Journal of Medical Systems

, Volume 36, Issue 2, pp 463–473

AMI Screening Using Linguistic Fuzzy Rules

Authors

    • Faculty of Computer Science and Information TechnologyUniversity of Malaya
  • Awang M. Bulgiba
    • Julius Centre, Faculty of Medicine, CRYSTAL, Faculty of ScienceUniversity of Malaya
  • Adel Lahsasna
    • Faculty of Computer Science and Information TechnologyUniversity of Malaya
Original Paper

DOI: 10.1007/s10916-010-9491-2

Cite this article as:
Ainon, R.N., Bulgiba, A.M. & Lahsasna, A. J Med Syst (2012) 36: 463. doi:10.1007/s10916-010-9491-2

Abstract

This paper aims at identifying the factors that would help to diagnose acute myocardial infarction (AMI) using data from an electronic medical record system (EMR) and then generating structure decisions in the form of linguistic fuzzy rules to help predict and understand the outcome of the diagnosis. Since there is a tradeoff in the fuzzy system between the accuracy which measures the capability of the system to predict the diagnosis of AMI and transparency which reflects its ability to describe the symptoms-diagnosis relation in an understandable way, the proposed fuzzy rules are designed in a such a way to find an appropriate balance between these two conflicting modeling objectives using multi-objective genetic algorithms. The main advantage of the generated linguistic fuzzy rules is their ability to describe the relation between the symptoms and the outcome of the diagnosis in an understandable way, close to human thinking and this feature may help doctors to understand the decision process of the fuzzy rules.

Keywords

AMIFuzzy rulesPrediction systemMultiobjective genetic algorithm

Introduction

Ischemic heart disease affects many people worldwide, often leading to sudden death by acute myocardial infarction (AMI). According to World Health Organization, 7.1 million people die yearly from ischemic heart disease, especially in developed countries [1]. In addition, experts expect ischemic heart disease to be the leading cause of death worldwide [2].

AMI is a medical emergency which needs immediate intervention and activation of the emergency medical services [3]. A study [4] shows that 40,000 people, who were wrongly identified as non-AMI patients and discharged from the US Emergency Department, had ultimately an AMI. In addition, this group accounts for 20% to 39% of malpractice dollars awarded in US emergency medicine.

AMI is related to chest pain symptom which is the second most common symptom reported in US emergency departments after abdominal pain [4]. Chest pain has numerous potential causes ranging from ordinary ones such as benign muscle pull to the most life-threatening cause like AMI [5].

Chest pain diagnosis is a challenging task mainly because of two reasons. The first is the large degree of uncertainty of the diagnosis due to the large number of possible diagnosis while the other reason is the limited time available for the clinician to make the diagnosis, especially in the emergency room [6]. Under these circumstances, it is difficult to make an accurate diagnosis and distinguish between AMI and non-AMI cases [7]. To deal with this diagnostic problem in a more effective way and to reduce malpractice liability, many chest pain diagnostic systems [731] were developed to serve as decision support tools to help the physician to discriminate or to classify the patients with chest pain into AMI and non-AMI patients. Most of these systems are based on artificial intelligence (AI) techniques because they are more robust to deal with decision making problems than the conventional methods [32]. Artificial Neural Networks (ANNs), one of the most popular AI techniques, have demonstrated their ability to accurately identify AMI in patients admitted because of chest pain [817]. ANNs, however, have a major drawback which is the lack of transparency as they are essentially black box systems. As a result, the user is prevented from knowing about the decision process of ANNs. Support vector machines (SVMs) were also applied to aid the early diagnosis of AMI [18]. The results show the robustness of the methods to discriminate between the AMI and non-AMI groups, but like ANNs methods, they suffer also from the lack of transparency.

