key: cord-0843153-ldndikl2
authors: Sabri-Laghaie, Kamyar; Babroudi, Naeira Elyas Pour; Ghoushchi, Nazli Ghanbari
title: Re-evaluation of the healthcare service quality criteria for the Covid-19 pandemic: Z-number fuzzy cognitive map
date: 2021-08-05
journal: Appl Soft Comput
DOI: 10.1016/j.asoc.2021.107775
sha: 71ec7e0e8c72ed5328b832cfb356cf9514591823
doc_id: 843153
cord_uid: ldndikl2

Hospitals as healthcare centers have faced many challenges with the Covid-19 spread, which results in a decline in the quality of health care. Because the number of patients referred to hospitals increases dramatically during the pandemic, providing high quality services and satisfying them is more important than ever to maintain community health and create loyal customers in the future. However, health care quality standards are generally designed for normal circumstances. The SERVPERF standard, which measures customer perceptions of service quality, has also been adjusted for hospital service quality measurement. In this study, the SERVPERF standard criteria for health services are evaluated in the Covid-19 pandemic. For this purpose, by considering the causal relationships between the criteria and using Z-Number theory and Fuzzy Cognitive Maps (FCMs), the importance of these criteria in the prevalence of infectious diseases was analyzed. According to the results, hospital reliability, hospital hygiene, and completeness of the hospital with ratios 0.9559, 0.9305, and 0.9268 are respectively the most influential criteria in improving the quality of health services in the spread of infectious diseases circumstances such as the Covid-19 pandemic. A review of the literature shows that in previous studies, comprehensive research has not been done on prioritizing the criteria for measuring the quality of health services in the context of the spread of infectious diseases.

In December 2019, a new strain of the Covid-19 virus appeared in Wuhan, China. The number of people with this disease has increased rapidly worldwide, and official reports indicate that as of January 18, 2021, 95.2 million people were infected, and 2.03 million had died. The virus is widespread and affects general public [1, 2] , economy [3, 4] , culture [5, 6] , ecology [7] , environment [8] , health systems [9] and other fields [10, 11, 12] . Hospitals are often the central point of health care, and have played a vital role in responding to this crisis [13] . Accordingly, one of the most important public health measures to reduce the virus's spread rate is the rapid diagnosis and isolation of infected people [14] . Covid-19 is a unique disease due to the high prevalence, possibility of an epidemic, lack of primary scientific data, and media coverage. Therefore, these features face hospitals with many new challenges [15] .

These challenges start before the suspected patients of Covid-19 infection enter the hospitals because predicting a potential increase in cases is critical to hospitals' readiness. Also, the patient increase can lead to bed shortages and the need for more medical staff [13, 15] . After the arrival of patients suspected of Covid-19 in the hospital, the correct diagnosis is one other crucial step. After this step, patient management and isolation in emergency and intensive care units, triage, and scarce resource management are other possible challenges [13] . Logistics and transfer of patients for radiological and surgical examinations and separation of Covid-19 patients from others are also problematic. Infectious and hazardous waste management is conspicuous during infected patient care. Throughout this period, from the beginning of the pandemic until now, protecting healthcare personnel on the front lines and preventing nosocomial infections has been a significant challenge [16, 17, 18] . Like other infectious diseases, infection prevention and control is especially important in hospital and healthcare environment. What challenged this fact is the lack of personal protective equipment and freshman staff, the physical and psychological stress of dealing with a pandemic, intensity of work and lack of rest, need for training, etc. One other crucial issue is increasing awareness of health care providers to prevent and control infectious respiratory disease in the hospitals [17, 18] . Facing any of these challenges means a decline in the quality of hospital health services. To evaluate, address and tackle these challenges, criteria for measuring the quality of health services in different areas have been defined. However, most healthcare quality standards and scales are designed for typical situations and may not necessarily be appropriate in crisis times, such as the Covid-19 pandemic [19] .

