Kidney Research and Clinical Practice 2017 Mar; 36(1): 29-38  https://doi.org/10.23876/j.krcp.2017.36.1.29
A computer-aided diagnostic system for kidney disease
1Department of Industrial Engineering, University of Sistan and Baluchestan, Zahedan, Iran, 2Department of Industrial and Manufacturing Systems Engineering, Kansas State University, Manhattan, KS, USA, 3Department of Management Engineering, Istanbul Technical University, Istanbul, Turkey
Correspondence to: Farzad Firouzi Jahantigh, Department of Industrial Engineering, University of Sistan and Baluchestan, 98164-161 Zahedan, Iran. E-mail: firouzi@eng.usb.ac.ir
Received: May 10, 2016; Revised: September 4, 2016; Accepted: October 4, 2016; Published online: March 31, 2017.

This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract

### Background

Disease diagnosis is complicated since patients may demonstrate similar symptoms but physician may diagnose different diseases. There are a few number of investigations aimed to create a fuzzy expert system, as a computer aided system for disease diagnosis.

### Methods

In this research, a cross-sectional descriptive study conducted in a kidney clinic in Tehran, Iran in 2012. Medical diagnosis fuzzy rules applied, and a set of symptoms related to the set of considered diseases defined. The input case to be diagnosed defined by assigning a fuzzy value to each symptom and then three physicians asked about each suspected diseases. Then comments of those three physicians summarized for each disease. The fuzzy inference applied to obtain a decision fuzzy set for each disease, and crisp decision values attained to determine the certainty of existence for each disease.

### Results

Results indicated that, in the diagnosis of seven cases of kidney disease by examining 21 indicators using fuzzy expert system, kidney stone disease with 63% certainty was the most probable, renal tubular was at the lowest level with 15%, and other kidney diseases were at the other levels. The most remarkable finding of this study was that results of kidney disease diagnosis (e.g., kidney stone) via fuzzy expert system were fully compatible with those of kidney physicians.

### Conclusion

The proposed fuzzy expert system is a valid, reliable, and flexible instrument to diagnose several typical input cases. The developed system decreases the effort of initial physical checking and manual feeding of input symptoms.

Keywords: Computer-aided diagnosis, Diagnosis, Expert systems, Fuzzy logic, Kidney diseases
Introduction

According to global research by the year 2011, chronic kidney disease will affect more than 36 million people around the world with a serious risk. Among nine seemingly healthy people, the research shown that one person has some symptoms of chronic kidney diseases [1]. Chronic renal failure is a severe and irreversible disorder of kidney function that prevents body from balancing fluids, electrolytes, and metabolism [2]. The five important causes of increased global attention to chronic kidney disease include growing prevalence of the disease, the hidden actual outbreak, high cost, subsequent increase of cardiovascular diseases, and increased efforts to find effective solutions to prevent disease progression [3]. Unfortunately, chronic renal failure is usually asymptomatic, and the exact number of patients is unclear. Currently, 1.5 million people around the world are under hemodialysis or kidney transplantation. If governments and people disregard it, this statistic may be doubled within the next few years. Iran has the highest international statistics for the prevalence of kidney diseases, since kidney diseases indicate 15% to 20% growth in Iran. Data shows that Iran has more than 7 million renal failure patients, and other people are not aware of this possible disease. In 2005, 22,376 patients in Iran with advanced renal failure were treated with end-stage renal disease (ESRD) methods (2% peritoneal dialysis, 50% hemodialysis, and 48% kidney transplantation). This number is expected to raise to more than 40,000 people, over the next five years [4].

