A Fuzzy-Based Decision Support Model for Selecting the Best Dialyser Flux in Haemodialysis

Decision making is an important procedure for every organization. The procedure is particularly challenging for complicated multi-criteria problems. Selection of dialyser flux is one of the decisions routinely made for haemodialysis treatment provided for chronic kidney failure patients. This study provides a decision support model for selecting the best dialyser flux between high-flux and low-flux dialyser alternatives. The preferences of decision makers were collected via a questionnaire. A total of 45 questionnaires filled by dialysis physicians and nephrologists were assessed. A hybrid fuzzy-based decision support software that enables the use of Analytic Hierarchy Process (AHP), Fuzzy Analytic Hierarchy Process (FAHP), Analytic Network Process (ANP), and Fuzzy Analytic Network Process (FANP) was used to evaluate the flux selection model. In conclusion, the results showed that a high-flux dialyser is the best option for haemodialysis treatment.


INTRODUCTION
Decision making is currently one of the most critical management issues because several criteria and alternatives often exist for every decision.It is crucial to make the proper decisions in both the short and long terms because they define the survival, success, or growth of an organisation.In general, the decision-making process should consider not only concrete criteria, such as technical and economic properties, but also social, environmental, and political factors [1].
In addition to data collection, an efficient and cost-effective decision-making process should apply decision-making techniques.In the current highly competitive environment, the application of decision-making systems or methodologies gives an organization a competitive advantage.In most decision-making cases, there is more A Fuzzy-Based Decision Support Model for Selecting the Best Dialyser Flux in Haemodialysis than one criterion to evaluate, and such decision-making processes are called Multi-Criteria Decision Making (MCDM) [2].Due to the widespread use of high technology, the recent decisions made in the healthcare sector are accompanied with many alternatives available.The physicians or healthcare professionals involved in the decision-making process of selecting any medical device, disposable product, or treatment alternative must evaluate the status of the patient, various criteria, and the alternatives available.Particularly in cases of chronic illnesses, routine decisions need to be made frequently.
In end-stage renal disease (ESRD), the progression of renal failure is characterized by the deterioration of various biochemical and physiological functions [3].Only a small portion of ESRD patients are treated with a renal replacement therapy or renal transplantation [4,5].The vast majority of ESRD patients are treated with haemodialysis with an extracorporeal circuit that consists of disposable products, such as fistula needles, bloodlines, dialysers, and haemodialysis concentrates.Dialysis treatments are performed at public, private, and non-profit centres, in hospitals and limited-care facilities, and at patients' homes [4].
The dialyser is the most important component in haemodialysis machine because it removes uremic toxins.Dialysers are also called artificial kidneys and can be classified according to their characteristics, such as membrane type and geometric structure.The flux of a dialyser is also one of these classification criteria [6].Dialysers are classified as low-flux or high-flux [6], and the dialyser flux is selected by nephrologists or dialysis physicians.The dialyser flux selection process is a complicated process due to a large number of haemodialysis patients, the treatment frequency, the cost of each treatment, and the available dialyser alternatives.
The aim of this study is to systematize the dialyser flux selection process through the use of MCDM techniques, such as Analytic Hierarchy Process (AHP), Fuzzy Analytic Hierarchy Process (FAHP), Analytic Network Process (ANP), and Fuzzy Analytic Network Process (FANP).The MCDM techniques used in this study, the decision support software (DSS), and the proposed dialyser flux selection method are described in the methodology section, followed by the results of the application, discussion, and the conclusion.