While the only objective of most of the above mentioned systems [830] is the classification accuracy, a few [7, 31] consider also the transparency (also called interpretability) as a second objective. Recently, with development of data mining and knowledge discovery research areas, the concept of transparency in medical decision support system has gained more attention and is considered to have quality almost as important as accuracy [7, 33]. The classification accuracy criterion is used to evaluate the capability of the diagnostic system to correctly assign the patient to the appropriate group while transparency reflects its ability to describe the relation between the symptoms of the patient and his diagnosis in an understandable way. Unlike ANNs and SVMs, fuzzy rules have been advocated as a key tool for expressing the knowledge underlying the system and describing the inputs–outputs relation in natural linguistic rules of the form of IF–THEN rules which allows the user to make valuable interpretation and analysis [34]. These rules are generated using a fuzzy inference scheme, which in some respects, simulates human thinking mechanism and reasoning procedure [35]. In addition, fuzzy logic reasoning is suitable for handling decision problems with uncertainty and partial information [34]. These features of fuzzy rules make them a suitable tool for developing medical decision support system for chest pain diagnosis [35].

There are two ways for generating fuzzy rules: manual and automatic. Using the first way, fuzzy rules are set manually based on the expert knowledge [19, 20] while an automatic generation of rules is performed in the other way using a learning method and a representative data set. Due to the complexity of chest pain diagnosis problem, the difficulty of manually setting the values of fuzzy rules parameters, the availability of the data and the recent development of machine learning algorithms, the automatic fuzzy rules generation has dominated the fuzzy rules generation process in fuzzy chest pain diagnosis systems [2231]. ANNs [2229], evolutionary techniques [30] and decision tree methods [31] are the most commonly used methods to generate and optimize fuzzy system for AMI classification. Most of these systems used the electrocardiogram (ECG) or symptoms as a tool for AMI diagnosis, and their main objective is to optimize the classification accuracy of the AMI fuzzy system. The main disadvantage of these methods is, however, that the transparency of fuzzy rules is often lost during the learning of its parameters [36].

Some studies [7, 31] point to the importance of the transparency in chest pain diagnosis system by extracting understandable rules which can be used for both knowledge discovery and AMI classification. In [7], a genetic programming algorithm is proposed to extract understandable IF–THEN crisp rules for classifying patients with chest pain into different classes based on their symptoms. The authors highlight the importance of the transparency in AMI classification system for understanding the decision process of the system. The use of crisp rules instead of fuzzy rules, however, has limited the capability of chest pain diagnosis because in contrast to crisp rules, fuzzy rules allow partial and simultaneous fulfillment of rules while rule can either be applied or not in the case of crisp rules [37]. In other words, partial applicability of the fuzzy rules is possible. In another study, Exarchos et al. [31], employed the decision tree algorithm C4.5 in the first step to generate crisp rules from data set. These rules are used for both classification and knowledge extraction. In the next step, the generated rules were transformed into a fuzzy model and then optimized using global optimization to increase its classification accuracy. The resulting fuzzy decision tree system is used for ischaemic beat classification in ECG recordings which is a key step in the AMI classification process. Although the fuzzy model achieved better classification accuracy compared with decision tree C4.5, the transparency of fuzzy model is lost during the optimization process of its classification accuracy. It is important, then, to maintain the transparency in the fuzzy rule-base system during the learning process even though it may affect the fuzzy system classification accuracy. Therefore, the tradeoff between the accuracy and the transparency in the fuzzy system modeling has to be taken into consideration during the design process of the fuzzy system.

Recently, multi-objective evolutionary algorithms have shown their effectiveness in finding the best tradeoff between the conflicting objectives [33]. The hybrid genetic-fuzzy techniques use the effectiveness of the genetic algorithms search to provide learning capabilities to fuzzy systems. This approach has not been applied in developing decision support system for chest pain diagnosis In this study, a multi-objective genetic algorithm is applied to identify the relevant factors that help in the diagnosis of acute myocardial infarction (AMI) in the Malaysian population. Furthermore, descriptive fuzzy rules with clear linguistic meaning are generated. These rules describe the relation between the attributes of the patient (symptoms) and the outcome of his diagnosis in natural language that will help doctors to understand the decision process of the fuzzy rules. However, as with all computer-based medical decision support system for diagnosis, the rules should not be used for clinical diagnosis without consulting experienced physicians.