The natural development of various diseases, the unclear nature of medical data, and the intrinsic vagueness of medical problems require a reliable framework that can deal with the ambiguity by permitting variable and multiple class memberships and facilitating approximate reasoning. Therefore, the fuzzy logic is a valuable tool for describing medical concepts by dealing with them as fuzzy sets [5,6]. Fuzzy logic applied in medical systems [7] almost 20 years after its introduction by Zadeh [8]. Moreover, it has recently prompted interesting implementations [9,10]. Medical diagnosis and prognosis problems are the prime examples of decision making in the face of uncertainty. Dealing with uncertainties is a common problem in pattern recognition, and use of the fuzzy set theory has given rise to many new methods of pattern recognition for medical diagnosis [11]. Disease diagnosis is complicated since patients may demonstrate similar symptoms, but the expert physician may diagnose different diseases. Therefore, this study will assist expert physicians when they have fuzziness in that thinking process [12,13]. The current study introduces a simple and efficient method to create fuzzy expert systems for medical diagnosis. The methodology is general and can be used to diagnose a wide range of diseases. In order to demonstrate the concept of this article, first we study kidney are going to propose our general method which can be used for diagnosis of different diseases. Then, we will apply the proposed method to the collected data in order to create a prototype computer program that can infer accurate diagnosis decisions based on patient data.

Methods

### Medical diagnosis problems

Diagnosis and prognosis are the tasks of medical science. The most important problems in medical diagnosis and prognosis are [14]:

• i) Limited observation and subjectivity of the specialist,

• ii) uncertainties and incompleteness in medical knowledge, and

• iii) short time influence on diagnosis.

These difficulties must be recognized during a medical decision. A patient may demonstrate a set of symptoms that can be attributed to several diseases, but these symptoms may not be strictly numerical. In observing these symptoms, physicians with different professional levels and clinical experience may differ in their diagnoses, resulting in misdiagnosis. In addition, due to unknown noise in the acquisition process, the use of computers in medical diagnosis and prognosis has become necessary, especially due to the increasing size and number of medical data.

### Fuzzy expert system for medical diagnosis

Through this study, a fuzzy expert system developed that employed a set of fuzzy membership functions and rules instead of applying Boolean logic for reasoning about data. Leung et al [15] defined a general structure of the fuzzy system as the main part of a fuzzy use. The following four stages, carried out in order, describe the structure:

• 1) Fuzzy functions: Membership functions defined on the input variables are applied to their actual values to determine the degree of truth for each rule premise.

• 2) Deduction: The truth value for the premise of each rule is computed and applied to the conclusion part of each rule, resulting in one fuzzy subset to be assigned to each output variable for each rule.

• 3) Combination: All fuzzy subsets assigned to each output variable are combined to form a single fuzzy subset for each output variable.

• Defuzzification: This is an optional step that is used when the fuzzy output set needs to be converted to a crisp number.

Medical diagnosis often entails careful examination of a patient to test the existence and strength of symptoms related to a suspected illness in order to decide whether or not the patient suffers from that illness [11]. Because, for example, a symptom such as hematuria may be very strong for one patient but moderate or very weak for another patient. The method of combining a set of symptoms (features and their strengths) to accurately obtain a diagnosis is determined by the physicians’ experience. In the current study, we utilized the physicians’ experience and saved them in sets of fuzzy tables. Three physicians were asked about the possibility of a disease according to patients’ symptoms. For increasing accuracy and in order to achieve better result, comments from a greater number of physicians could be investigated. However, findings of this study revealed that the comments of three physicians are enough. Through this study, the general model is developed for n physicians and was examined and resolved for three physicians.

4) Fuzzy deduction applied to create a computer program that can automatically realize the certainty whether a patient with identified symptoms suffers from any one of a set of suspected illnesses. This certainty for every suspected disease specified by a crisp percentage value. We assumed a set of m diseases S and defined a collective set of n features I relevant to these diseases. Let

$S={s1,s2,s3,…,sm}I={i1,i2,i3,…,in}$

In order to identify patients’ symptoms, they tested against all symptoms in set I and a fuzzy value allocated to each symptom. Fuzzy values chosen from the following set:

${Very Low,Low,Moderate,High,Very High}$

For example, one feature can be determined as < Hematuria, Moderate >. By checking the ill person for all n features of set I and ascribing a suitable fuzzy value for each feature, the set of patient’s symptoms S would be obtained as follows:

$Un={,,,…,}$

Where vi is the fuzzy value allocated to the feature ii when testing the patient, i = 1, …, n.

