The measurement of the quality of health care services can be important from the perspective of different stakeholders: the view of service providers with goals such as promoting profitability, the viewpoint of social health insurance aiming to minimize costs and the patient-oriented view with the main focus on health service recipients with goals such as satisfaction with the services received and improving health. But it seems that high quality services can cover the goals of all stakeholders at the same time. Providing appropriate and high-quality health care services prevents unnecessary patient referrals and consequently additional costs (Sharifi et al., 2021). Also, previous studies have confirmed the direct relationship between the quality of health care services with increasing profitability and market share of service providers in a competitive environment (Naidu, 2009; Meesala and Paul, 2018; Altuntas and Kansu, 2019).

An organization providing health care services (such as a hospital) needs accurate knowledge of patient satisfaction as an integral part of the quality of health care services (Pekkaya et al., 2019; Altuntas and Kansu, 2019). This is because increasing patients’ satisfaction with health care services by increasing the quality of services received, leads to several achievements such as improving their loyalty (Fatima et al., 2018; Meesala and Paul, 2018) and competitiveness of hospitals, etc. (Chen and Yeh, 2015).

Understanding what factors can affect patients’ perceptions of the quality of services they receive is of considerable importance not only to patients; but also, to service providers, governments, and other stakeholders (Li and He, 2020). As health care providers prepare themselves to face the challenges of the Industrial Revolution 4.0, patient oriented, value driven, health care quality management plans should include efforts to identify and satisfy patients’ needs and preferences (Rahim et al., 2021).

Due to this importance, one of the issues of previous research has been to identify and determine the factors affecting the quality of health care services in order to be able to consider the appropriate criteria for determining, controlling and improving the quality of services. However, there have been limited studies in the field of patients’ perceptions of service quality dimensions (Gill and White, 2009).

Given the importance of health care quality, to date we have seen numerous studies and researches that have sought to introduce dimensions and indicators affecting the quality of health care services (Li and He, 2020). In general, health care quality assessment items are used and studied differently according to the views of researchers because there are no standard measurement items (Lee, 2017). Vouri (1982) introduced efficiency, effectiveness, accuracy and quality improvement of scientific-technical competencies as important factors in the quality of health care services (Lee, 2017). Donabedian (1988) introduces the dimensions affecting the quality of healthcare services including structure, process and results. According to the model of Grönroos (1984), patients evaluate the quality of health care services based on two dimensions: technical quality (result of received services) and functional quality (manner and process of received services). Carman (1990) presented tangibles, reliability, safety, empathy, convenience, and cost as items to measure health care service quality. Scobie et al. (2006) also presented health care service quality in the following six dimensions: tangibles, accessibility, timeliness, efficient costs, values, policy, and implementation to improve quality, understanding the expected value of patients, and capabilities of the service provider. Otani et al. (2009) considered the dimensions affecting the quality of health care services as admission process, staff care, nursing care, physician care, food and room. Lee (2017), by focusing on health care processes and results, attempted to measure health care service quality through tangibles, empathy, efficiency, safety, and degree of improvements of health care service. Li and He (2020) categorized the health care service quality assessment into six main dimensions including tangibles, responsiveness, professional competence, professional capability, reliability, and administrative policy.

However, over the years, the most famous and practical model of health care service quality on which other models have been presented is the service quality gap model called SERVQUAL, proposed by Parasuraman et al. (1985, 1988), an instrument with 5 main dimensions for measuring the quality of services from the customer’s perspective. It should be noted that its dimensions have been various in different models and it has been used mostly in the form of four-dimensional, five-dimensional and six-dimensional categories (Li and He, 2020). This model has been extensively studied in recent years in various service areas such as the quality of health care services. This has led to the formation of a version of the SERVQUAL model called HealthQual. HealthQual is a multidimensional scale that measures the quality of health care services from the patient’s point of view (Sharifi et al., 2021; Asiamah et al., 2021; Nemati et al., 2020; Ampaw et al., 2020; Lee, 2017).

Based on the HealthQual model for health care service quality evaluation, patients measure their satisfaction with the quality of services received, based on 5 main dimensions. Empathy (refers to understanding patients’ problems by staff and trying to meet them, paying attention to each patients, assurance (is concerned with reassuring and polite behaviour of hospital staff towards patients, existence of staff with the necessary ability and qualification to answer patients’ questions, safe hospital equipment), responsiveness (entails willingness of hospital staff to help patients, respond to their requests, informing them of the methods of complaining about the services received and providing fast services), reliability (is concerned with provision of accurate and error-free services by hospitals to patients at the promised time), and tangibles (encompasses physical facilities, equipment and appearance of hospital staffs).