The rest of the paper is organized as follows. Section “Data set” describes the data set used in this study while a brief description of the multi-objective genetic algorithms used in this study is given in Section “Multi-objective genetic algorithms”. In Section “Methodology”, the methodology is detailed and the results and discussion are given in Section “Results and discussions”. Finally, conclusions are drawn in Section “Conclusions”.

Data set

The data set used in this study was extracted from the electronic medical record system (EMR) in Selayang Hospital, a large tertiary-level hospital in Malaysia. It contains the records of 887 patients presented at the Emergency Department for chest pain complaints. All the necessary information about the patient that may be in relation with the chest pain problem is registered using the chest pain clerking form (see Table 1 for more details). In addition, the diagnosis decision whether the patient has AMI or not is also available and it is based on discharge diagnosis. The final decision of the diagnosis is made by specialist physicians after taking into consideration ECG readings, cardiac enzymes and other investigations like angiograms. Thus the diagnosis of AMI was confirmed after all these investigations were carried out. This data set was used in [16] to identify the factors that help to diagnosis acute myocardial infarction (AMI) in order to use them in decision support system for chest pain. Table 1 shows the attributes of the AMI data clustered into groups [38].
Table 1

Independent variables selected from the AMI data

Group

Fields

Demographic

Age, citizen, race, sex, marital status

Nature of chest

Location, onset, pain, pattern, quality

Radiation of pain

Jaw, left arm, laterally, neck, locally, other parts

Relieving factors

Leaning forward, sitting up, GTN, rest, other means

Aggravating factors

Posture, meals, coughing, inspiration, exertion

Associated heart/lung symptoms

Cough, dyspnoea, oedema,orthopnoea, palpitations

Other associated symptoms

Collapse, headache, dizziness,fever, numbness, nausea, sweating, vomiting, fainting

Cardiac risk factors

Age N40, diabetes mellitus, family history, hypertension, physical inactivity, obesity, smoking, known case defaulted treatment, known case on treatment, high cholesterol levels

General examination

Pulses, pulse rate, respiratory rate,systolic BP, diastolic BP

Heart/lung examination factors

Air entry, breath sounds, chest expansion, chest wall, crepitations, heart sounds, JVP, percussion, pleural rub, praecordium, rhonchi

Other examination factors

Abdomen, central nervous(CNS), eye, face

Multi-objective genetic algorithms

Genetic algorithms are meta-heuristic techniques inspired by the evolutionary biology. Multi-objective genetic algorithms are classes of genetic algorithms which are used to solve problems that have multiple and even conflicting objectives [39].

There are two approaches in multi-objective genetic algorithms optimization. The first is to combine the various objective functions into a single function in a linear fashion using weight factors. The drawback of this approach lies in the determination of the optimal weight values that characterize the user preferences. The second approach finds non-dominated Pareto optimal set of solutions for all optimal compromises between the conflicting objectives. It is a practical approach as the decision maker can find solutions with different tradeoff levels. A number of algorithms have been proposed [3941], of which NSGA-II algorithm [42] is among the most widely-used multi-objective genetic algorithms in the literature.

Non-dominated genetic algorithm II

NSGA-II was introduced to overcome the drawbacks of NSGA [43] such as computation complexity, non-elitism approach, and the need for specifying a sharing parameter. This algorithm has two features which makes it an efficient algorithm. The first one is that fitness function of the solution is based on non-dominated ranking and a crowding measure (a measure of density of solutions in the neighborhood), and the other is the elitist generation update procedure. A non-dominated rank is assigned to each individual using the relative fitness. The concept of non-dominated solution can be defined as follows. Individual or solution ‘A’ dominates ‘B’ if the following two conditions hold:
  1. 1.

