Evaluating the Quality of Medical Services Using Intuitionistic Hesitant Fuzzy Aczel–Alsina Aggregation Information

. In modern civilization, individuals are increasingly concerned with evaluating the quality of medical services. Evaluation of the quality of medical services enables medical care providers to monitor and improve their service quality. Te evaluation of medical service quality is efciently addressed by the novel concept of Aczel–Alsina operators in an intuitionistic hesitant fuzzy (IHF) environment as multicriteria decision-making (MCDM) problem. Tus, this paper presents the IHF Aczel–Alsina weighted geometric operators for IHF information. We frst apply the Aczel–Alsina norms to IHF scenarios and present novel operations of intuitionistic hesitant fuzzy sets. Tis article develops a unique strategy for evaluating the quality of medical services based on the specifed operators, including a quantitative framework for evaluating medical service quality and a novel MCDM technique. Finally, this article presents a numerical example of the novel approach used to evaluate medical services for hospitals and compares it to conventional MCDM methods to highlight the suggested superiority method. According to the comparative results, our strategy outperforms the insufciency of lacking decision fexibility in the existing MAGDM method.


Introduction
In light of the signifcant development of medical services and the healthcare industry, the society is becoming more concerned about the quality of medical treatment and urging companies to enhance quality [1]. Additionally, the World Health Organization declared in 2000 that assessing a medical service provider's quality has been a worldwide problem [2]. Healthcare practitioners need an appropriate and efective approach for evaluating the quality of healthcare services in order to monitor and enhance the quality of medical services they provide. If patients want to receive better healthcare, they should evaluate various hospitals using a variety of factors in order to choose the best option. Numerous researchers have devoted to studies on the assessment of medical service quality on the basis of this framework. For example, Shieh [3] utilised the DEMATEL approach to identify the essential aspects in the quality of medical services, such as the atmosphere, registration system, and appearance. Mccarthy [4] classifed medical service quality like respect and care, effectiveness and continuity, suitability, and communication, efciency, meals, initial impression, and staf versatility. By combining the work of the previous researchers, Fei et al. [5] presented a set of medical quality assessment.
Te method of employing expert assessment data to analyse, rank, and select the best solutions using a specifc decision-making (DM) approach is known as multiattribute group decision making (MAGDM) [6][7][8]. Giving pertinent information is a necessary step in the decision-making process, as it is selecting one DM technique over others. As it is impossible to anticipate the future and because specialists' knowledge is limited, improving the MADM technique has become a hot topic in today's DM feld [9][10][11]. While analysing data, the uncertainty and incompleteness are always an issue. For instance, according to the idea of hard sets, an item either belongs to or does not belong to a particular class. However, many things in the real world could not be described in such detail [12,13].
Since the assessment problem of medical service quality is related to many factors and the evaluation fnding is the foundation of decision making (DM) on the selection of medical service provider, it may be regarded as a multiattribute decision-making (MADM) problem [14,15]. MADM refers to the process of assessing, classifying, and choosing the best options from a set of decision support data and a set of decision support models. Te most crucial parts of making a decision are specialists' knowledge and the choice of applicable decision assistance approaches. Expertise and the complexity of society have necessitated that the expansion and refnement of the MADM technique are better decisions in decision supporting difculties. In the DM process, there is inconsistency and uncertainty, and Zadeh's [16] idea of fuzzy sets (FSs) provides a highly effective technique to deal with these challenges. Following that, intuitionistic FSs (IFSs) [17] were developed, which used +ve and − ve membership grades to express uncertainty in decision-making processes. When presented with a DM issue, decision makers began to employ IF numbers to indicate their ranking for various choices. As a result, an increasing number of researchers are getting interested in IF data [18][19][20].
To compile the information gathered from the specialists, we will need to use some aggregation operators (Agop). Some Agops, such as the IF averaging operator, were created by Xu [21]. Some Einstein Agops, such as IFE averaging/ geometric operators, were introduced by Wang and Liu [22]. Yu and Xu [23] created a prioritised list of Agops and explored how they could be used to solve DM issues. Liu and Wang [24] used a linguistic IF technique to create several innovative Agops and an algorithm to solve complex uncertain DM situations. Xu and Yager [25] established the decision-making technique using Bonferroni means Agop under IF data.
On the basis of prioritised IF Agop under linguistic data set, Arora and Garg [26] constructed the group DMA. Zhao et al. [27] examined the uses of generalised IF Agops, such as the generalised IF averaing/geometric operators, to deal with uncertainty in Dcmp. Yu [28] demonstrated certain IF Agops depending on confdence levels and solved challenging realworld Dcmps. Yu [29] created the IF Agop and discussed its usefulness in decision making using Heronian mean. Jiang et al. [30] devised a decision-making strategy based on the IF power Agop and the entropy measure. Senapati et al. [31] developed an Aczel-Alsina (Acz-Aln) norm based on some IF Acz-Aln Agops and applied it to the IF MADM process [32]. Khan et al. [33] created new generalised IF soft details Agops and investigated their use in DM.
T-norms and t-conorms (e.g., Algebaric t-norm and tconorm, Einstein t-norm and t-conorm, Hamacher tnorm and t-conorm) are well-known as essential operations in FSs and other fuzzy systems [34]. Aczel and Alsina established the Acz-Aln t-norm and Acz-Aln t-conorm operations, which ofer the beneft of parameter adaptability [35]. Te goal of this research is to propose the Acz-Aln t-norm and t-conorm operations, as well as a list of new Agop, in an IHF context, and to develop a MAGDM strategy to solve the favoured ranking of alternatives in MADM utilising these operators. Assessing the quality of medical services as an MCDM challenge is an efective way to equip medical practitioners with a reasonable appraisal. We provide a novel Acz-Aln Agopbased approach for evaluating medical services. Finally, we demonstrate the supremacy of our technique by providing a numerical example and a comparison to the existing approaches. Depending on the outcomes, we can assist governments on how to improve the quality of medical care providers.