The results of the majority of previous studies confirm the validity of HealthQual model for evaluating the quality of health care services (Sharifi et al., 2021; Asiamah et al., 2021). In addition, a look at the quality standards of health care services in developed countries shows that in the service quality indicators of these countries, the dimensions of the HealthQual model have been significantly emphasized and this has increased the acceptance of this model. The dimensions of empathy, reliability and tangible factors are in accordance with the American JCI standard, reliability and tangible factors are in accordance with the Australian ACHSI standard and tangible factors are in accordance with the Canadian ACI standard (Lee, 2017).

Despite all the advantages and practicality of the SERVQUAL model in evaluating service quality in previous research, some researchers have criticized it both conceptually and paradigmatically (Coulthard, 2004). According to the three-dimensional model of Donabedian (1988), the quality of health care services should be evaluated taking into account three aspects: structure, process and result. In SERVQUAL model, the focus is more on the structure and process of providing service instead of service quality results. Other issues that have been expressed in the critique of this model are concerns about how customers evaluate the quality of service in terms of expectations and perceptions, as well as the dimensions and universality of the five dimensions of SERVQUAL (Buttle, 1996). Lucadamo et al. (2021) argued that assessing health care patients’ expectations is a challenging issue; SERVQUAL is not appropriate and should be modified.

The provision of high-quality health care is an important issue, since its direct consequences are relief to suffering and improved health status in humans (Bowers and Kiefe, 2002). For the success of health care institutions and hospitals, accurate assessment of health care service quality is as important as understanding the constitution of the service delivery system (Büyüközkan et al., 2011).

Based on the literature, a number of methods have been developed to evaluate the quality of health care services. Fundamentally, they can be categorized into two basic groups: Stated Importance Methods (SIMs) and Derived Importance Methods (DIMs) (Grigoroudis and Spyridaki, 2003). In the first approach (SIM), customers are asked to complete detailed questionnaires (both expectations and perceptions on the key aspects of service quality) (Lupo, 2016). In SIMs, the perception and expectation of a customer is measured based on linguistic-numerical Likert type scales, which are simple to use, but need a significant enhance in the length of survey and can sometimes make an inadequate difference in ranks of the service dimensions (Tsai et al., 2011; Lupo, 2015; Pamucar et al., 2021). As a result, the customers’ self-expressed importance does not sufficiently measure the true relative importance of attributes (Deng and Pei, 2009).

In the DIM approach, relatively simple questionnaires are provided to customers and they only have to provide perceptions on service quality aspects along with the overall satisfaction degree of quality (Lupo, 2016). With this approach, the rating of expectations on service dimensions is statistically obtained by considering the relationships between performance in service aspects and overall customer satisfaction (Pandey, 2016). After conducting such surveys, there are several alternatives to examine satisfaction. These alternatives can be considered as structural equation modelling, factor analysis, multiple/logistic regressions, and the so-called Multicriteria Satisfaction Analysis (MUSA) (Deng and Pei, 2009; Ferreira et al., 2021). DIMs allow the recognition of underlying dimensions of quality and their relationship to overall distinguished quality or customer satisfaction, however they depend on a set of restrictions-normal data, linear relationships, multi-co-linearity, which diminishes the guarantee of generalization (Tsai et al., 2011). Hence, the implicit importance values of attributes determined through statistical approaches are biased and misleading (Deng and Pei, 2009).

Lately, multi-criteria decision making (MCDM) models are growingly considered in the literature to address these weaknesses (Tsai et al., 2011; Lupo, 2016; Pandey, 2016). MCDM methods are on the basis of some general principle that customers’ attitudes toward certain services depend on their evaluation of service aspects based on the importance given to them (Lupo, 2016). In this method, on the one hand, there is no need to use the Likert scale to calculate weights, and instead, pairwise comparison approaches or standard scales are used, and on the other hand, there is no necessity to use large volumes of data and observe common assumptions in statistical methods. Due to these advantages, these methods have been considered in the field of evaluating the quality of hospitals and health services by some researchers in recent years. Table 1 shows the most important studies conducted in this area.

Based on the information provided in this table, the following points can be summarized.

First, review of the literature indicates that several dimensions and criteria affect the quality of health care services, and this has made the issue of measuring their quality a complex and multi-criteria issue (La Fata et al., 2019).

The differences in the dimensions and criteria considered in different researches indicate the need to localize the health care service quality measurement model in accordance with the studied conditions and related features. However, the framework that is appropriate for Iran and, in particular, the case under study was not determined.