Analytic Hierarchy Process (AHP)
The Analytic Hierarchy Process (AHP), first proposed by Thomas L. Saaty in the 1970s, is one of the MCDM techniques that consider the relative importance of alternatives.In summary, the AHP considers both objective and subjective criteria and involves pairwise comparisons.Its flexibility in terms of its potential use for the analysis of complex problems and its user friendliness have made the AHP one of the most popular MCDMs [1,7].AHP has been used for selection, evaluation, resource allocation, and forecasting in fields such as manufacturing, engineering, social science, and politics [8].In any AHP model, the goal is set at the top of the hierarchical structure and is followed by the main criteria.If applicable, sub-criteria are written under the corresponding main criterion.The alternatives of the AHP model are set at the bottom of the hierarchy.A schematic representation of the AHP structure is given in Figure 1.
The AHP methodology is based on the well-defined mathematical structure of consistent matrices and their associated right eigenvector's ability to generate true or approximate weights.In AHP, the criteria or alternatives are compared with respect to a criterion in a natural, pairwise mode.Individual preferences are converted to ratioscale weights, which can be combined into a linear additive weight w(a) for each alternative a.The alternatives can then be compared and ranked.
The AHP model includes the following axioms: reciprocal, homogeneity, hierarchic composition, and involving expectations.The reciprocal axiom implies the following: if alternative i is compared to alternative j, the comparison is defined as a ij , and if alternative j is compared to alternative i, the comparison is defined as 1/a ij .The homogeneity axiom states that complexity should be structured in a hierarchy of homogenous clusters.The third axiom, namely hierarchic composition, stresses that judgments about or the priorities of the elements in a hierarchy do not depend on lowerlevel elements.The final axiom implies the involvement of the expectations [1].
The AHP methodology features the following steps: 1. Definition of the problem 2. Observation of the system 3. Construction of the hierarchical structure 4. Definition of the comparisons 5. Synthesis

Evaluation and results
The common scale shown in Table 1 is most often used to compare the criteria and alternatives.

Analytic Network Process (ANP)
Another MCDM technique is the Analytic Hierarchy Process (ANP) developed by Saaty in 1996.In ANP, the alternatives that affect the objective are grouped by their relationships to each other.ANP supports not only hierarchical problems but also problems modelled as a network.Because of the interaction and dependency of a higher-order criterion on a lower-level sub-criterion, it is not always possible to model every problem hierarchically.
In comparison to the AHP, the ANP has a more general structure.In ANP, there is a feedback mechanism which allows the dependency both among criteria and alternatives and among alternatives.More complex decisions can be modelled appropriately with ANP [1].
The ANP structure is composed of clusters and the influences between the clusters.One of the clusters contains the alternatives.The influences can be either inner dependency or feedback from another cluster.The inner dependency is shown with a curved arrow pointing to the same cluster.The straight arrows represent the dependencies between the clusters, and the cluster that the arrow points to influences the root cluster of the arrow.Figure 2 shows the schematic representation of the ANP structure.First, pairwise matrices for each criterion with the affected criteria of all the clusters have to be constructed.To be able to define the priorities in feedback mechanism models, a super-matrix method is developed.With a super-matrix, it is possible to consider all of the interactions between the effected criteria and the affecting criterion.A super-matrix is composed of pairwise comparisons of all of the possible pairs' priorities.In any super-matrix, the clusters are represented by C N , N = 1, 2…., n, the elements of clusters are shown with e Nn , and the priority vectors are denoted with Wij.A common scale shown in Table 1 can be used for the comparisons.
The ANP methodology features the following steps:

Fuzzy Analytic Hierarchy Process (FAHP) and Fuzzy Analytic Network Process (FANP)
Fuzzy set theory was first introduced by L.A. Zadeh in 1965 to deal with the vagueness of human thought.It was oriented toward the rationality of uncertainty due to imprecision or vagueness.The most important contribution of fuzzy set theory is its capability to represent vague data.Furthermore, the theory allows the definition of mathematical operators and programming that can be applied to the fuzzy domain [9].In fuzzy sets, instead of crisp values such as 0 and 1, the interval between these values is basically used to define the membership.The fuzzy sets are defined by Zadeh as a class of objects with a continuum of membership grades.The value is determined based on a membership function.In general, a triangular membership function as presented in Figure 3 is used.In this function, x 1 is the smallest possible value, x 2 is the most promising value, and x 3 is the largest possible value [1,2,9].
The fuzzy AHP and the fuzzy ANP can be solved by various fuzzy approaches.In this study, Chang's Extent Analysis is employed because of its simplicity and common usage [2,10].Step 1: For each object i, the fuzzy synthetic extent value is obtained using the following equation:

Journal of
. ( The value of is obtained by the following operation: .
The value of is obtained using the following operation: Step 2: The degree of possibility for two fuzzy numbers, M 1 = (l 1 , m 1 , u 1 ) and

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A Fuzzy-Based Decision Support Model for Selecting the Best Dialyser Flux in Haemodialysis Triangular membership function [2].
Here, and are two triangular fuzzy numbers.
The last equation can be expressed as follows in Figure 4: (5) Step 3: The degree of possibility for a convex fuzzy number M to be greater than k convex fuzzy numbers M i , i = 1, 2, ...., k can be defined by (6) Assuming that d′(A i ) = minV(S i ≥ S k ) for k = 1, 2, ...., n; k ≠ i, the weight vector can be provided as (7) where Step 4: Finally, the normalized weight vectors can be computed as where W is a non-fuzzy number [2,10,11,12,13].