    ‘A’ is strictly better than ‘B’ in at least one objective, and

     
  2. 2.

    ‘A’ is no worse than ‘B’ in all objectives.

     
The elitism-preserving mechanism of NSGA-II is outlined as follows:
  • Step 1:  Generate an initial population with N chromosomes.

  • Step 2:  Generate an offspring population by iterating the following procedures N times:
    1. 1.

      Select a pair of parent solutions from the current population.

       
    2. 2.

      Generate an offspring from the selected parent solutions by genetic operations.

       
  • Step 3:  Merge the offspring population and current population. Then select the best N solutions from the merged population to construct the next population.

  • Step 4:  If a prespecified stopping condition is satisfied, terminate the execution of the algorithm. Otherwise return to Step 2. In the former case, we choose all the non-dominated solutions in the merged population in Step 3 as the final solution.

Controlled elitist genetic algorithm

It is a variant of NSGA-II proposed by Deb and Goel [44] for controlling the extent of the elite members of the population to maintain the diversity of the population for convergence to an optimal Pareto front. The controlling mechanism is accomplished by allowing only a certain portion of the population to contain in the currently-best-non-dominated solutions. The controlled NSGA II has a better convergence property than the original NSGA II [44]; and for this reason we choose it for our study. Controlled NSGA II is applied for feature selection procedure and for fuzzy system optimization.

Methodology

The methodology used in this study consists mainly of two steps. The first is feature selection procedure which aims at reducing the input dimension by choosing a subset of relevant features, while the second step is the optimization phase in which the fuzzy sets are replaced by well defined linguistic variables to produce a transparent fuzzy system as well as an accurate fuzzy system. During these two steps, controlled NSGA II is employed to find the required balance between the transparency and the classification accuracy in the fuzzy system. The steps are outlined below.

Feature selection using multi-objective genetic algorithm

The aim of this process is to select a subset of features that are relevant to the target concept. An irrelevant feature is either redundant or it does not affect the target concept in any way [45]. By applying this preprocessing step, we aim to reduce the number of features in the fuzzy system to a relatively small set that will still provide relatively accurate results. The modeling objectives of fuzzy system S in this step can be written as follows:
$$ Maximize \,\, f_{acc}(S) , \,\, Minimize f_{input}(S) $$
(1)
where facc(S) is the fuzzy system classification accuracy measured by the area under the ROC curve or AUC for short, and finput(S) is the total number of selected features of fuzzy system S.

To optimize simultaneously these two objectives, controlled elitist genetic algorithm (controlled NSGA II) is applied. The results of this step are Pareto-front solutions that represent a number of fuzzy models with different accuracy-number of inputs values. The fuzzy model chosen in this case is based on the need of the user, that is, if the accuracy is more important than the transparency then a fuzzy model with high accuracy and a high number of features will be chosen. The objective in this study is to find a fuzzy model with good classification accuracy and a relatively small number of features.

Chromosome representation  The chromosome representation of S which represents the selected features is denoted by a concatenated binary bit string of the length n where n is the total number of features in the data set such that each binary bit denotes whether a given input is selected or not during the feature selection process. In this implementation, the selected features are set to 1 while the non-selected features are set to 0.

Genetic operators  A new population P of chromosomes (fuzzy systems) is generated using the genetic operations: selection, cross-over and mutation. To generate a new fuzzy system S, a pair of parent fuzzy systems is selected from the current population using tournament selection based on the Pareto ranking and the crowding distance . In order to maintain the diversity in the next population, the best non-dominated solutions are kept down to only 35% of the population. In addition, the crowding measure is used to calculate the crowding distance for each individual on a non-dominated front. After the selection step, the uniform crossover and uniform mutation with range of 0.01 are applied. These genetic operations are also applied for fuzzy system optimization step (next step).