Any given disease has a set R of kn related features, which is a subset of collective features set I. Table 1 indicates an empty fuzzy table for the disease profile, and it illustrates five fuzzy values for each related feature ri, i = 1, …, k.

Expert physicians must offer suitable values for every entry in the disease profile table based on their experiences. This should be carried out for every disease in the set of considered diseases S. To demonstrate how should tables be filled, Tables 2 and 3 are two typical example profile tables for two diseases according to an expert physician. Similar profile tables also obtained for the rest of the considered diseases in the set S.

In order to diagnose various diseases, some linguistic variables can be assigned including Yes, Maybe, and No as triangular or trapezoidal fuzzy sets. In this study, trapezoidal fuzzy sets considered, as demonstrated in Fig. 1.

$μNo(x)={f1(x)=1x$μMaybe(x)={g1(x)=x-cd-cc≤x$μYes(x)={h1(x)=x-gh-gg≤x

In this study, each physician also asked to weight certain symptoms for a given disease Sj. For instance, a physician asked to identify the importance of dysuria symptom in diagnosis of kidney stone disease. The weightings that each physician assigned to certain symptoms were linguistic variables and selected from the following set:

${Very Low,Low,Medium,High,Very High}$

Similarly, the following trapezoidal fuzzy sets defined for the linguistic variables, as demonstrated in Fig. 2.

Weights and ratings given by a physician for the symptoms of kidney stones and kidney infections were in Tables 4 and 5.

### Fuzzy pattern recognition for medical diagnosis

Disease symptoms set M are obtained when a patient is examined for diagnosis. A typical example for a set of symptoms is given in Tables 6 and 7 for two different diseases, which shows fuzzy values for all features in the collective set I. These profile tables are considered for all diseases, but here there are tables for two diseases in order to demonstrate how they should be filled out. The strength of a non-measurable feature can logically be determined by a fuzzy value; however, other measurable features, such as proteinuria, hypertension, and blood sugar, can be identified by real values in different scales. The subsection number 2.7 presents those fuzzy features.

Considering q number of physicians observing the disease Sj, the comment of each physician regarding the symptom ri about the possibility of disease Sj calculated as

$xijp∈{No,Maybe,Yes}$

where i ∈{1, 2,…, n}, j ∈{1, 2,…, m}, p ∈{1, 2,…, q}.

Since each (Yes, Maybe, and No) fuzzy set is defined as fuzzy numbers, xijp is equal to one of the defined fuzzy numbers.

$xijp=(aijp,bijp,cijp,dijp)$

Comments incorporated using the method by Tsaur et al [16], which combines comments of some experts in order to judge an alternative and makes an overall valuation of the fuzzy judgment. Hybrid fuzzy diagnosis of the possibility of disease Sj with regards to symptoms ri can be calculated as

$xij=(aij,bij,cij,dij)$

where $aij=1q∑p=1p=qaijp, bij=1q∑p=1p=qbijp, cij=1q∑p=1p=qcijp, dij=1q∑p=1p=qdijp$.

Then, the trapezoidal fuzzy number xij transformed to a crisp number. Assume xij is the defuzzification of xij using the center of area method. Thus, the aim is to find a reasonable interval, so that if xij is classified in that interval, determination of whether it belongs to Yes or Maybe or No linguistic variable could be made. Then, the answer should be considered to Equations 13.

$f2(x0)=g1(x0)→x0=bd-ac(b-a)+(d-c)$$g3(x1)=h1(x1)→x1=eh-fg(e-f)+(h-g)$

Hence:

• If , then the overall fuzzy decision is No.

• If xij ∈(0,x0], then the overall fuzzy decision is Maybe.

• If xij ∈(x0,x1], then the overall fuzzy decision is Yes.

xij ∈(x1,100] Then, a hybrid profile table for each kidney disease is made, in order to facilitate the further By utilization of these hybrid diagnosis in the next steps. acquired

Similarly, in order to obtain the total weight of each feature in the diagnosis of disease Sj, wijp can be assumed to be the given weight for ri symptoms in the diagnosis of disease Sj by physician p. Therefore, wijp is defined as one of the above-mentioned trapezoidal fuzzy numbers:

$wijp∈{Very Low,Low,Medium,High,Very High}$

where i ∈{1, 2,…, n}, j ∈{1, 2,…, m}, p ∈{1, 2,…, q}.