Second, in most researches, the weight/importance is calculated using common multi-criteria decision-making methods such as AHP and ANP and based on pairwise comparisons between service aspects from customers’ point of view. These pairwise comparisons, on the one hand, allow the calculation of actual relative importance of attributes, and on the other hand, due to the use of standard scales, eliminate the problems related to Likert scale and ordinal data. However, one of the main problems of these two methods is the need for a high number of pairwise comparisons; so that if there are n criteria, the number of pairwise comparisons should be n ( n − 1 ) / 2 (Rezaie, 2015). Since the number of dimensions and criteria used in the field of quality assessment of health services is generally high, the time consumption and the possibility of inconsistencies in the evaluation process reduce the possibility of implementing these methods. The SWARA method presented by Keršuliene et al. (2010) uses the advantages of pairwise comparisons between factors. Also, because after ranking the criteria, each criterion is only compared with the previous criterion, fewer comparisons are required, and therefore this method is more efficient and effective in practice (Dahooie et al., 2020).

Third, a review of previous research trends shows that the use of definite numbers has gradually diminished in this area (Mardani et al., 2019). In most researches, evaluations related to assessment of service aspects have been done in the form of linguistic variables and then using theories such as fuzzy, these variables have been converted into interval-valued information that have their own special computational operators. The reason for this should be sought in the fact that most researchers have used the linguistic variables or Likert scale to measure the quality of health care services and summarize the opinions of a large number of people and then convert them into definite numbers. However, linguistic variables have been criticized by researchers due to the influence of factors such as subjectivism, judgments, selection and priority of evaluators on the final results in the field of quality evaluation of health care services (Afkham et al., 2012; Lupo, 2016; Li and He, 2020). In other words, the linguistic variables are imprecise and have imperfect knowledge of data and fuzziness (Singh and Prasher, 2019). Fuzzy number theory, on the other hand, makes it possible to take uncertainty and imperfect knowledge of data into account in the decision-making process of experts and can be well applied to perform calculations in cases where linguistic variables are used (Akdag et al., 2014).

Despite the mentioned features, literature review shows the low share of fuzzy MADM methods in the studies based on service quality evaluation models (Yucesan and Gul, 2020). Also, few decision-making methods have been used by researchers in this field (Mardani et al., 2019). However, new methods have been proposed in the field of MADM methods, each of which has its own advantages and features (Dahooie et al., 2019). Numerous studies in the field of fuzzy numbers also show that this set of numbers also has several shortcomings under real-world conditions. This has led to developments such as type-n fuzzy sets, hesitant fuzzy numbers, etc. (Dahooie et al., 2020). One of these most important shortcomings occurs in determining the exact value of the upper and lower bounds of the membership function in a set of traditional fuzzy numbers which led to the introduction of interval-valued fuzzy numbers by Gorzałczany (1987). This challenge is especially important in cases where the evaluation is done qualitatively and in the form of linguistic variables (Gorzałczany, 1987). Therefore, in view of what has been described before, special attention should be paid in the field of service quality evaluation.

Fuzzy number set theory was first proposed by Zadeh (1965) to deal with vague and ambiguous information in the decision-making process (Liu et al., 2021). Type-1 fuzzy set developed by Zadeh (1965) considers a crisp number in the range of 0 to 1 for the membership value. The exact membership function of a fuzzy set is not easily obtained in some conditions. In these cases, type-1 fuzzy sets do not work efficiently for linguistic assessment (Ghorabaee et al., 2016). This led to several developments in this theory and the formation of type-n fuzzy sets, hesitant fuzzy numbers, etc. (Dahooie et al., 2020). The interval-valued fuzzy numbers introduced by Gorzałczany (1987) have eliminated the shortcomings of the traditional fuzzy approach in determining the exact value of the upper and lower bounds of the membership function (Vahdani et al., 2014). This is especially important in cases where assessment is conducted qualitatively and in terms of linguistic variables (Gorzałczany, 1987).

Like other types of generalized fuzzy numbers, interval-valued fuzzy numbers can be triangular or trapezoidal numbers. Interval-valued triangular fuzzy numbers ( A ˜) (IVTFN) in general are represented as follows (Fig. 2): (1) A ˜ = [ A ˜ L , A ˜ U ] = [ ( a l ′ , a m ′ , a u ′ ; ω A ′ ) , ( a l , a m , a u ; ω A ) ] .

In the above relation, A ˜ L and A ˜ U represent the lower and upper triangular fuzzy numbers, respectively, A ˜ L ⊂ A ˜ U ; μ A ˜ ( x ) is the membership function and represents the degree to which an event may be a member of A ˜ ; μ A ˜ L ( x ) = ω A ′ and μ A ˜ U ( x ) = ω A , which are lower and upper membership functions, respectively. In a special case if ω A ′ = ω A = 1, then these numbers are converted into normalized interval-valued triangular fuzzy numbers (Fig. 3) and are represented as the following relation: (2) A ˜ = [ A ˜ L , A ˜ U ] = [ ( a l , a l ′ ) , a m , ( a u ′ , a u ) ] .