Fuzzy optimization using multi-objective genetic algorithm

The approach applied to optimize fuzzy rules consists of two steps:
  • 1.  Fuzzy structure initialization First, the initial Mamdani fuzzy system [46] is generated using Fuzzy C-Means Clustering (FCM) method [47]. It is a widely used fuzzy clustering algorithm and it is employed in the first step to establish the structure of the fuzzy system by defining the proper number of fuzzy rules. The generated Mamdani fuzzy rules are written as:
    $$\begin{array}{rll} Rule\ R_{j}&:&If\ x_{1} \ is \ A_{j1} \ and \ldots and \ x_{n}\ is \ A_{jn} \\ &&then\ y \ is \ C_{j} \end{array}$$
    (2)
    where Rj is the label of the j-th fuzzy rule, Aji is an antecedent fuzzy set defined over the input xi and Cj is a fuzzy set representing the consequent class and defined over the output y. All the fuzzy sets are represented by Gaussian functions.
  • 2.  Fuzzy sets replacement Replace the fuzzy sets of the generated fuzzy system by new fuzzy sets as the fuzzy sets resulting from clustering or learning method are usually not interpretable [36]. On the other hand, the new predefined fuzzy sets have clear linguistic interpretations such as low, average and high. The linguistic values of each fuzzy set, Aji, for each attribute xi have to be defined before starting the replacement process. In our case, we use three linguistic values: low, average and high where each of the linguistic values is defined within a specific range of values. Figure 1 shows an example of three linguistic values for the age attribute in AMI data. These new fuzzy sets replace the existing fuzzy sets of the credit amount attribute in the fuzzy rule based system. This idea is similar to that applied by [48].

https://static-content.springer.com/image/art%3A10.1007%2Fs10916-010-9491-2/MediaObjects/10916_2010_9491_Fig1_HTML.gif
Fig. 1

Linguistic fuzzy sets of the AGE attribute AMI data

The replacement of existing fuzzy sets by the new fuzzy sets must consider the following:
  • The replacement of an existing fuzzy set Aji of the rule Rj by \(A^{'}_{ji}\) where \(A^{'}_{ji}\) is one of the linguistic values defined over the xi attribute (\(A^{'}_{ji}\) could be for example either low, medium or high).

  • The replacement procedure has to improve the classification accuracy of the fuzzy system .

  • In addition to the five linguistic values, ’don’t care’ is another linguistic value and it refers to unimportant fuzzy sets that can be deleted without effecting the fuzzy system performance.

Problem formulation  Let Ki be the number of linguistic values or possible antecedent fuzzy sets for each attribute xi. In addition, ‘don’t care’ is considered as another fuzzy set. In this case, we have (Ki + 1) linguistic values for each i-th attribute (i = 1,2,..., n) and each antecedent fuzzy set Aji is selected from one of the Ki linguistic values and ‘don’t care’. The total number of possible combinations of the antecedent linguistic values is (K1 + 1)*(K2 + 2)*...*(Kn + 1).

The task now is to search for the best combination of these antecedent linguistic values that achieve the two objectives, namely maximize the classification accuracy and maximize the transparency by increasing the number of ‘don’t care’ fuzzy sets in the rule base. These two objectives of the fuzzy system S can be written as follows:
$$ Maximize \,\, f_{acc}(S), \,\, Maximize \,\, f_{trans}(S) $$
(3)
where facc(S) is the classification accuracy of the fuzzy system measured by the area under the ROC curve or AUC, and ftrans(S) is the transparency measured by the number of ‘don’t care’ fuzzy sets in the rule base.
Chromosome design  The chromosome is coded as follows:
$$\begin{array}{rll} Chr_{i}&=&\langle \nonumber \underbrace{A_{11}, \ldots, A_{1i}, \ldots, A_{1n}, C_{1}}_{\small (rule1)},\ldots ,\notag\\ [4pt]&& \underbrace{A_{j1} , \ldots A_{ji} \ldots A_{jn} C_{j}}_{\small (rule j)},\ldots, \\&& \underbrace{A_{m1},\ldots, A_{mi},\ldots A_{mn}, C_{m}}_{\small (rule \, m)}\rangle \end{array}$$
(4)
where n and m denote respectively the number of features and fuzzy rules. Aji is the linguistic antecedent value such as ‘low’ and ‘average’ for the i-th attribute and Cj is a consequent class (positive or negative).