So, each of the {Very Low, Low, Medium, High, Very High} fuzzy sets are defined as fuzzy numbers. Thus, wijp as equation 10, is equal to one of the fuzzy numbers related to {Very Low, Low, Medium, High, Very High}.

$wijp=(eijp,fijp,gijp,hijp)$

Hybrid fuzzy weight of symptoms ri in diagnosis of disease Sj is calculated as

$wij=(eij,fij,gij,hij)$

where $eij=1q∑p=1p=qeijp, fij=1q∑p=1p=qfijp, gij=1q∑p=1p=qgijp, hij=1q∑p=1p=qhijp$.

The trapezoidal fuzzy number wij is transformed to a crisp number using the center of area method.

If wij is the defuzzification of wij, let:

• s[f] = the crisp number obtained for feature f

• rij = jth relevant feature of the ith disease

• Pij[rij, v] = certainty of the presence of the ith disease when relevant feature rij has a crisp number xij

• δij = diagnosis decision of the ith disease based on relevant feature rij

• ki = total number of relevant features for the ith disease

• wij = hybrid weight of the rij feature in diagnosing the ith disease

• σi = overall diagnosis decision for ith disease.

The impact of the rij feature on the diagnosis decision can be directly obtained from the hybrid profile table obtained Pij[rij, v]. According to the hybrid diagnosis of the three physicians, the fuzzy value v is obtained from the patient’s symptoms for the feature rij as s[rij]. The effect δij is one of the fuzzy sets Yes, Maybe, and No, denoted as

$δij=Pij [rij,s[rij]]$

By summarizing the impact of all ki related features, the overall diagnosis decision for the ith disease would be acquired by

$σi=(∑j=1j=kiwijδij)/(∑j=1j=kiwij)$

The weighting factor wij is introduced to help physicians determine that some features have more or less importance than other features when diagnosing a disease; therefore, appropriate relative values should be set to the weights. If physicians consider all features with the same importance, the weighting factor is equal for all features. In this case, the weighting step is not necessary and there is no need to fill the weight tables. Then, Equation 13 can be simplified as;

$σi=1ki∑j=1j=kiδj$

The final step is to acquire crisp values that specify the certainty of existence for every disease in set S.

### The model application

Three physicians considered in the model for this case study. Considering the set of diseases S, expert physicians’ experiences obtained in a set of fuzzy tables which each set determined the profile for one illness. In order to denote assurance of the illness existence, three trapezoidal fuzzy sets (Yes, Maybe, and No) considered, as are demonstrated in Fig. 3. Entries in the disease profile tables would be chosen from these fuzzy sets.

$μNo(x)={1x<1020-x1010≤x<20$$μMaybe(x)={x-1020-1010≤x<20120≤x<6070-x70-6060≤x<70$$μYes(x)={x-6070-6060≤x<701x≥70$

Related intervals for No, Maybe, and Yes defined as No = (0, 0, 10, 20), Maybe = (10, 20, 60, 70), Yes = (60, 70, 100, 100); and X0 = 15, X1 = 65.

The following example demonstrates how the model works:

• Suppose that a given disease si has 10 associated symptoms, all of which have identical weight in the diagnosis. Therefore,

$ki=10wij=1;for all,j=1,…,10.$

• Suppose that comments by three physicians are combined using the mentioned method. When applying Equation 14 to realize the diagnostic decisions (δij, j = 1, …, 10), the result is 7 Yes, 2 Maybe, and 1 No.

• The overall diagnostic decision is

$σi=(7 Yes+2 Maybe+1 No)/10$

This fuzzy set is illustrated in Fig. 4.

• The center of area method is considered for defuzzification. Let:

ci = the centroid of the overall diagnosis decision fuzzy set

• cy = the centroid for the Yes fuzzy set

• qi = certainty of the presence of the considered disease si in percent

Therefore, the crisp decision value for disease di is calculated as shown in Equation 18. If the results are Yes for all related symptoms of di, the decision is 100%.