Researchers have used different scales to evaluate the service quality in the healthcare industry. Donabedian [37, 38, 39] is the first person who studied the quality of healthcare services. SERVQUAL and SERVPERF are also the most widely used models in measuring health services' quality [20] . In general, these scales or their modifications have been broadly selected to assess the quality of health services [26, [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] . Also, Lee [58] developed the HEALTHQUAL model based on the SERVQUAL scale. Another model is the PubHosQual (Public Hospital Service Quality) model, developed from a patient perspective [60, 61] . Similarly, the HospitalQual model was derived from the development of SERVPERF. [62] . Researchers have also used multi-criteria decision analysis (MCDA) methods to assess the quality of health services. To identify the most effective criteria for the quality of health services, Büyüközkan et al. [21] used the SERVQUAL scale criteria and evaluated the quality of health services using fuzzy AHP. Also, to find the criteria for hospitals' success in meeting customer expectations for the quality of health services, Shieh et al, [63] used SERVQUAL scale criteria and DEMATEL method to find more effective criteria [63] .

However, most of the measuring service quality models have shortcomings [20] . Brown et al. [64] discussed the problems of measuring the difference between customer expectations and their perception of service performance on the SERVQUAL scale. Also, many shortcomings in the main SERVQUAL scale addressed by Babakus and Boller [65] , including methodological problems and the need to use appropriate criteria for each type of service, and major problems in measuring the difference between expectation and perception of service performance. On the other hand, the data collected for the SERVQUAL scale may be memory-based or intentional, as most of the data is collected after the service is provided [66] . Specialized in hospitals, Reidenbach and Sandifer-Smallwood [55] showed the existence of measurement problems on the SERVQUAL scale. Moreover, service quality expectations may not play a role in the relationship between service quality and other critical measures mentioned in [43] . Similarly, Cronin and Taylor [35] stated that the service quality could be adequately assessed only with the customer's understanding of performance and introduced the SERVPERF model. One of the limitations of SERVQUALderived models such as the PubHosQual model is that these models are designed specifically for the Indian healthcare system and do not include healthcare services' technical aspects [60, 61] . Also, the HospitalQual model's limitation is that it is designed for the in-patient department of Indian hospitals only. Distinctive characteristics of health services such as intangibility, heterogeneity, simultaneity, complex nature, different interests of service providers, and the need to address ethical considerations are barriers to comprehensive quality management methods in health care centers [67] . Zineldin [68] expressed that models for measuring the quality of health services are designed for the Western world and are not necessarily suitable for developing countries; therefore these countries should design appropriate models for their health care systems. It is essential to mention that almost none of the methods and models of evaluating the quality of health services did consider correlation and each criterion's effect on other criteria of the service quality evaluation models, except some MADM methods, including the ANP and DMATEL methods [69] . Also, these models and methods do not consider the reliability and ambiguity in the information received from individuals to evaluate the quality of services. In the real world, uncertainty is an inevitable phenomenon, and most of the information on which the decision-making process is implemented suffers from uncertainty [70] . We also know that since all services contain abstraction, health centers' quality of services is inevitably vague (fuzzy) [71] . Therefore, there is a need for a new approach to assessing the quality of health services which preserve the benefits of previous methods and covers the relevance and effectiveness of criteria and also the reliability and ambiguity of information.

In this study, the Z -number theory, which Zadeh [72] first introduced, is used to cover data reliability. The information that underlies decisions can only be practical when they are reliable. This theory was presented as a general version of the uncertainty for calculating unreliable numbers. This theory, unlike fuzzy theory, considers reliability of numbers [73] . The Z-number concept has been used in many fields, especially in economics, decision analysis, and risk assessment for anticipation and rule-based characterization of imprecise functions and relations [72] . In healthcare, researchers have also benefited from multicriteria decision analysis methods with Z-numbers, including the work of Chen et al. [74] which adopted a new multi-criteria group decision method in the Z-number environment to select a sustainable method for managing healthcare waste. They used Z-number in expert comments and evaluation of their reliability. In one of the recent articles to improve the quality of health services, key indicators that affect the hospital's performance have been identified. In this study, Jiang et al. [75] achieved this goal through an extensive group evaluation method using linguistic Z-number and DEMATEL approach. They used the Znumber theory to comprehensively and flexibly collect decision information and prevent distortion and crucial information loss. Also, Hsu et al. A [76] used a combination of Znumber and DEMATEL to assess the healthcare industry's development. They used Znumbers to optimize ordinary fuzzy numbers and increase expert opinions' reliability.