The length of the chromosome is (n + 1)*m . We use four linguistic values: low, average, high and ‘don’t care’. Each of these linguistic values is defined by a number. In our case, we set the values 0, 1, 2 and 3 to denote ‘don’t care’, low, average and high respectively. For the consequent class, we set 0 and 1 for negative and positive class respectively. In this case, each antecedent condition Aji ∈ {0,1,2,3} and the consequent class Cj ∈ {0,1}.

The following example is presented to explain this idea. Assume that we generate a fuzzy system with three inputs and two rules in the clustering step and then we get the string ‘01202321’ as one of the best Pareto solutions at the end of the multi-objective optimization process. Figure 2 shows the decoding process of the ‘01202321’ string. Since we have three inputs and one output, the length of string encoding one rule is four. Decoding process of the previous string results in the following rules:
  • Rule1:  If input1 is don’t care and input2 is low and input3 is average than outcome is negative

  • Rule2:  If input1 is average and input2 is high and input3 is average than outcome is positive

https://static-content.springer.com/image/art%3A10.1007%2Fs10916-010-9491-2/MediaObjects/10916_2010_9491_Fig2_HTML.gif
Fig. 2

Chromosome coding with three inputs and two rules

Fuzzy system validation

Validation of fuzzy models is an important step to evaluate their prediction accuracy [49]. In this paper, we apply a common validation technique called tenfold cross-validation where the data set is randomly split into ten mutually exclusive subsets S1, S2, ..., S10 of approximately equal size. The fuzzy rules are trained and tested ten times; each time fuzzy rules are trained on nine subsets and tested on the tenth St subset where t ∈ { 1,2,...,10}. This method is applied to eliminate the bias in the data set [53].

To measure the discriminating power or the classification accuracy of the fuzzy rules, we use the area under the Receiver operating characteristic (ROC) curve or AUC for short, a measure that is commonly used in the medical community to evaluate the diagnostic power of tests for diseases [50].

In addition to the classification accuracy, another criterion which is the transparency should be considered. Transparency can be evaluated through the following criteria: (1) the ability to represent the knowledge characterizing the relations between the knowledge characterizing the relations between the features and their outputs in a series of linguistic fuzzy rules and (2) the number of fuzzy sets per rule [36].

To evaluate our fuzzy system, its accuracy and the transparency should be evaluated with other works applied on the same data set. Bulgiba and Fisher [16] applied neural networks on the same data set. Hence, a comparison between our method (genetic-fuzzy) and their method (Neural networks) will be presented in the following section. The advantages as well as the limitation of each method will be discussed.

Results and discussions

Feature selection

This step aims at selecting the relevant features, i.e. finding a set of features which simultaneously includes the least number of features and can provide good classification accuracy. The results of this step are Pareto-front solutions that represent a set of fuzzy models with their corresponding values of classification accuracy and number of selected features. Table 2 shows the two fuzzy systems FS1 and FS2 selected based on the two objectives (accuracy, number of selected inputs) and which are equally Pareto optimal alternatives. As mentioned before, the first objective is to increase the classification accuracy by maximizing the AUC of the fuzzy classier, while the second objective is minimizing the number of selected features. The choice of solution is based on the users preference; that is whether the user needs a fuzzy system with a fewer number of inputs (less complexity) or higher AUC value (more accurate). Since our main objective is to select the minimum number of factors, the first solution FS1 which includes five inputs is chosen. Thus, the selected features are sex, onset of pain, pulse rate, systolic BP and aspartate transaminase. These five features are identified as the most relevant features and are used for the next step to build the final fuzzy system.
Table 2