Motivation and Gap of Study.
Te literature had a large number of AOs based on t-norm (TN) and t-conorm (TCN). Uninorms were frst introduced to the FS theory by Deschrijver and Kerre [36]. IF AO was created by Xia et al. [37] using Archimedean TN and TCN.
IF AOs were created by Wang and Liu [22] utilising Einstein TN and TCN. Based on Einstein TN and TCN, Wei and Zhao [38] presented induced hesitant interval-valued AOs. Liu [39] created interval-valued IF (IVIFS) AOs using Hamacher TN and TCN. By utilising Dombi TN and TCN, Ullah et al. [40] established interval-valued TSF AOs. IF power AOs were created by Zhang et al. [41] utilising Frank TN and TCN. Tis TN and TCN had a signifcant impact on the use of FSs in decision making. A novel pair of TN and TCN that is more fexible than the previous TN and TCN listed above was initially introduced by Aczel and Alsina [35]. Senapati et al. [42] developed the Aczel-Alsina AOs for the IFS framework as well as for interval-valued IFSs (IVIFSs) and discussed the application to MADM, and both highlight the importance of the Aczel-Alsina TN and TCN due to the variableness of the involved parameters. We can infer from the investigation abovemenioned that the AOs used in MADM are complicated by actual phenomena. Naeem et al. [43] presented the decision methodology based on the picture fuzzy Aczel-Alsina geometric aggregation operators to tackle the uncertainty in decision making problems.
Te information should be handled more readily in order to get the optimal alternative in MADM. Moreover, IHFSs operate in a more ambiguity-tolerant environment than IFSs, IVIFSs, Pythagorean FSs (PyFSs), q-rung orthopair FSs (qROFSs), and spherical FSs (SFSs). Te usage of Aczel-Alsina TN and TCN in the framework of IHFSs has not yet been discovered. Tese elements inspire us to formalise the idea of Aczel-Alsina AOs in the design of IHFSs and then investigate how they apply to MADM. Using this structure, the problem is additionally categorised by changing the physical importance of the reference parameters. For the following reasons, many novel aggregation operators (AOs), including the IHF Acz-Aln operations operators, are recommended as follows: (a) IFS and HFS are related ideas that provide IHFS decision makers more latitude. (b) IHFS uses approximate spaces for hesitation as opposed to IFS. (c) Weighted averaging and geometric aggregation operators are unable to account for experts' levels of knowledge with the examined items when performing initial evaluation; however, IHF Acz-Aln AOs can. (d) Te IHF Acz-Aln AOs are simple and cover the decision-making process; therefore, this article aims to address more complex and advanced data. (e) In the suggested work, all faws are fxed.
Te following are the objectives of the paper: (1) In order to make up for the lack of algebraic, Einstein, and Hamacher operations and to depict the relationship between IHFNs, we develop a series of Acz-Aln operations for IHFNs. (2) In order to support IHF data, we develop Acz-Aln Agop to IHF Acz-Aln Agop: IHF Acz-Aln weighted geometric (IHFAWG) operator, IHF Acz-Aln order weighted geometric (IHFAOWG) operator, and IHF Acz-Aln hybrid weighted geometric (IHFAHWG) operator. (3) We developed an algorithm to handle MAGDM problem using IHF information. (4) We used a MAGDM problem regarding the quality of medical care providers to describe the suitability and reliability of the proposed IHF Acz-Aln Agop. (5) Te results demonstrated that the developed approach is incrementally more potent and produces more authentic fndings than existing approaches.
Te following is the order in which the rest of this article is organised. Section 2 discusses the basics of t-norms, tconorms, Acz-Aln t-norms, IHFSs, and a number of operational principles in the context of IHFNs. Section 3 discusses the Acz-Aln operating rules as well as the characteristics of IHFNs. In Section 4, we interpret several IHF Acz-Aln Agops and discuss their distinguishing characteristics. In the next section, we will look at the MADM problem with the help of IHF Acz-Aln Agop. In Section 6, we present a novel method for assessing the quality of medical services by seeing it as an MCDM problem. Te new technique aids in the efciency and accuracy of assessing the quality of medical services, allowing medical service providers to enhance and amaze their customers. In Section 7, we examine how a parameter infuences DM results. Section 8 contrasts the results of the suggested Agop to those obtained through existing Agops, and it summarises the article and makes recommendations for further research.