$qi=(ci/cy)×100%$

For this example, the values of ci and cy are 0.55 and 0.87, respectively, demonstrating that the certainty of the presence of the considered disease is 89%, as shown in Fig. 4.

### Features with different type of value

For symptoms that have a different type of value such as type or color, attributes other than severity are important in disease diagnosis. For example, for urinary symptom, the color of a patient’s urine (e.g., yellow, white, or orange) can prompt medical diagnosis of a certain disease. Consequently, a physician diagnoses the disease depending on the patient’s urine color and in accordance with medical experience. For instance, yellow color of urine can lead a physician’s diagnosis to Maybe for kidney stone disease.

### Displacement of measurement attributes

In this research, the signs for quantifiable features such as hypertension and edema are determined as a numeric value. For the sake of simplicity, fixed tables arranged by the physician may be employed to map these numeric values into fuzzy values from the set {Very Low, Low, Moderate, High, Very High}. This solution may be sufficient in some cases; however, the following describe a solution that is more precise and avoids unexpected changes. Glomerular filtration rate (GFR), a test used to determine kidney function, is used for illustration of the point. GFR estimates how much blood passes through tiny filters, or glomeruli, in the kidneys each minute [17].

Fig. 5 shows five fuzzy sets that map percentage values of GFR. As shown in the figure, GFR levels were very low (0–15), low (15–38), medium (30–60), mild to moderate (60–90), and high (90 and above).

Suppose that the following information is saved in the profile table of disease di:

• If the GFR is Medium; certainty of the existence of di will be Maybe.

• If the GFR is High, certainty of the existence of di will be Yes.

Therefore, the diagnosis decision δij for disease di according to the GFR value of 8% is the upper limit of two fuzzy sets: 0.3 Maybe and 0.6 Yes, as illustrated in Fig. 6. This can be included in Equation 13 to evaluate the overall decision.

The above solution can be generalized to contain features that are identified by two numeric values, such as blood pressure, leading to four possible fuzzy sets. The minimum rule should be employed to combine the pairs of fuzzy sets by the AND operator [11].

Results

In the current study, we presented diagnosis decisions acquired by the developed prototype fuzzy expert system using a typical case study. A cross-sectional descriptive study was conducted in a kidney clinic in Tehran. During the nine-week study, 85 patients randomly considered against the suspected diseases in the clinic. Medical diagnosis fuzzy rules formulated and applied using MAT-LAB software (Mathworks, Natick, MA, USA). The prototype system checked for seven suspected kidney infections, that were more common in the nation, and considered a total of 21 features. Symptoms identified by physically examining a patient and manually feeding the input into the prototype program. Obtained diagnosis decisions for all suspected diseases are presented in Table 6 and 7, and output fuzzy sets for the overall diagnosis of two diseases with common symptoms are illustrated in Fig. 7 (refer to Tables 2 and 3).

Based on the input symptoms, the prototype expert system gave a high certainty level of 63.3% for kidney stone and lower levels for all other suspected infections (Table 8). In addition, the result agreed completely with the diagnosis of human expert physicians. Appropriate selection of membership functions for the three fuzzy sets as Yes, Maybe, and No also improved the final results. In the present study, we employed the shapes shown in Fig. 3 and tried various parameter values in order to increase the output certainty level of the most possible disease and decrease that of all others.