Another approach to investigate the relationship and ambiguity of factors affecting health services' quality is the fuzzy cognitive mapping (FCM) method. In this study, fuzzy cognitive maps (FCMs) have also been used to cover the ambiguity of service quality and consider [71] . FCMs have been adopted in many research fields; in some applications, the dynamic features and FCM learning methods have been used to model, analyze, and forecast to improve system performance. These applications include engineering, business, medicine, environment, etc. [79] . For instance, researchers have applied evolutionary fuzzy cognitive maps to improve predictive performance, including the prediction of lung infections [80] , the prognosis of prostate cancer, and leukemia in [81] and [82] , respectively. FCMs are also applicable to develop dynamic decision support systems for medical informatics decisionmaking [83] . Amirkhani et al. [84] discussed in detail the applications of FCMs in medicine, health, and treatment.

In this research, a new method is adopted to evaluate health services' quality with a Covid-19 pandemic case study. This method combines the SERVPERF scale and the Z-number Fuzzy Cognitive Map approach. The SERVPERF scale was selected because of the relationships between patient's perception and their satisfaction with services and the effect of patient's satisfaction on their future behaviors [24] . It is noteworthy that SERVPERF requires half of SERVQUAL data [36] , and this reduces the burden of requiring large amounts of data during the Covid-19 pandemic due to the less access to experts. This method's main advantage is determining each criterion's effect on the other (using FCM) and covering the data's reliability (using the concept of Z numbers) [70] . The purpose of this study is to update standards in terms of ranking the criteria for measuring the quality of health services through a Covid-19 pandemic case study. The results of this study can be mentioned to improve the quality of health services, which is vital in two ways: 1) socially: it leads to patient health. Better care for patients means better system performance, and better learning of the treatment staff means professional advancement which supports the patient's safety [85] , 2) economic: leads to patient satisfaction and has a positive effect on the patient's willingness to reuse the services of that hospital [29] and also expands the "word of mouth" marketing [22] . Therefore, the main contributions of this research are as the following:

1-Modifying the healthcare service quality criteria for the pandemic of infectious diseases, 2-Prioritizing the healthcare service quality criteria in the context of the spread of infectious diseases, 3-Proposing an approach based on Z-number theory and FCMs to evaluate the service quality scales by considering the interactions among service quality criteria and uncertainty of experts.

The remainder of this paper is organized as follows. In section 2, the theories and models used in this paper are described. Section 3 discussed the proposed approach. The case study and the results are explained in sections 4 and 5, respectively. Finally, concluding remarks are given in section 6.

The purpose of this study is to evaluate the criteria for measuring the quality of health services by considering the epidemic conditions of infectious diseases, such as the conditions caused by the prevalence of Covid-19. Therefore, the emphasis of service quality criteria provided in the SERVPERF standard is examined by using a combined approach based on Z-number theory and fuzzy cognitive map. First, the SERVPERF scale is discussed, focusing on health services; then, the Z-number theory and the fuzzy cognitive map method will be explained.

The SERVQUAL model measures service quality based on the difference between customer expectation and their perception of service performance [34] . However, in previous studies, several problems were raised to measure the difference between customers' expectations and their perception of service performance [64] [65] [66] . Cronin and Taylor [35] proposed the SERVPERF model to solve the problems of the SERVQUAL model. They believed that customers' expectations of service performance did not reflect "their understanding of service quality"; therefore, they developed the SERVPERF scale based solely on customer perceptions of service performance. The SERVPERF model offers more reliable estimation, better convergence, and discriminant validity, as well as more significant explained variance, and consequently less bias than SERVQUAL [29, 86] . Finally, they concluded that SERVQUAL is not a suitable scale for evaluating service quality and proposed the SERVPERF model. SERVPERF criteria are the same as SERVQUAL criteria, including 22 criteria (measures), divided into five categories: 1) Tangibles, 2) Reliability, 3) Responsiveness, 4) Assurance, and 5) Empathy. Tangibles refer to the equipment, facilities and appearance of the personnel. Reliability is the ability to do the services reliably and correctly. Responsiveness implies the readiness to provide on-time services and help clients. Assurance denotes the knowledge and ability of employees to build trust in customers. Finally, empathy points toward the care and attention to customers. Based on the SERVQUAL scale, these 22 criteria can be answered in two ways, once about expectation and once about perceived performance quality; that means 44 data must be taken from each person. However, for the SERVPERF scale, 22 data per person are required, only in terms of perceived performance. This SERVPERF feature facilitates the data collection process [36] . However, the literature review indicates that the proposed framework and SERVPERF measurement criteria are not always efficient [24] . Accordingly, it may be necessary to remove, modify or add some criteria [23] . In this regard, health services such as services provided in hospitals have been adjusted [26] . Due to differences in health care conditions during infectious epidemics, a new interpretation of some J o u r n a l P r e -p r o o f Journal Pre-proof SERVPERF scale criteria may be required. For this purpose, the SERVPERF scale criteria in health services have been revised, taking into account the epidemic conditions using experts' opinions. A description of these criteria is available in Table 1 (Appendix 1).