Fundamental Concepts
We will look at some key topics in this section that will be signifcant in the creation of this article.

Aczel-Alsina Norm
Acz-Aln norms are two useful processes that have the beneft of being changeable with the parametric activity [40,41].

Aczel-Alsina Operation for IHFNs
We discussed Acz-Aln operations in relation to IHFNs, taking into account Acz-Aln t-norm and Acz-Aln t-conorm.

Aczel-Alsina Geometric Aggregation Operators for IHFNs
Acz-Aln norms-based novel Agop under IHF information are proposed in this section.
Proof. Using mathematical induction, the proof of Teorem 2 is derived as follows: Step-1: for l � 2, we get By Defnition 13, we have Terefore,
We have to show that Teorem 2 is true for l � d + 1.
Hence, Teorem 2 is valid for all l.
We may show the following characteristics properly by employing the IHFAOWG operator.
We may show the following characteristics properly by employing the IHFAHWG operator.
Te created IHF Acz-Aln geometric operators were used to resolve the MCDM problem in this research, and the process for sorting the best raking from alternatives is as follows: Step 1: identify a set of characteristics that are relevant for the evaluation problem being solved. A literature review is conducted to acquire potential evaluation qualities, which are then fltered by a technical committee to produce a suitable list of evaluation attributes.
Step 3: collected specialist uncertain data: IHFWA/ IHFWG to combine the specialist uncertain data in decision support issues, aggregation operators are used.
Step 4: illustrate the signifcance (weighting) of the attributes to be considered R 1 , R 2 , . . . , R m using IHF entropy measure as follows:

Scientifc Programming
Step 5: aggregated data: developed IHF Acz-Aln geometric operators exploited to aggregate the specialist uncertain data of decision support problems.
Step 6: according to the score function in Defnition 10, the score values of I ℶ (ℶ � 1, 2, . . . , l) are derived." Step 7: all options are sorted in highest to the lowest depending on the scores, and the best one with the highest score value is chosen.