Further details on these numbers and their related algebraic operations are provided in Dahooie et al. (2020), Mohammadian et al. (2021).

In the context of MADM approaches, various methods have been provided to determine the criteria weights (Liu and Li, 2021). However, many of them are not only complicated, they are also not accurate enough. Hence, Keršuliene et al. (2010), introduced the SWARA method, a relatively less complex approach (Karabasevic et al., 2016). This method is user-friendly, less complicated and less time consuming. It also gives decision makers the opportunity to choose and assess the criteria and set their weights, while enabling experts to use their knowledge and experience in the research area (Hashemkhani Zolfani et al., 2018; Kumar et al., 2022). The initial version of this method was not efficient in the face of situations where decision makers’ information is unreliable and incomplete. Stević et al. (2022) discussed the use of the fuzzy SWARA method and proposed an improved approach to address the criticisms of this method. Considering the points raised about IVTFN numbers (eliminating the shortcomings of the traditional fuzzy approach in determining the exact value of the upper and lower bounds of the membership function), the development of this method based on this IVTFN numbers has been considered in this research. Details on how to calculate are provided in Dahooie et al. (2020, 2022), so here is just a summary of the steps.

The scale of linguistic variables used in this study to calculate the weight of the criteria is presented in Table 2.

Among the MADM methods that have been developed with the aim of ranking and evaluating the alternatives, the ARAS (Additive Ratio Assessment) method (Zavadskas and Turskis, 2010) has had a growing trend since 2010 due to advantages such as ease of implementation and comprehensibility, the possibility of determining the utility degree of each alternative compared to the optimal alternative (Pareto optimal solution) and rank reversal resistant (Liu and Xu, 2021). Given the benefits of IVTFNs, an extended version of ARAS-IVTFN is considered in this study. A summary of the steps is provided below (read more in Dahooie et al., 2018, 2022).

The scale of the linguistic variables used in this study for scoring alternatives and final ranking is presented in Table 3.

As described in the previous sections, in this study, first, the standard SERVEQUAL model was considered as the basis of the work. Thus, the 5 main dimensions presented by Parasuraman et al. (1985, 1988) were selected which have been considered in most articles. Then, based on the standard definitions of these dimensions and considering the articles that used this model in the field of health services, an attempt was made to determine the initial list of sub-dimensions. At the end, the list was provided to committee members and two experienced professors in the form of Delphi process. Finally, after four rounds, this model was localized in the form of 5 main dimensions and 23 sub-dimension. The final dimensions and sub-criteria are shown in Table 4.

As mentioned in the research steps section, in the first step, the importance and weight of each of the criteria and sub-criteria of the HealthQual model have been calculated using the SWARA-IVTFN method. For this purpose, first the weights of the main criteria and then the weights of the sub-criteria were calculated and then the weight of the criteria was multiplied by the weight of the sub-criteria to obtain the final weight of each of the sub-criteria. The results of the developed SWARA method based on interval-valued triangular fuzzy numbers for the first team are shown in Table 5. As shown in the third column of this table, the team representative is asked to sort the criteria in descending order of importance. In the following, calculations have been made based on the steps of the developed SWARA-IVTFN method. The results of the second, third (equation (3)), fourth (equation (4)) and fifth (equation (5)) step are given in the next columns of this table, respectively.

Then, in order to calculate the final weight of the criteria, the geometric means of the weights for all three teams were obtained and then normalized. The final results are shown in Table 6. In this table, the first column shows the final weights of the first team, which is presented in the last column of Table 5. Note, however, that the data in Table 5 are entered based on the priority of the criteria, and therefore some values have been substituted with each other to transfer to Table 6. The next two columns are the results of the weights for the other two teams (which are not presented in the text due to space constraints). The final column is the weights obtained from the geometric average weight of three different teams.

In order to create a suitable basis for display and analysis, the final values of the weights were calculated based on equation (6), the results of which are presented in Fig. 4.

Finally, the results of calculating the weight of the criteria were provided to the committee members and approved by them.

As mentioned, although the main purpose of this article is to provide a framework for evaluating the quality of health services, it can also be used to rank hospitals and health centres. To show how it works in this area, an attempt was made to prioritize ten hospitals using the ARAS-IVTFN method.

According to the steps described in the research methodology, each of the selected teams presented their evaluation for each of the ten subordinate hospitals (H1–H10) based on the criteria of the final model in terms of linguistic variables presented in Table 3. Table 7 presents the evaluation of each hospital based on the identified criteria.