.
In the literature, AHP is mainly criticized due to the possible occurrence of rank reversal phenomenon caused by adding or deleting an alternative [61][62][63][64]. Adding a new alternative includes new information in the model, and therefore the decision needs to be reevaluated [65]. Unfortunately, the rank reversal problem occurs not only in AHP, but also in many other decision making approaches such as Borda-Kendall method, SAW, TOPSIS, and crossefficiency evaluation method [61]. However, this limitation did not affect our analysis since we did not need to add or delete any new intervention alternatives.
For the illustrative study, expert opinion for the evaluations was needed, so a professor of infectious diseases and clinical microbiology, an infectious disease physician, a clinical microbiology physician, two internal medicine physicians, a family physician, and an anesthesiology and reanimation physician in Turkey acted as DMs. Based on their evaluation, declaration of emergency, quarantine/ lockdown of patients and those suspected of infection, and curfew are determined as the best three intervention strategies among the evaluated ones.
In this research, intervention strategies are evaluated without taking into consideration the interventions' timing. In reality, the timing of the intervention, with respect to the beginning and peak of the epidemic, and duration of the application of the intervention are really significant. erefore, when making decisions, DMs need to take those into consideration, as well as intervention strategy rankings. Based on these, the proposed hesitant F-AHP approach can be adopted and utilized by policy makers, governors, national public health departments, and physicians for the evaluation of countries' intervention strategies for COVID-19 and other future similar epidemics. Also, for future research, various other potentially conflicting quantitative and qualitative criteria can be taken into consideration, and interactions, dependencies, and feedback relationships between them can be investigated with hesitant fuzzy analytic network process (hesitant F-ANP).

Data Availability
All the data used to support the findings of this study are included within the article.

Conflicts of Interest
e author declares that there are no conflicts of interest regarding the publication of this article.