Numerical Representation of the Suggested Method
We approach an uncertain challenge of assessing the quality of healthcare care in verifying the usefulness and adaptability of the created strategy to the MADM challenge.

Case Study: Evaluating the Quality of Medical Services.
Te assessment framework for evaluating the quality of medical services developed in this article contains four parameters. Te following provides an explanation of the alternatives for evaluating the quality of medical services: Te focus of this research is nearly entirely on evaluating the medical care process at the level of physician-patient interaction. As a result, it excludes processes that are primarily concerned with the successful delivery of medical care in the community. Furthermore, the administrative components of quality control are not addressed in this study. Many of the studies discussed here arose from the urgent requirement to assess and control the quality of care in organised medical care systems. Nonetheless, these studies will be discussed solely in terms of their contribution to evaluation procedures rather than their broader social objectives. Specifc construction standards have a signifcant impact on health maintenance and enhancement, as well as the safety and comfort of people in health care facilities. Health-care institutions are unusual structures in which several habitats coexist. A wide variety of people, activities in each setting, and risk factors are all implicated in the pathogenesis of a wide range of diseases. Nursing units, operating theatres, diagnostic facilities (radiology units, laboratory units, and so on), outpatient departments, administration areas (ofces), dietary facilities, linen services, engineering services and equipment areas, corridors, and passages are all classifed using functional organisation criteria. Health professionals, staf members, patients (long-stay inpatients, acute inpatients, and outpatients), and visitors make up the hospital population. Te processes include activities particular to health care-diagnostic, therapeutic, and nursing tasks-as well as activities common to many public facilities, such as ofce work, technological maintenance, and food preparation. Physical agents (ionising and nonionising radiation, noise, lighting, and microclimatic factors), chemicals (e.g., organic solvents and disinfectants), biological agents (viruses, bacteria, and fungi), ergonomics (postures, lifting, and so on), and psychological and organisational factors are among the risk factors (e.g., environmental perceptions and work hours). Four general topics on quality assessment were quite useful in the preparation of this study.
(1) Hospital environment (R 1 ): the patients and the hospital are inextricably linked. Patients visit hospital for treatment, and they are happy with the clean environment produced by the providers. Te hospital environment is infuenced by a variety of elements, including travel accessibility, ward space, ward's quietness, patient and medication care, and environmental characteristics that restrict or improve communications. When a patient's surrounding is exceedingly loud, he or she may have difculty sleeping or being comfortable, impairing their ability to heal. Te patients like the clean and secure atmosphere provided by the medical service provider. Environmental services (ESs), often known as housekeeping or cleaning services, is a phrase used specifcally in healthcare to guide the act of cleaning and disinfecting medical devices, patient rooms, and other public area inside healthcare facilities by highly trained support service workers. ES assist reduce HAIs and prevent diseases from spreading. (2) Medical procedures (R 2 ): a medical procedure is a sequence of actions performed in the provision of healthcare to accomplish a purpose. A medical assessment is conducted to ascertain, quantify, or diagnose a patient's condition or parameter. Te medical procedure is impacted by a number of factors, including the availability of the medical care, the information collected during the assessment, the diagnostic process, and continued health guidance. Due to the sheer risk of becoming infected spreading and/or resource constraints (both apparatus and manpower), the acceptability and capability of conducting abortion interventions and surveillance throughout a pandemic infuenza outbreak are likely to be altered. To improve outcomes in critically sick patients treated in and outside intensive care units (ICUs, careful planning for operation execution and monitoring will be required. Although there are little data to support conclusive recommendations, the following standard operating procedure (SOP) is based on the understanding of infuenza features, experience from prior respiratory epidemics (such as SARS), specialist consensus, and a safety-frst attitude. In order to properly undertake monitoring and interventions in patients with and without infuenza sickness during an epidemic, ensure that suitable resources are accessible and appropriate protocols are implemented.