Discussion

This paper explained how to understand a specific disease process in its early stages using quantitative analysis and qualitative evaluation of the medical data. Applying fuzzy pattern recognition diagnosis methods in medical issues can simply handle the problems already solved using traditional recognition techniques. The present study aimed to develop a new method in fuzzy logic that can be used to diagnose kidney diseases. A methodology presented that utilizes the experience of skilled physicians and saves it in fuzzy tables to indicate disease profiles. The most obvious finding of the study was that results of diagnoses of kidney diseases (e.g., kidney stone) using the proposed fuzzy expert instrument which was fully compatible to those of kidney physicians. Complete agreement with the diagnosis of human expert physicians obtained in many experiments with various input symptoms in each case study. The created system may be augmented to decrease the effort of initial physical examination and manual feeding of input symptoms. Although, empirical findings in this study provide a new understanding of fuzzy medical diagnosis, the study has some limitations. First, the number of patients and controls used in the study was relatively small. Second, the findings were limited by use of a cross-sectional design. Association of these factors should be investigated in future recognition-based technique studies. Another cohort could be considered in order to test the efficiency of this method. Third, efficiency of existing standard algorithms for analyzing in medical diagnosis can be improved by applying other hybrid soft-computing techniques. Also, the use of fuzzy integrated methods can be more efficient in decision making problems [18]. Further research regarding the role of fuzzy logic would greatly help in solving medical diagnosis problems.

Figures
Fig. 1. No: (0, 0, a, b), Maybe: (c, d, e, f), Yes: (g, h, 100, 100).
Fig. 2. H, High (6, 7, 8, 9); L, Low (1, 2, 3, 4); M, Moderate (3, 4, 6, 7); VH, Very High (8, 9, 10, 10); VL, Very Low (0, 0, 1, 2).
Fig. 3. Fuzzy sets for the certainty of the presence of disease.
Fig. 4. ci = 0.55, cy = 0.87, qi = 90%.
Fig. 5. Fuzzy sets for glomerular filtration rate (GFR) values.
Fig. 6. Fuzzy set of the diagnosis decision for a glomerular filtration rate of 8%.
Fig. 7. Output fuzzy sets for the diagnosis decision of two infections.
Tables

Fuzzy value table for the disease profile

Relevant featureFuzzy value of the symptom
Very LowLowModerateHighVery High
r1
r2
rk

Profile for kidney stone based on a physician’s experience

Properties featureVery LowLowModerateHighVery High
Flank pain bilateralNoYesYesMaybeYes
Flank pain unilateralNoMaybeMaybeYesYes
HematuriaYesMaybeMaybeYesYes
Chill and feverYesYesMaybeMaybeMaybe
Nausea and vomitingYesYesYesNoNo
Frequency and urgencyNoMaybeMaybeYesYes
Urine pusMaybeMaybeMaybeMaybeMaybe
DysuriaNoMaybeYesYesYes

Profile for kidney infection according to physician experience

Properties featureVery LowLowModerateHighVery High
DysuriaMaybeMaybeYesYesYes
Urinary frequencyMaybeYesYesYesYes
Cloudy urineMaybeYesYesYesYes
Purulent urineMaybeMaybeYesYesYes
Hematuria or leukocyturiaNoMaybeYesYesYes
NucturiaMaybeMaybeMaybeYesYes
HesitencyYesYesYesYesYes
SuprapubicYesYesYesMaybeMaybe
Abrupt fever and chillNoMaybeYesYesMaybe
Unilateral or bilateral flank painNoMaybeMaybeYesYes
Nausea and vomitingYesYesMaybeNoNo
Spumy urineYesYesMaybeYesMaybe

Fuzzy weight profile for kidney stone according to a physician’s experience

Properties featureVery LowLowMediumHighVery High
Flank pain bilateral
Flank pain unilateral
Hematuria
Chill and fever
Nausea and vomiting
Frequency and urgency
Urine pus
Dysuria

Fuzzy weight profile for kidney infection according to a physician’s experience

Properties featureVery LowLowMediumHighVery High
Dysuria
Urinary frequency
Cloudy urine
Purulent urine
Hematuria or leukocyturia
Nucturia
Hesitency
Suprapubic
Abrupt fever and chill
Unilateral or bilateral flank pain
Nausea and vomiting
Spumy urine

Typical symptoms for a given input case

FeatureFuzzy value
Flank pain bilateralModerate
Flank pain unilateralModerate
HematuriaHigh
Chill and feverLow
Nausea and vomitingModerate
Frequency and urgencyHigh
Urine pusVery Low
DysuriaVery High

Typical symptoms for a given input case

FeatureFuzzy value
DysuriaVery High
Urinary frequencyVery High
Cloudy urineHigh
Purulent urineLow
Hematuria or leukocyturiaHigh
NucturiaModeratet
HesitencyHigh
SuprapubicHigh
Abrupt fever and chillHigh
Unilateral or bilateral flank painLow
Nausea and vomitingVery Low
Spumy urineLow

Obtained diagnosis decisions for the case study

DiseaseCertainty level (%)
Kidney infection0.451
Polycystic kidney disease0.399
Nephroangiosclerosis0.282
Kidney stone0.633
Chronic renal failure0.381
Renal tubular acidosis0.151
IgA nephropathy0.282

IgA, immunoglobulin A.