Fuzzy logic is a flexible and convenient method to translate and represent the knowledge of experts and verbal expressions in a mathematical manner. Also, fuzzy logic is a valuable method by which ambiguity and uncertainty of data can be dealt with [88] . Fuzzy logic which is based on fuzzy set theory, first proposed by Zadeh [87] . In fuzzy set theory, each component is characterized by a membership function between [0,1]. Therefore, membership function determines the extent that an element belongs to a set [89] . In the following, some definitions of fuzzy sets are explained.

A which is defined in the reference set U .

indicates the extent to which x U  belongs to ' A . Among the fuzzy numbers, triangular fuzzy number (TFN) is used in this study, which is defined as follows:

The TFN is stated as a triple   , , l m u , whose membership function is represented by Equation (2) and Figure (1 Definition 3: linguistic variables are defined as variables that take words and sentences in human or machine languages. Linguistic terms are utilized to express the values of a linguistic variable. For example, when "quality" is considered as a linguistic variable, the terms "low medium," "low," "medium high," and "high" can be used as a set of terms [90] . Linguistic variables can be defined as fuzzy numbers.

Converting fuzzy numbers to crisp numbers is called defuzzification. A defuzzification method combines specific properties of a fuzzy set into a crisp number. There are several defuzzification methods. In this research, the center of gravity (COG) / center of area (COA) method is employed. This method provides a crisp value based on the center of gravity of the fuzzy set [91] . A sample defuzzified fuzzy set is represented in Figure ( 

In the real world, uncertainty is an inevitable phenomenon. Humans have considerable ability to decide rationally based on inexact, inaccurate, or inadequate information. Formulating this ability is a challenge that is almost impossible to overcome. In this regard, Zadeh [72] has introduced a concept called Z-number which is an orderly pair of fuzzy numbers displayed as Z = ( A , B ). Where, A is a fuzzy subset of the X domain and B a fuzzy subset indicating component A 's reliability. A and B are usually described in linguistic terms. For example, A and B for "temperature" can be described as "high" and "completely confident", respectively. (3) and (4) are used to convert the fuzzy set B to a crisp number [73] .

For instance, assume that a fuzzy number corresponding to "Very High" equals (0.65, 0.8, 0.9) and a fuzzy number corresponding to "Medium" equals (0.3, 0.5, 0.7). Also, let Z = ( A , B ) be a Z-number with each of its components equal to A = (Very High) and B = (Medium). Therefore, we have Z = [(0.65, 0.8, 0.9), (0.3,0.5,0.7)]. Equation (3) 

FCMs are a soft computing tool created by combining fuzzy logic, cognitive maps, and neural networks to take advantage of their core benefits [94] . FCM was first introduced by Kosko [92] , which is a way to demonstrate knowledge of systems formed by uncertainties, causal relationships, and complex processes [93, 83] . Each FCM consists of concepts and causal relations between them. In general, concepts represent the system's components or the factors that affect it [78] . In a graphic diagram, each concept is plotted by a node, and a directional arc plots each causal relationship according to Figure 

relationship on the j C concept, ij w , is displayed with an arrow starting at i C and reaching the end of the arrow at j C . FCMs have several advantages, some of which include:

• Application of the model to analyze the scenarios, simulate and measure the impact of resizing each concept on the whole system, and predict the behavior of the system in case of improvement or weakening of other parameters [94] , • A helpful tool for designing knowledge base and modeling complex systems [94] , • Easier construction and parameterization than other knowledge development projects [83] , • No need for experts to quantify causal relationships [77] , • Get more information on the relationships between concepts than traditional maps [59] , • Expressing hidden relationships [59] , • Capable of handling the full range of system feedback structures, including densitydependent effects [83] , • It is dynamic and able to combine and adjust [59] , • Extremely versatile and advantageous based on the involvement degree of the participants [97] .

