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The world’s population is aging. Age is more than just a number. One single major challenge of policymakers across geographies is to arrange efficient healthcare services to upgrade the living standards of the aging population. In recent years, there has been a significant surge in the number of patients with various chronic diseases associated with a variety of risk factors requiring long-term treatment. Under these complexities, the decisions by caregivers cover the critical ripple effects [8]. So, a tiny mistake by them can be irrecoverable and fatal for patients [1]. However, various stakeholders of healthcare industries, including managers and legislators, hardly furnish precise and crisp information. The inherent uncertainty in the data brings fuzzy set theory into the forefront. Whereas the fuzzy set theory has been widely applied to deliver the acceptable solutions to diverse healthcare and medical issues, researchers are employing several recent tools, like type 2 fuzzy set, intuitionistic fuzzy set, and many more for higher efficiency. Here, the present review briefly focuses on only following three major sub-areas of applications of fuzzy set theory and its derivatives in healthcare and medical problems:

1 A. selection of medical equipment, material, and technology,

2 B. service quality and risk assessment typically in chronic diseases, and

3 C. decision making and the role of operations research.

A. Selection of Medical Equipment, Material, and Technology In recent times, researchers categorized the interrelationship (with several alternatives) among medical types of equipment and materials. So, they could present numerous approaches and methods regarding the assessment and selection of types of equipment, materials, and projects.

In recent years, [3] presented an empirical case study on the robot selection problem by extending the PROMETHEE method under fuzzy environment. Their novel approach included the simultaneous exploration of crisp objective data and fuzzy subjective data. They found how the appropriate robot selection could help to enhance the value of products and thereby resulted in the increased satisfaction of patients, relatives, and caregivers. Around the same time, a study in this area along with potential applications in manufacturing industries was performed in [2]. He extended the classical VIKOR method for robot selection under uncertainty. He employed the interval type-2 fuzzy set to get more degrees of freedom to real-life problems. As well, he analyzed the stability of the proposed method through seven sets of criteria weights and the Spearman correlation coefficient. [4] performed a well-established study by amalgamating two fuzzy-based hierarchal processes, namely fuzzy AHP and fuzzy VIKOR in mobile robot selection. Their study focused on the total ownership of cost as a key parameter in the selection of the robot. Along with some modern technology marvels, like the robotic automation system and Internet of Health Things (IoHT), the modified fuzzy AHP and fuzzy VIKOR methods were applied to determine the ranking of robots and thereby to select the best mobile robot at the hospital pharmacy. Next, [5] found how millions of people received frequent health pieces of advice to lead a healthy life. They noted that while the IoT devices could generate a large volume of data in the healthcare environment, the cloud computing technology could be rewarding for secured storage and accessibility. Additionally, they applied a new systematic approach for the people, who were severely affected with diabetes, by generating the related medical data through some repository dataset and the medical sensors. Their suggested classification algorithm was called the fuzzy rule-based neural classifier that could more effectively diagnose the disease and the severity than classical methods. On the other hand, whereas most researches recognized the hospitals to act as the main sub-section of the healthcare system, they assumed the hospitals at different locations to be at par and homogeneous. However, Omrani et al. [6] studied the non-homogeneous nature of services offered to various patients by the hospitals at different locations. So, they found that these hospitals were unsuitable for comparison. Accordingly, they proposed a clustering technique to deal with a lack of homogeneity among DMUs and thereby to measure the hospitals in different places. Again, [7] addressed the impact of various harmful factors in the information security of healthcare devices. They employed a fuzzy-based symmetrical AHPTOPSIS method. However, they could test the method only at one local hospital software of Varanasi, a city of India. The work by [8] found the drawbacks of type 1 fuzzy set theory and used the finite interval-valued type 2 Gaussian fuzzy number as a powerful tool to measure uncertainty in healthcare problems. This could solve a real economic evaluation of medical device selection problem from the perspectives of clinicians, biomedical engineers, and healthcare investors. Part A of Table 2.1 lists some very recent articles in this area of research. This way, numerous researchers have put their best effort to tackle the uncertainty intrinsic to healthcare and medical problems.

Table 2.1 Very recent articles focusing on applications of fuzzy set theory in healthcare and medical problems.