Figure 4.
Triangular membership function showing an intersection between M 1 and M 2 [11].

Decision Support Software (DSS)
Organizations use DSSs for making decisions based on many criteria.Various DSSs have been developed since the early 1970s [14].The DSS used in this study DSSw, was developed by Turkish Naval Academy (Istanbul, Turkey).It helps decision makers use AHP, FAHP, ANP, and FANP simultaneously and is able to analyse models with up to three levels of criteria, namely main criteria, sub-criteria, and sub-sub-criteria.DSSw was developed in the Microsoft Visual C# programming language and retrieves data from Microsoft Excel.It is able to analyse any model and can include up to nine main criteria, nine sub-criteria for each main criteria and nine sub-sub-criteria for each sub-criteria [2].
The procedures to use DSSw are the following: 1.The criteria and alternatives are entered into a previously constructed Excel worksheet.2. The software constructs a table to enter the influences between the criteria used for ANP and FANP.3. The pairwise matrices produced by the Excel worksheet are filled by the user.4. The consistency ratio of each matrix is calculated by the software, and in the case of a consistency ratio greater than 0.1, the user is warned.5.The software makes all of the calculations for AHP, FAHP, ANP, and FANP after all of the matrices are completed.

Dialyser Flux Selection Model
The choice of membrane polymer, the membrane form, and its physical and biological properties have changed continuously over time due to clinical demands [6].Dialysers are classified based on their various characteristics.For instance, there are two types of dialyse constructions: parallel plate and hollow fiber.Recently, the most widely used dialysers are the hollow fiber dialysers.Dialysers can also be classified as cellulosebased and synthetic-based depending on the membrane employed.Another classification regards the permeability or flux of dialysers.Dialysers can be categorized into high-flux and low-flux dialysers.There are also middle-flux dialysers, but these are not widely used.The difference between high flux and low flux is the ultrafiltration coefficient [6,15].

Low-Flux Dialysers
Cellulose-based membranes were the first commercial membranes for dialysis.They operate with a low flux.After the invention of synthetic-based membranes, some synthetic low-flux dialysers have been produced [6].
Low-flux dialysers are mostly used in standard haemodialysis treatments [16].The mechanism for molecule removal in standard haemodialysis is diffusion, which enables the removal of substances with a molecular weight within a certain range.The sieving coefficients of low-flux dialysers are shown in Figure 5.

High-Flux Dialysers
Membranes of high hydraulic permeability (high-flux) started to be commercialized in 1971.Since 2000, the use of high-flux membranes has increased to 66% worldwide [17].

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A Fuzzy-Based Decision Support Model for Selecting the Best Dialyser Flux in Haemodialysis In contrast, the high-flux dialyser usage remains at 25.4% in the Turkish market [18].The growth of high-flux dialyser usage in Turkey is apparently slower than the world average.High-flux membranes are more permeable to substances of greater molecular weight.In contrast to low-flux dialysers, convection and diffusion are the mechanisms of molecule removal in high-flux dialysers [6].High-flux dialysers can be used in high-flux dialysis, haemodiafiltration, and haemofiltration.The sieving coefficients of high-flux and low-flux dialysers are compared in Figure 5.