Each FCM is implemented in three steps, which are:

1. Constructing a network: identifying concepts and causal relationships by experts, 2. Determining each concept's overall effectiveness: experts determine each concept's overall effectiveness with verbal terms, which have corresponding fuzzy numbers.

This attribute is displayed with 0 A . The overall impact rate expresses how each concept affects the entire system, 3. Determining the type and impact rate of one concept on another: Experts also determine the type (in terms of positive or negative) and the extent of the impact of each concept on another one in linguistic terms, which have corresponding fuzzy numbers. This feature is named as weight matrix and is denoted by W . This attribute is a fuzzy number for any concept and after converting to a crisp number, it is a real number that belongs to the range between -1 and 1.

In general, three types of causal relationships are as follows: [96] 1. If 0 ij w  , then criterion i C has a positive impact on criterion j C . In words, by

If 0 ij w  , then criterion i C has a negative impact on criterion j C . In words, by

The fuzzy nature of FCM is only when experts use linguistic terms to determine the vector 0 A and the weight matrix W . In other words, fuzzy operations are not used in implementing the steps of FCM [93] . In this regard, the values in vector 0

are repeatedly updated by equation (5).

where, t i A is the overall effectiveness of concept i C in the iteration t , ji w is the weight of the connection from concept j C to the concept i C in the iteration 1 t  , and N is the number of concepts. The function ( ) f x is a threshold function for converting the results to a number in the range [0, 1] or [-1, 1]. Bueno and Salmeron [98] showed that the sigmoid function, as represented by equation (6), has the best performance among other threshold functions.

In equation (6),  is a real positive number that models the slope of the function. Vector t i A is iteratively updated by equations (5) and (6) until a stopping condition is met [95] . The resulting vector A contains the overall importance of different concepts. In general, there J o u r n a l P r e -p r o o f are two methods for determining the stopping condition of the FCM algorithm: 1) difference between two consecutive vectors is less than a predetermined value, and 2) a predefined number of iterations is performed.

In this section, an approach is presented to update the criteria of healthcare quality standards. In this approach, an attempt has been made to cover some of the shortcomings of healthcare quality assessment models. In this regard, SERVPERF, Z-number, and FCM benefits, which were explained in detail in the first section, have been used. The proposed approach is presented in eleven steps as follows:

Step 1. Select the SERVPERF scale criteria which are suitable for the healthcare services. At this stage, criteria from the original scale may be removed, modified, or added.

Step 2. Obtain initial vector 0 A . In this regard, K experts are asked to determine the overall relative importance of each criterion via a Z-number, Z = ( A , B ). In words, experts give to linguistic terms for each question, one for answer of the question, A , and the other for the reliability of the answer, B .

Step 3. Convert Z-numbers in 0 A to TFNs by using equations (3) and (4).

Step 4. Integrate the expert opinions. In this paper, the Max Mamdani operator [91] is utilized for integrating the TFNs derived from the opinions of experts. Therefore, vector 0 A of K experts are integrated to give a single vector 0 A .

Step 5. Defuzzify TFNs in vector 0 A . At the end of this step, the most important criteria based on 0 A are chosen for obtaining the matrix W and performing the FCM.

Step 6. Obtain the matrix W . In this regard, K experts are asked to determine the impact of the selected criteria in step 5 on each other via Z-numbers.

Step 7. Convert Z-numbers in W to TFNs by using equations (3) and (4).

Step 8. Integrate the expert opinions by the Max Mamdani operator. Therefore, the matrix W of K experts are integrated to give a single matrix W .

J o u r n a l P r e -p r o o f

Step 9. Defuzzify TFNs in matrix W .

Step 10. Use the defuzzified 0 A and W to perform the FCM. The FCM repeatedly updates the values in vector 0 A to find the overall importance of healthcare service quality criteria.

These steps are schematically presented in Figure (4) . 