Author(s)	Approach	Purpose of the study	Outcome
Part A: Selection of medical equipment, material, and technology
Moreno-Cabezali and Fernandez-Crehuet [24]	Fuzzy logic in risk assessment.	Survey to assess potential risks.	Identified the most critical risk.
AlZu’bi et al. [25]	3D fuzzyC-means algorithm.	3D medical image segmentation.	Parallel implementation to be 5× faster than the sequential version.
Ozsahin et al. [23]	FuzzyPROMETHEE And fuzzy MCDM.	Solid-state detectors in medical imaging	Most suitable semiconductor on basis of detectors.
Masood et al. [22]	Hybrid hierarchical fuzzy group decision making.	Selection of conceptual loudspeaker prototype under sustainability issues.	Optimal conceptual prototype design among 4 alternatives.
Part B: Service quality and risk assessment typically in chronic diseases
Vidhya and Shanmugalakshmi [29]	Big Data and neuro fuzzy-based method	Analysis of multiple diseases using an adaptive neuro-fuzzy inference system.	Determined the entropy of the CFI count.
Akinnuwesi et al. [28]	Hybridization of fuzzy-Logic and cognitive mapping techniques.	Decision support system for diagnosing rheumatic–musculoskeletal disease.	87% accuracy, 90% sensitivity, and 80% specificity.
La Fata et al. [26]	Fuzzy ELECTRE III.	Evaluated the service quality in public healthcare.	Significant service attributes factors.
Samiei et al. [27]	Neuro-fuzzy inference system.	Risk factors of low back pain.	Identified four major risk factors to low back pain.
Part C: Decision making and the role of operations research
Vaishnavi and Suresh [30]	Fuzzy readiness and performance importance indices.	To implement agility in healthcare systems.	Continuation of assessment readiness helps to improve readiness.
Detcharat Sumrit [31]	Fuzzy MCDM approach.	Supplier selection for vendor-managed inventory in healthcare.	Institutional trust, information sharing, and technology as major evaluation criteria.
Rajput et al. [33]	Fuzzy signed distance technique.	Optimization of fuzzy EOQ model in healthcare industries.	Determined optimal total cost under variable demand.
Salazar and Sanz-Calcedo [32]	cognitive mappings.	operations on energy consumption and emissions in healthcare centers.	connection to energy, environmental efficiency, and maintenance condition.

B. Service Quality and Risk Assessment, Typically in Chronic Diseases The world’s population is aging. The proportion of the elderly (+65) is greater than ever and is estimated to be double within the European Union within the next 50 years [13]. Whereas the improvements to the quality of life and advances in medical science in the last few decades craft the aging of the population, a higher ratio of the aged population makes it necessary for caregivers to concurrently tackle with more patients suffering from a variety of chronic diseases. This way, the upholding of quality service by assessing the risk turns to be more and more challenging for caregivers.

An empirical case study [9] was conducted with data from nine public hospitals in Silica, Italy, on four core quality parameters and fifteen main service items. He introduced a new fuzzy measurement method for assessing the quality of service in healthcare. To elicit accurate estimates of service quality requirements, the fuzzy AHP approach was used. He found that successful internal communication of service quality accomplishments should minimize the differences between the needs of customers and how workers view those needs. The authors [10] presented several of the shortcomings of several existing algorithms in the form of an enormous number of rules and the mining of non-interesting rules, along with the time of pre-processing and the rate of filtration. Then to address the limitations based on the user request and the visualization of discovered rules, they provided a fuzzy weighted-iterative concept.

Again, [11] provided under an interval-assessed intuitionistic fuzzy environment a hybrid MCDM model and thereby evaluated the probability of node failure. They combined the interval-valued intuitionistic fuzzy ANP (for matching with the uncertainty of information) and the proportional assessment approach (for decision making). However, the subjective weight used in their method relied much on caregivers’ opinions and thus was not flawless. Besides, due to the complexities of systems and service, there could arise different kinds of interrelationships between the failure modes. However, this was dodged in this study. Around the same time, [12] presented a decision-making approach that predicted heart failure risk. They integrated the fuzzy AHP and fuzzy ANN in the suggested approach. Also, they could establish that their method had 91.10% accuracy in results in comparison with other conventional ANN models Table 2.2.

Recently, [14] identified several drawbacks of the highly popular gerontechnology and telerehabilitation systems, such as the failure of those systems to assist patients and experts, both, regarding the progress of rehabilitation. They proposed a fuzzy-semantic framework based on well-known assessment criteria to determine the physical state of the patient during the recovery process. They used an API, however, called the Kinect API, which was a closed source API and only usable for Kinect interface patients. This made it less valuable for the process. There were also ample scopes for therapists and patients, alike, to determine their operation. Again the emphasis on privacy issues is one main factor in the acceptability of any technology or system. The study [15] focused on the safety assurance of an elbow and wrist rehabilitation medical robotic device in terms of robot and patient safety. Using the fuzzy logic method that discovered the degree of protection during the use of the robotic system, data uncertainty was discussed. However, their procedure was only tested numerically in a group of 18 patients through a clinical trial.