The Model
Selection of the flux type in haemodialysis treatment is one of the decisions that are routinely made by the dialysis personnel.In this study, a decision support model was constructed to select the best dialyser flux for haemodialysis.
The criteria were selected based on an in-depth review of the literature and comments from key decision makers [4,19,20,21,22,23,24,25,26].Based on this analysis, the model was constructed with the following eight main criteria: cost, membrane material, medical assessment, technical infrastructure, knowledge, clearance, ultrafiltration coefficient, and toxin removal mechanism.The main criterion used for the medical assessment consists of three sub-criteria, including the removal of high-molecular-weight substances, anaemia correction, and survival.The model includes two flux alternatives, namely low flux and high flux.The hierarchical structure for AHP and FAHP is illustrated in Figure 6.The network structure of the model for ANP and FANP is presented in Figure 7.The criteria for selecting the best dialyser flux are further described as follows: Cost: Reimbursement for chronic dialysis accounts for a substantial portion of healthcare costs [27].In price-sensitive markets such as Turkey, cost could be an independent decision criterion, even though cost is very closely linked to quality or properties of a dialyser.Membrane material: There are two distinctive classes of membrane materials, synthetic and cellulosic.Recently, 91% of the dialysers used worldwide were synthetic [6].There are many types of synthetic membrane materials, and membrane material is one of the determinants of the degrees of dialyser biocompatibility and performance [6].Moreover, the quality of the dialysis treatment is significantly affected by the polymer material chosen for dialysis membranes [5].Some examples of synthetic membranes are polysulfone, polyacrylonitrile, and polyethersulfone [6].
Medical assessment: The adequacy of a haemodialysis treatment is influenced by many factors, but the long-term well-being of a patient is the priority.A dialysis physician's decision should be based on an overall assessment.In this study, under medical assessment, the removal of high-molecular-weight substances, anaemia control, and survival are prioritized.
Anaemia: Renal anaemia is a major cause of morbidity and mortality in ESRD patients, and also lowers quality of life and cardiovascular functions [28,29,30,31,32].Erythropoietin (EPO) deficiency, chronic blood loss, haemolysis, malnutrition and inflammation or infections are some causes of anaemia.Although Ayli et al. showed that high-flux membranes improve control of anaemia while allowing a progressive reduction in the exogenous EPO dose by 25 -45%, one of the most recent prospective controlled studies by Schneider et al. reported that high-flux dialysis offered no superior effects on haemoglobin levels [33,34].
Survival: Mortality in ESRD patients is very high compared with that in the general population [26,35].The adequacy and biocompatibility of the dialyser have direct or indirect effects on mortality.In addition to the common risk factors of mortality, ESRD patients are subjected to uraemia-related risk factors, such as anaemia, inadequate dialysis, and chronic inflammation.
Technical infrastructure: It has been proven that a dialyser is not a safe barrier to bacterial degradation products that might exist in the dialysate [19].There is a risk of back filtration from the dialysate to the blood side [36,37,38].The pressure gradient between the blood and the dialysate side is the identifier of back filtration [39].Back filtration happens in conventional high-flux dialysis conditions with membranes having an ultrafiltration coefficient greater than 30 ml/h•mmHG•m 2 [39].For that reason, the back filtration risk is higher in high-flux dialysers.As a result, additional precautions must be taken in the treatment of the water [38].One of the solutions to cope with back filtration is using dry powder bags for the bicarbonate concentrate and dialysis fluid filters in producing dialysis fluid [25,38].
Knowledge: Healthcare professionals have to be aware of the flux differences.It is crucial that the medical benefits are understood.High-flux and low-flux dialysers have been compared in many retrospective and prospective studies [33,40,41,42].
Clearance: Removing uremic toxins from the blood side to the dialysate side is the most important function of a dialyser."Clearance" is the special term used to define the amount that is removed over a unit of time.This value, determined by in vitro laboratory testing, is presented as a table in the product brochure or instructions for use [6].
Ultrafiltration coefficient (UF Coeff.):The water permeability of a dialyser is characterised by the membrane ultrafiltration coefficient [6].In addition to the toxins, the excess fluid in the body should also be removed during dialysis treatment.This water permeability is defined as the volumetric flow rate of water per unit area of membrane for unit pressure gradient [6].Dialysers with a UF Coeff.greater than 15 ml/h/mmHg are classified as high-flux dialysers [38].
Toxin removal mechanism: The only toxin removal mechanism in low-flux dialysis is diffusion, while toxin is removed by both diffusion and convection in high-flux dialysis.Higher-molecular-weight substances, such as beta-2-microglobulin, can be removed by convection [6,19,43].
The influences between criteria for ANP and FANP are shown in Table 2.
Dialyser selection, including flux selection, is usually performed by dialysis physicians or nephrologists.The inputs for this model were gathered via a questionnaire completed by dialysis physicians and nephrologists.Pairwise comparisons between the criteria and alternatives were made using this questionnaire, as shown in Appendix.A total of 75 questionnaires were distributed to dialysis physicians and nephrologists working in hospitals and dialysis clinics in Turkey, and 47 questionnaires were returned.Some of the questionnaires were filled during direct visits, and some were sent by mail.Two of the questionnaires were eliminated due to missing information.Thus, 45 questionnaires were assessed in this study.The inputs that are essential for the computational part of DSSw were gathered by the questionnaire.