In this study, the SERVPERF scale criteria are adjusted to investigate hospitals' special conditions during the Covid-19 pandemic crisis. In this regard, the 22 criteria which had been adapted for the hospital by Gilbert et al. [26] and finally reached 15 criteria, were reviewed. To this end, two experts were interviewed: the supervisors of patients with Covid-19, each with 25 years of work experience in different hospitals. The classification of research criteria of Shieh et al. [63] and Büyüközkan et al. [21] , who evaluated health services using MCDA methods, were also used for the defined conditions. Finally, using the results of our expert interviews, considering [21] and [63] researches, some performance [26] and technical [99] criteria were added to the modified SERVPERF scale criteria. We also revised some of the criteria to adapt the healthcare conditions. The Table 1 (Appendix 1) . After determining the criteria, experts answered questions during a questionnaire. The experts included three experienced physicians working with the care of patients with Covid-19 patients. In this questionnaire, two sets of questions were asked of the experts by applying a particular assumption.

Assumption: All criteria are in their ideal state during the Covid-19 pandemic and not in experts' workplaces. Table ( 2) and Figure (5) [83] , and to answer Part B as described in Table  ( 3) [73] . For instance, one of the expert questionnaires is collected for the first question according to After collecting data through a questionnaire, Z-numbers were converted to TFNs using equations (3) and (4). All conversions are given in Table (5) according to the values in  Tables (2) and (3). Expert opinions were then merged using the Max Mamdani operator. After this step, a vector of 0 A was obtained from the opinions of all three experts. In the next step, TFNs were converted to crisp numbers using the COG / COA non-fuzzy method. At the end of this step, by comparing the scores obtained for each of the criteria in the vector 0 A , the criteria that have a higher priority are identified. With the identification of the most priority criteria, the second question is entitled [77] , and to answer component B as described in Table ( 3), [73] . Experts are asked through a questionnaire. After collecting data through a questionnaire, Znumbers were converted to TFNs using equations (3) and (4). All conversions are given in Table (7) according to the values in Tables (3) and (6) . Expert opinions were then merged using the Max Mamdani operator. After this step, a matrix of W was obtained from the opinions of all three experts. In the next step, TFNs were converted to crisp numbers using the COG / COA non-fuzzy method. At the end of this step, FCM is utilized to determine the J o u r n a l P r e -p r o o f most important criteria for the quality of healthcare services. In this research, FCMExpert [93] software is used for the implementation of FCM. J o u r n a l P r e -p r o o f

The experts' general opinion regarding the importance of the criteria in the context of the outbreak of the Covid-19 virus led to the initial prioritization of the criteria (primary vector 0 A ), as shown in Table ( 8) . Based on the results, it seems that the prioritization of the criteria is quite reasonable. 

This section examines the relationship between the challenges encountered in the Covid-19 pandemic situation and the criteria that have the highest priority, according to Table (8) . The difficulties of triage management and scarce resource management [13] , protecting front-line healthcare staff and preventing nosocomial infections [16, 17, 18] , as well as the challenge of scarcity of personal protective equipment is associated with the priority of the C1 criterion (up-to-date equipment and facilities). Also, the challenge of predicting the increase in hospital readiness and increasing the need for treatment staff and the challenge of shortage of refreshed treatment staff [13, 15] mentions the priority of the C15 criterion (sufficient number of staff in proportion to the number of patients). The challenge of preventing nosocomial infections, the logistical challenge and the transfer of infected people to separate them from other clients, as well as the logistics and transfer of other patients for radiology and surgical examinations [16, 17, 18] and the challenge of infectious and hazardous waste management is relevant to prioritizing C4 (Hospital J o u r n a l P r e -p r o o f hygiene). It also seemed that the challenges of protecting healthcare personnel at the forefront and preventing nosocomial infections and the lack of personal protective equipment mentioned earlier, lack of freshman treatment staff, the physical and psychological stress of dealing with a pandemic, intensity of workload and lack of repose, and ultimately need for training and awareness of healthcare professionals to prevent and control respiratory infections, all influence prioritizing of the C20 index (adequate hospital support from employees, so that employees can do their job well).