Table 2.2 Abbreviations with descriptions.

Abbreviation	Description
VIKOR	Vlsekriterijumska Optimizacija I Kompromisno Resenje
AHP	Analytic Hierarchy Process
ANP	Analytic Network Process
MCDM	Multi-Criteria Decision Making

The very latest papers focusing on this area are included in Part B of Table 2.1.

C. Decision Making and the Role of Operations Research The majority of researchers focusing on applications of fuzzy set theory in healthcare and medical problems used some existing decision-making processes or derived new ones. They found that the decisions of caregivers primarily aim to lower the health risk of patients while maximizing the health benefits and patients’ choice, thereby increasing the satisfaction of all parties. However, there involved numerous criteria, such as social, environmental, material, managerial, professional, and many more criteria, in the wider setting of medical and healthcare models [17]. Since the crisp decision-making methods under several qualitative and quantitative contradictory issues strived to avoid the complexities with tolerance to doubts and stakeholders’ favoritism, the fuzzy set theory was employed to represent the inherent impreciseness of data and thus to present an efficient, rational and explicit decision process [21].

Among recent studies, [16] presented a detailed survey by considering 142 articles published in the period 2000–2014. While they found the maximum number of publications focusing on applications of operations research in healthcare around the year 2008, they noted a surge in numbers post 2014. In the same edited volume of 2017, they presented a comprehensive survey in this area. They considered a longer period: 1966–2016 to study the advancements of this domain. By considering some relevant recent papers under each class of consideration, their analysis categorized the various approaches and methods applied in healthcare research. [13] provided a thorough analysis of the applications of decision-making and fuzzy set theory to solve health-related problems in a widely admired article. In the period from 1989 to 2018, their statistical findings ranked the year 2012 as first among the acclaimed papers. They also found that the various AHP and hybrid approach approaches were commonly used to rate different service quality applications in the healthcare industry.

Again, [34] shared the applications of operations research in healthcare supply chain management under ambiguity have been vividly demonstrated. By fuzzy set and probability theories, they represented the uncertainty in results, both, and thus could deliver the right medication to the right people at the right time and in good condition to combat the disease. Next, [17] posed an important question as to whether, by proper examination, hospitals could incorporate lean thought. First, various lean concepts and components implemented in healthcare institutions were defined. Next for healthcare organizations, a fuzzy-logic based lean implementation evaluation approach was deployed and then numerically studied. Although this study was validated in only one Indian hospital, it introduced some of the legislators’ futuristic and implementable action plans. The study [44] developed a model to measure the leanness of hospitals and then validated the model by discussing the corresponding initial version with select academic experts. This way, they determined two criteria for organizations, namely the ability to participate in the study, and the commitment to implement lean principles. Finally, a multi-attributes fuzzy logic-based ranking method was established to present the leanness index.

Recently, [18] performed the identification of enablers, criteria, and attributes of leanness to constitute the measures of assessment of hospitals under fuzzy environment. Their method could help to provide the measures to address the weaker attributes and thereby to further enable the enhancement of lean performance.

In a rather real-life-oriented study [19], Pythagorean fuzzy data were considered, in which different evaluation data were provided in the form of Pythagorean fuzzy decision matrices regarding the feasible alternatives. The entries were taken from the views of experts and were described by fuzzy numbers from Pythagoras Table 2.2. In order to solve the resulting MCDM problems under uncertainty, they also broadened the application of the classical TOPSIS system. The most appropriate location and priority setting for buying the best healthcare technology could be decided by this process.

In another fresh-taste study [20], the emphasis was on a muchdiscussed issue of workplace hazards, including protection and effectiveness of health workers against public abuse. To define and prioritize control measures of aggression, their innovative approach used fuzzy AHP and Fuzzy Additive Ratio Assessment. They described the solution as the best advice for controlling violence against health workers by increasing the number of security personnel and training staff.

Below, Part C of Table 2.1 presents some very recent related articles published in highly acclaimed journals. This way, above deliberations, find ample scopes of research on applications of fuzzy set theory on the health-care and medicine problems.