References
1. Shiba, N, and Shimokawa, H (2011). Chronic kidney disease and heart failure--Bidirectional close link and common therapeutic goal. J Cardiol. 57, 8-17.
2. Phipps, WJ, Monahan, FD, Sands, JK, Marek, JF, Neighbors, M, and Green, CJ (2003). Medical-surgical nursing: Health and illness perspectives. St. Louis: Mosby
3. Gao, SW, Oliver, DK, Das, N, Hurst, FP, Lentine, KL, Agodoa, LY, Sawyers, ES, and Abbott, KC (2008). Assessment of racial disparities in chronic kidney disease stage 3 and 4 care in the department of defense health system. Clin J Am Soc Nephrol. 3, 442-449.
4. Biniaz, V, Nemati, E, Tayebi, A, Sadeghi Shermeh, M, and Ebadi, A (2013). The effect of vitamin C on parathyroid hormone in patients on hemodialysis with secondary hyperparathyroidism: a double blind, placebo-controlled study. Nephrourol Mon. 5, 962-966.
5. Steimann, F (2001). On the use and usefulness of fuzzy sets in medical AI. Artif Intell Med. 21, 131-137.
6. Gadaras, I, and Mikhailov, L (2009). An interpretable fuzzy rule-based classification methodology for medical diagnosis. Artif Intell Med. 47, 25-41.
7. Phuong, NH, and Kreinovich, V (2001). Fuzzy logic and its applications in medicine. Int J Med Inform. 62, 165-173.
8. Zadeh, LA (1965). Fuzzy sets. Inf Control. 8, 338-353.
9. Belacel, N, and Boulassel, MR (2001). Multicriteria fuzzy assignment method: a useful tool to assist medical diagnosis. Artif Intell Med. 21, 201-207.
10. Chen, SM (1994). Weighted fuzzy reasoning algorithm for medical diagnosis. Decis Support Syst. 11, 37-43.
11. Begum, SA, and Devi, OM (2011). Fuzzy algorithms for pattern recognition in medical diagnosis. Assam Univ J Sci Technol. 7, 1-12.
12. Roychowdhury, A, Pratihar, DK, Bose, N, Sankaranarayanan, KP, and Sudhahar, N (2004). Diagnosis of the diseases--using a GA-fuzzy approach. Inf Sci. 162, 105-120.
13. Saritas, I, Allahverdi, N, and Sert, IU 2003. A fuzzy expert system design for diagnosis of prostate cancer., 4th International Conference on Computer Systems and Techonologies, 2003, Rousse, Bulgaria, Abstract.
14. Melek, WW, and Sadeghian, A (2009). A theoretic framework for intelligent expert systems in medical encounter evaluation. Expert Syst. 26, 82-99.
15. Leung, RWK, Lau, HCW, and Kwong, CK (2003). On a responsive replenishment system: a fuzzy logic approach. Expert Syst. 20, 20-32.
16. Tsaur, SH, Chang, TY, and Yen, CH (2002). The evaluation of airline service quality by fuzzy MCDM. Tour Manag. 23, 107-115.
17. Sebasky, M, Kukla, A, Leister, E, Guo, H, Akkina, SK, El-Shahawy, Y, Matas, AJ, and Ibrahim, HN (2009). Appraisal of GFR-estimating equations following kidney donation. Am J Kidney Dis. 53, 1050-1058.
18. Jahantigh, FF, Malmir, B, and Avilaq, BA (2016). An integrated approach for prioritizing the strategic objectives of balanced scorecard under uncertainty. Neural Comput Applic.