Regarding the priority of the C21 criterion (unique attention from hospital staff), experts said in an interview that hospital staff's complete attention has a significant impact on improving the patient's condition and even saving their life. Correctly diagnosing Covid-19 and the need for training and awareness of health professionals (other than infectious disease physicians) on ways to prevent and control respiratory infections [17, 18] has led to the importance of C9 criteria (the reliability of the hospital) and C11 (accuracy) and C18 (reliability of the hospital staff in terms of their knowledge). Regarding prioritizing the C14 criterion (the constant desire of hospital staff to help the patient), experts also said in an interview that the hospital staff's constant willingness to help the patient has a significant effect on accelerating the patient's recovery. Finally, the challenge of logistics and transfer of infected for separation from other clients and the logistics and transfer of other patients for radiology and surgical examinations led to the importance of C16 (completeness) and C5 (building layout). As illustrated, 12 of the independent criteria for measuring the quality of health services challenged in the Covid-19 pandemic are among the first to sixth priorities in the initial prioritization. In these critical situations, the provision of services that satisfies the customer becomes more critical, which means that the dependent C25 criterion of overall customer satisfaction has also been challenged. However, the initial prioritization for the high priority criteria in Table (8) is without considering the causal relationships between these 12 criteria. The causal relationships between these 12 criteria are illustrated in Figure (7) . The W matrix, which represents the causal relationships' values between these criteria, is given in Table (9). J o u r n a l P r e -p r o o f Also, Figure (7) shows the cognitive map related to these 12 criteria plus the concept of patient satisfaction. In this cognitive map, each concept is proportional to its corresponding value in the initial prioritization of criteria (initial state vector 0 A ) and the magnitude of the causal relationship between i C on j C and ij w on the arc that starts from the concept i and ends with the tip of the arrow to concept j, which is displayed with a number between 1 and -1. Accordingly, the density of causal relationships in Figure (7) is very high, so there is a need for a new prioritization that addresses these causal relationships. In this research, the FCM algorithm has been implemented to achieve this new prioritization. With this algorithm's implementation, the initial prioritization of the criteria (initial state vector 0 A ) has reached convergence after five iterations. The process of convergence to an equilibrium is illustrated in Figure (8) . The values of the concepts in each iteration are also shown in Table ( 10) . In this Table, zero is the same as the original state vector 0 A . The stop criterion for running the FCM algorithm was to reach a specific convergence point with an accuracy of 0.001. The slope of the threshold function was considered 0.5 to specify 12 criteria in exactly 12 prioritizations. Table ( 11) , the criteria's prioritization has changed significantly after the causal relationship between them has been applied. This change is due to the causal relationships between the criteria. Considering the dependent criterion C25 (overall patient satisfaction) scored the highest, this illustrates that the high-ranked criteria strongly influence patient satisfaction. Therefore, to increase the patient's understanding of hospital health services and satisfaction, the prioritization results of Table (11) should be invested in, respectively.

Investing in healthcare quality metrics based on new prioritization has a more significant impact on increasing patient perceptions of healthcare quality. This new prioritization comprises the causal relationships between these 12 challenging criteria. A comparison of the two prioritizations before and after causal relationships is given in Table (12). J o u r n a l P r e -p r o o f As it figured in Table 12 , before applying the causal relationship, the C1 criterion, which indicated that the hospital was equipped with up-to-date equipment, was a top priority. But after using causal relationships, C9, which shows the reliability of the hospital, is the first one. This means that improving C9 will be more effective than enhancing C1 to increase patients' perception of health service quality and satisfaction. Similarly, the priority of other criteria is determined by considering the causal relationships between them. Also, the application of the proposed method has led to a better distinction of ranking criteria.

This section will introduce the essential criteria of each category for measuring the quality of health services based on prioritization after applying causal relationships. According to Table ( 13), improving C4 (hospital hygiene) will be the most effective investment to increase patients' perception of health services in the tangible area. Improving C9 (hospital reliability) will be the most effective investment to increase patient's perception of health services in reliability. Improving C16 (completeness) will also be the most effective investment in increasing patient responsiveness to health services. Improving C20 (adequate hospital support for staff to do their job well) will be the most effective investment to increase the patient's understanding of health care. Finally, improving C21

J o u r n a l P r e -p r o o f (unique attention from hospital staff) will be the most effective investment to increase patient empathy in healthcare. Table 13 . Initial prioritization and prioritization evaluation after causal relationships (FCM implementation) in five categories of healthcare quality assessment criteria.