RESULTS
Using the developed model and DSSw, the best dialyser flux was selected with AHP, FAHP, ANP, and FANP.The geometric averages of the questionnaire responses were calculated.The pairwise matrices were determined and entered into DSSw.Figure 8 shows a screenshot of the results in DSSw.The results of the model are summarized in Table 3, showing that high-flux dialyser is a better option than low-flux dialyser for haemodialysis treatment by all four methods.

DISCUSSION
Advantages that are claimed to be provided by high-flux dialysers have been discussed in several multicentre, retrospective and prospective studies [33,40,41,42,44].The worldwide usage of high-flux membranes for dialysis patients has increased from 46% in the year 2000 to 66% in the year 2009 [45].In Turkey, the usage rate of high-flux dialysers in 2011 was 25.4% [18], which is far below the world average.The reason may be solely the very low reimbursement rate, which is $69 per haemodialysis treatment.This amount is very low compared to countries such as the USA, Germany, Belgium, Netherlands, UK, and France, as discussed by Vanholder et al. [27].
The selection of the flux of dialysers involves the consideration of many parameters; it is difficult to prioritize among them.The reason underlying the low usage of high-

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A Fuzzy-Based Decision Support Model for Selecting the Best Dialyser Flux in Haemodialysis flux dialyser in Turkey is the consideration of only the cost of the dialysers.However, flux-selection decisions change when factors such as high-molecular-weight substance removal, anaemia control, survival, toxin removal mechanism, and clearance are also considered.MCDM techniques are used in a wide variety of fields for decision making, including medical device selection.No study has been conducted on MCDM usage in dialyser selection.Only one study (Ronco et al. [16]) has proposed a database for all of the dialysers available on the market, that enables users to compare and select dialysers based on product specifications.Using the model developed in this study, it is possible to include related criteria when making a decision on the type of dialyser.This study is the first in the literature to propose a decision support model for dialyser flux selection.There are three main limitations of this study.First, the criteria might differ with a different group of key decision makers.Second, the current results are based on questionnaires completed by physicians in Turkey only, and may not be applicable to other parts of the world.Another limitation is that the current results are based on only 45 questionnaire responses received.The model can be applied to a future study involving a larger group of physicians in a wider geographical region.

CONCLUSION
In managing chronic diseases, the same decision has to be made routinely with only slight changes.Making the decision process systematic would save time and increase both the efficiency of the process and cost effectiveness.Selecting the best dialyser flux for dialysis, which is addressed in this study, is a good example of routing decisionmaking in chronic disease management.Efficient selection and effective usage of dialysers are of great importance to the physician in terms of the treatment quality and, to the patient, in terms of quality of life and survival.Governments around the world all 316 A Fuzzy-Based Decision Support Model for Selecting the Best Dialyser Flux in Haemodialysis  attempt to control the rising costs of dialysis because they constitute an important part of healthcare expenses [27,46,47].However, the priority of governments should be ensuring quality of care in addition to controlling the costs.
In this study, a model for selecting the best dialyser flux was constructed based on MCDM techniques, including AHP, FAHP, ANP, and FANP.High-flux dialysers were found to be the best alternative by all four techniques employed in this study.This study suggests that high-flux dialysers may be more widely accepted in coming years.Further research can be conducted by including more MCDM methods, such as ELECTRE, TOPSIS, and VIKOR, and involving a larger group of physicians in a wider geographical region.

Figure 6 .Figure 7 .
Figure 6.Hierarchical structure of the model for AHP and FAHP.

Figure 8 .
Figure 8. User interface of the DSSw showing the results of the decision support model for the selection of the best dialyser flux.