Scientifc Programming
(3) Service attitude (R 3 ): a hospital is a platform where families go to get their health problems fxed and receive treatment. Due to their trauma, the patients are already in a condition of anguish and worry. Te patients want to be treated with respect, cared for, and reassured. Tey require a promise of hope that their condition will improve as a result of treatment at the aforementioned facility. Tey must receive a favourable attitude from the hospital's healthcare specialists in order to fnd consolation. Any profession benefts from having a positive attitude since it provides it an edge. However, in the healthcare feld, attitude is extremely important, with a positive attitude being a requirement. Yes, when in the hospital, all healthcare staf, from the most senior surgeons and physicians to the most junior ward boy, must maintain a happy demeanour and a caring demeanour. Tis is due to the fact that the attitude of healthcare personnel in a hospital has an impact on the hospital's relationship with its patients. Patient relationship management is essential for any hospital's performance, as delighted patients result in increased referrals and repeat business. Patient happiness, on the other hand, is more dependent on the attitude of healthcare workers, which is what healthcare HR management focuses on in order to achieve hospital efciency. Professional healthcare consulting organisations provide positive attitude training to hospital workers in order to assist them maintain a friendly and caring attitude toward patients. Tis boosts income and improves the hospital's reputation by increasing patient happiness and loyalty. Having a superb customer service attitude entails being aware of client expectations, going above and beyond, and acting as a customer supporter. Expressing helpfulness, sincere passion, and respect has an efect on customer behaviour, converting uninterested customers to loyal ones. Te administration's attitude plays a vital role in the process of delivering medical services. A multitude of factors impact service attitude, including patience in answering queries, prevarication in responding, prejudice in service, and efciency in achieving fndings. (4) Medical expenses (R 4 ): medical expenditures incurred during the provision of medical services are crucial and must be within the patients' acceptable fnancial reach. Medication costs, medical examination charges, fee transparency, prescription prices, hospital bed costs, expenditure correspondence, charge precision, and food costs are all encompassed in the context of healthcare expenses. Te participants in our full medical insurance plan (FMIP) and the supplementary medical insurance plan (SMIP) have lately noticed that their donations have increased in order to avoid a predicted increase in insurance premiums beginning in January 1998. Apart from paying the higher payments, the participants can take steps to help keep future premium increases to a minimum. In today's competitive medical-care industry, medical product and service consumers have a variety of options when it comes to medical spending. A group insurance plan's participants create a risk community, and in such a community, each individual's consumption patterns infuence the overall plan's performance and thus directly afect the amount of premiums paid to the insurer. As a result, we would want to encourage all members of our medical insurance plan to use the same caution and discipline while incurring medical expenses as they would when making a large purchase or repairing a car. In such instances, one would undoubtedly take the time to shop around for the best deal before spending the money. Te same is true for medical care, where a customer can learn about his or her options, get cost estimates, and/or "shop around" for the best value for money before making a decision.
While it is true that medical treatment, more than other products/services, incorporates nonquantifable factors such as trust, it is nevertheless crucial to be aware that we have rights and options as patients. It is also critical to send a message to medical providers that their charges and rates will be scrutinised. Te mindset that "the insurer pays regardless" is a certain way to boost premiums. As a result, it is critical that we take responsibility for our collective medical insurance plan and exercise extreme caution when it comes to medical spending.
Assume that the set of hospitals is I � I 1 , I 2 , I 3 , I 4 and R 1 , R 2 , R 3 , R 4 be a set of criteria for assessing the quality of medical services specifed by a weight vector σ � (0.1, 0.3, 0.5, 0.1) T . Te following are the various steps involved in developing a novel scheme for evaluating the quality of medical services on the basis of suggested operators: Step 1: the specialist matrices of IHFNs is enclosed in Table 1 Step 2: Table 2 evaluates the normalized decision matrices after normalisation Step 5(a): employed IHFAWG operator to integrate aggregated data enclosed in Table 3 as follows: Step 5(b): employed IHFAOWG operator to integrate aggregated data enclosed in Tables 4-6 Arranged row wise normalized matrix Step 5(c): employed IHFAHWG operator to integrate aggregated data enclosed in Tables 7-10 Step 6: observing the score function in Defnition 10, the score values of I ℶ (ℶ � 1, 2, 3, 4) are enclosed in Table 11: Step 7: under all the suggested Acz-Aln operators, I 3 has the largest score value; therefore, I 3 is our fnest choice in terms of giving attributes.