Results of the feature selection procedure (FSP) using multi-objective GAs

Before FSP

Initial FS

No of feature

Labels of features

AUC value

48

See Table 1

0.56

After FSP

FS1

5

Sex,

0.73

Onset of pain,

Pulse Rate,

Systolic BP,

Aspartate transaminase,

FS2

7

Age,

0.75

Sex,

Quality of pain,

Radiation to left arm,

Aggrav by exertion,

CAD risk family history,

Diastolic BP

Optimization of fuzzy system

This step aims at (1) replacing the existing fuzzy sets with well defined linguistic fuzzy sets, (2) reducing the number of fuzzy sets by deleting the irrelevant ones from the rule based, and (3) optimizing the classification accuracy.

Table 3 shows an example of the Pareto-front solutions of the first subset S1. These solutions are equally Pareto optimal alternatives and each of these solutions can be used based on the modeling objective of the user. Since the prediction classification is important in our case, it is necessary to maintain the accuracy prediction as high as possible while improving the transparency by reducing the number of fuzzy sets involved in the fuzzy system. As a result, the first solution sl1 which has the highest prediction accuracy is selected for the first subset. The same procedure is applied for the other subsets. Table 4 shows the selected solutions for all subsets. The average fuzzy sets per rule is reduced from five fuzzy sets per rules—where each fuzzy set corresponds to one of the five selected inputs—to 2.9 fuzzy sets per rule while the AUC value slightly dropped from 0.73 to 0.72. That is, there is an improvement of 42% of the transparency against 1% of decreasing in the accuracy. Therefore, using this initial result, we may say that by using this approach the transparency of the fuzzy system is improved while the classification accuracy is almost maintained.
Table 3

AUC values of pareto-front solutions of the first subset and their corresponding number of selected fuzzy sets

Solutions

sl1

sl2

sl3

sl4

sl5

sl6

sl7

sl8

sl9

sl10

All fuzzy sets

85

85

85

85

85

85

85

85

85

85

Selected fuzzy sets

45

45

45

45

42

42

25

25

20

20

AUC training

0.74

0.73

0.74

0.73

0.73

0.73

0.68

0.58

0.5

0.58

AUC testing

0.71

0.70

0.71

0.64

0.64

0.62

0.67

0.58

0.5

0.58

Table 4

AUC values of selected fuzzy systems for all subsets and their corresponding number of selected fuzzy sets

Subsets

S1

S2

S3

S4

S5

S6

S7

S8

S9

S10

Aver

All F. sets

85

85

85

85

85

85

85

85

85

85

85

Selected F. sets

45

45

53

43

55

49

45

49

55

51

49

Initial F. sets /rule

5

5

5

5

5

5

5

5

5

5

5

Selected F. sets /rule

2.6

2.6

3.1

2.5

3.2

2.9

2.6

2.9

3.2

3

2.9

AUC training

0.74

0.75

0.72

0.69

0.75

0.74

0.74

0.73

0.74

0.73

0.73

AUC testing

0.71

0.63

0.82

0.74

0.63

0.58

0.72

0.75

0.81

0.76

0.72

The ROC curve of the optimized fuzzy system of subset 3 which achieves the best classification accuracy at 0.82 is presented in Fig. 3. This fuzzy system is considered as the best classifier and therefore we can use its rules for prediction, i.e. to differentiate between the positive and negative classes of AMI.
https://static-content.springer.com/image/art%3A10.1007%2Fs10916-010-9491-2/MediaObjects/10916_2010_9491_Fig3_HTML.gif
Fig. 3