As shown in Table ( 13) , by calculating the average ratios of each category, the categories can also be ranked. Figure (9 .a) shows the ranking of categories based on average ratios before and after applying causal relations. After applying causal relationships, the Reliability category with the highest average ratio is ranked first, Responsiveness is ranked second, Tangible is ranked third, and Empathy and Assurance are ranked fourth and fifth, respectively. In this way, when constraints force the hospital to invest in one or two categories, it is possible to select the most effective categories. The details of category ranking, namely the ratio of each criterion before and after the causal relationships, are given in Figure (9 Details of the criteria ratios can be seen before and after the causal relationships in Figure  11 . In other words, the opinions of individual experts and the integrated opinion of experts are presented in Figure 11 . Expert opinions are given in the first three columns for each criterion. In the fourth and fifth columns, their final merged views are shown before and after the FCM, respectively. As can be seen, in most cases, the opinions of experts are similar. Also, the green column, is higher in all criteria than all other columns, which indicates the effect of causal relationships on increasing ratios and changing the prioritization of criteria.

J o u r n a l P r e -p r o o f Figure 11 . The ratios resulted from the opinions of experts

In the Covid-19 pandemic, hospitals should pay attention to the needs and expectations of patients under the existing conditions and challenges and improve the quality of their services to satisfy the patient. Using the updated SERVPERF relatively following the current conditions and challenges and benefiting from the FCM algorithm can be one of the practices to identify the criteria that need improvement. According to the results of this study, to increase the patient's understanding of the quality of health services and to satisfy its needs, hospitals should meet the criteria and invest in the criteria of C9 (hospital reliability), C4 (hospital hygiene), C16 (completeness), C1 (up-to-date equipment and facilities), C11 (accuracy) and then on other criteria in the order of Table ( 11) , to make the most effective choice despite the limited resources.

As hospitals faced several challenges during the COVID-19 pandemic, the quality of hospital healthcare declined sharply. Addressing the quality of healthcare in a pandemic is essential in two ways. First, human health and lives are at stake, and it is necessary to provide more reliable services at this time [21] . Second, in a pandemic situation where the number of patients referred to hospitals is much higher than before, the patient's inferior perception of health services leads to severe patient dissatisfaction with the services provided [20] . However, all health care quality standards have been designed and applied to normal conditions. In previous studies that have mainly dealt with the SERVQUAL and SERVPERF measures, the interaction of the criteria of these standards has not been considered in the analysis. Therefore, in this study, the importance of effective criteria in the quality of health services in hospitals in the spread of infectious diseases was evaluated by considering the interactions they can have on each other. This study aimed to identify the most important criteria for measuring the quality of health services in pandemic conditions of diseases such as Covid-19. Limited resources and critical circumstances require that the criteria, which are chosen to improve healthcare quality, be selected more intelligently. Therefore, in this study, using the Z-Numbers and FCM algorithm, we evaluated the causal relationships between the criteria of health services by adopting the SERVPERF standard to identify the most critical criteria in the outbreak of infectious diseases. For this purpose, the opinions of experts were collected and evaluated. The results of this study indicate that the criteria by which healthcare service quality can be evaluated, have casual relationships. The outputs clearly represent that the weights of criteria increase after the implementation of FCM. Also, the ratio of overall satisfaction from the healthcare services significantly increase after implementing the FCM. To this end, the importance of these criteria should be evaluated considering their interactions. In this regard, to improve the quality of health services more effectively during the pandemic, the following criteria should respectively receive more attention from the healthcare system: 1) hospital reliability, 2) hospital hygiene, and completeness, 3) equipping the hospital with up-to-date equipment, 4) accuracy, and constant desire of hospital staff to help the patient, 5) adequate physical facilities, 6) sufficient and appropriate proportion of medical staff to the number of patients, 7) unique attention from hospital staff, 8) adequate hospital support for staff to do their job well, 9) reliability of hospital staff in terms of knowledge, and finally 10) the facility layout of the building. On the other hand, reliability of healthcare system is the most important category of service quality criteria. Similarly, responsiveness, tangible, empathy, and assurance are respectively the other categories that should gain attention. The results of this study can be helpful to adopt better health care strategies and policies that lead to an increase in the quality of services in hospitals in pandemic conditions.

J o u r n a l P r e -p r o o f Appendix 1: support for staff so that staff can do their job well sufficient, they can take leave and will not have to work overtime, so they will perform better during their normal working hours; Because they had enough time to rest and recover .

-Psychological and psychological support of employees .

-Support for quality of Coronavirus protective equipment for staff . J o u r n a l P r e -p r o o f

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