Comparison Analysis
To show the applicability and appropriateness of the established operators-based methodology, we compared the approach based on the suggested operator in accordance with existing decision assistance approaches to validate the advantages and stability of the intuitionistic hesitant Acz-Aln Agops.        Peng et al. [46] evolved novel intuitionistic hesitant fuzzy weighted Agops to sort out the best alternative. Table 12 gives the comparison fndings and shows that the IHFWG operator is a special instance of our developed IHFAWG operator, and it acquires when ρ � 3 and w � (0.15, 0.15, 0.375, 0.325).
As a nutshell, our suggested solutions are expected to become more extensive and fexible than a few existing strategies for addressing IHF MADM problems. Te collected specialist data [46] are listed in Table 13: Comparative studies with collected specialist data by [22] is enclosed in Table 14 as follows: 7.1. Advantages. Te benefts are summarised as follows: (i) A multicriteria framework with a diferent approach to generating IF numbers is the IHF Acz-Aln method. (ii) By using the inverse sorting algorithm, the IHF Acz-Aln methodology standardises the home matrix elements, which permits I retention of the placement of normalized values on the measuring scale and the absence of domain shift or a distortion of the source data. (iii) Te display of expert preferences is substantially facilitated by the IHF Acz-Aln algorithm, which is   Table 9: Updated normalized specialist matrix of IHAHFNs.

Conclusion
Every day, we work with complex and cutting-edge data. We created approaches and tools for this kind of data in order to operate more efciently and compute thorough information. Te cost of condensing a large volume of data into a single value is a fundamental cost of aggregation. Te IHFS was developed as a very efective combination of an IFS and HFS for scenarios where each item has a range of possible values determined by MD and non-MD. We go into further detail about these strategies' benefts as follows: (i) First, it discusses the implementation of the IHFAWG, IHFAOWG, and IHFAHWG operators, which are capable of capturing the interrelationships between all attributes and highlighting possible factors. (ii) Second, it discusses various characteristics of the IHFAWG, IHFAOWG, and IHFAHWG operators   and also investigated some particular cases of the abovementioned operators and discussed their relationships between those operators in more detail. (iii) Tird, it develops a unique method for evaluating the quality of medical services via the use of a criterion framework and a scheme. We use this novel methodology to assess four hospitals in order to show the method's availability and conduct a comparison study to establish the method's effcacy and superiority. (iv) Te fnding is that our strategy has a lot of benefts and trustworthy in IHF data DM. In other words, we may have easily described fuzzy information and make the information aggregation method more transparent than certain existing systems by supplying a parameter. (v) Te existing Agops [46] do not make data aggregate more versatile. As a consequence, our suggested aggregation operations in IHF data DM are more comprehensive and reliable. (vi) Te concept of Acz-Aln Agops may be extended to other fuzzy environments for assessing the quality of medical services in the future. Additionally, group decision making [47,48] might be explored to strengthen the assessment result's robustness. (vii) In our next work, we will investigate the theoretical foundations of IHFS' Acz-Aln operations utilising cutting-edge decision-making techniques including TOPSIS, VIKOR, TODAM, GRA, and EDAS. We will also discuss how these methods are applied in a variety of felds, such as soft computing, robotics, horticulture, intelligent systems, social sciences, fnance, and human resource management.

Data Availability
Te data used to support the fndings of this study are included within the article.

Conflicts of Interest
Te authors declare that they have no conficts of interest.