ROC curve for fuzzy system of subset 3

In addition to the classification accuracy, the fuzzy sets used in these rules are well defined. Figure 4 shows the plot of fuzzy sets of the ’onset’ attribute. It consists of four values: sudden, exertion, gradual and others. Our method is designed, as described in Section “Fuzzy optimization using multi-objective genetic algorithm”, in such a way that ’onset’ variable takes one of these values or ‘don’t care’. As a result, these rules are understandable and readable as they contain only an average of three fuzzy sets per rule and expressed in natural language as shown in Fig. 5. Furthermore, this kind of rules indicates some relationship between the symptoms of a patient and his diagnosis, and therefore such a system can be used as a decision support tool.
https://static-content.springer.com/image/art%3A10.1007%2Fs10916-010-9491-2/MediaObjects/10916_2010_9491_Fig4_HTML.gif
Fig. 4

Plot of the fuzzy sets of the input ‘ONSET’

https://static-content.springer.com/image/art%3A10.1007%2Fs10916-010-9491-2/MediaObjects/10916_2010_9491_Fig5_HTML.gif
Fig. 5

Descriptive fuzzy rules of subset 3

Comparison with other studies  Bulgiba and Fisher [16] have applied neural networks on the same data set for chest pain diagnosis. The main objective of their study was to investigate the effect of the input selection on the neural network accuracy. The results achieved were compared with those achieved by the statistical method logistic regression. The authors found that neural networks outperformed logistic regression in all the cases but the difference was not statistically significant.

A comparison between the results of their study and our study using the accuracy and the transparency measures is given below.

Comparison using the accuracy and the transparency measures  As Table 5 shows, the AUC value of neural networks with nine inputs is better than the genetic-fuzzy with five and seven inputs. In addition, the genetic-fuzzy system with seven inputs is better than that with five and 2.9 inputs. This result is expected as there is, in general, a trade-off between the accuracy and the number of inputs selected [51]. In addition, neural networks accuracy is generally better than hybrid fuzzy systems such as neuro-fuzzy and genetic-fuzzy systems [52]. In a study conducted by [53], a comparison between neural networks and neuro-fuzzy system was made. The above mentioned study found that neural networks method is more accurate than neuro-fuzzy system. This result is in accordance with ours and this is due to the various approximations that are made in fuzzification/defuzzification and fuzzy arithmetic steps that affect the classification accuracy of the fuzzy system [53]. Hence, from this study, we can understand that neural networks are probably more accurate than genetic-fuzzy system but its use in chest pain diagnosis is questionable as neural networks are lack transparency and the physician may need to know about the working mechanism of the chest pain decision support system and how a particular conclusion was made. This information is important for the physician in order to be able to evaluate the system’s decision and whether to be considered or not. In such a case, it is reasonable to trade some accuracy for extra transparency [54]. Our method, on the other hand, considers the transparency in chest pain diagnosis system without neglecting its accuracy by maintaining a balance between these two objectives. Our approach is especially useful in understanding the inputs–outputs relation and performing data analysis.
Table 5

AUC values of ANNs and multi-objective genetic algorithms

 

ANNs

Multi-objective genetic-fuzzy

AUC testing

0.792

0.75

0.73

0.72

Number of inputs

9

7

5

2.9

Conclusions

In this study, a transparent fuzzy classifier system is generated from AMI data. To generate this fuzzy model, a feature selection method is first applied to reduce the number of features by selecting only the relevant ones. An optimization process is then performed to reduce the number of fuzzy sets while increasing the accuracy of the fuzzy system. In this system, the relation between the symptoms of a patient and his diagnosis is expressed through understandable linguistic fuzzy rules. This fuzzy system not only performs predictions but also analysis that can assist in AMI screening and diagnosis.

Acknowledgements

This research is supported by a fundamental research grant scheme from Ministry of Higher Education, Malaysia.

Copyright information

© Springer Science+Business Media, LLC 2010