Application of genetic algorithm-based intuitionistic fuzzy neural network to medical cost forecasting for acute hepatitis patients in emergency room

Abstract

Taiwan is an endemic area for chronic hepatitis disease. Since the early 1980’s, liver cancer has become the first cancer mortality causes among other cancers in Taiwan. Besides, liver cirrhosis and chronic liver diseases are the sixth rank and seventh rank in the causes of death, respectively. This is a serious disease affecting people’s health and it brings a lot of medical cost as well. This study develops a medical cost forecasting model for the acute hepatitis patients in the emergency room. In order to consider the uncertainty and hesitation in the human being’s thinking, this study employs the intuitionistic fuzzy logic (IFL) since it considers membership, non-membership, and hesitation values simultaneously. The proposed model combines the intuitionistic fuzzy neural network (IFNN) with Gaussian membership function and Yager-Generating function to enhance the performance of FNN. Furthermore, a back-propagation learning algorithm and genetic algorithm (GA) are applied in order to optimize the parameters and weights of the proposed IFNN. The proposed IFNN is applied to solve ten benchmark datasets including the nonlinear control and prediction problems. The computational results showed that the GA-IFNN is more efficient than conventional algorithms, such as an artificial neural network (ANN), a fuzzy neural network (FNN), and a support vector regression (SVR). In the real-world problem, the proposed method can really support physicians in planning medical resources and make a good decision to make the most efficient use of limited resources.

Keywords

Fuzzy neural network intuitionistic fuzzy logic intuitionistic fuzzy neural network continuous genetic algorithm medical cost forecasting

1 Introduction

Hepatitis is a medical condition defined by the inflammation of the liver and characterized by the presence of inflammatory cells in the tissue of the organ. It may occur with limited or no symptoms, but often leads to jaundice, poor appetite and malaise. Acute hepatitis lasts less than six months and chronic when it persists longer. Usually, a patient who has hepatitis should have several treatments in hospital before recovering. During the treatment period, the hospital needs to prepare medicines and medical applications. However, each patient has a unique condition. This situation raises a difficulty for the hospital in preparing the necessary medical resources. If the medical cost can be predicted in advance, the hospital can prepare for the related medical resources efficiently in order to provide high-quality treatment and avoid the unnecessary resource waste. Therefore, to reduce waste and increase the efficiency, developing a cost predicting system to predict medical cost for patients has become a very critical issue in hospital.

On the other hand, data mining techniques have been applied to many practical applications including healthcare. Among them, artificial neural network (ANN) is one of the most popular data mining techniques and has obtained many promising results. ANN is a system from neurophysiology models. In general, an ANN consists of a collection of simple, nonlinear computing elements, whose inputs and outputs are connected together, to form a network [1]. ANNs have been employed to solve the medical problems [2 –4]. In order to have both merits of ANN and fuzzy set theories, fuzzy neural network (FNN), which is another data mining technique, has been proposed and successfully applied to many areas, such as control, identification, prediction, pattern recognition, and bioengineering. FNNs inherit their learning ability from neural networks and their inference technology from fuzzy systems. Therefore, FNNs is able to solve the aforementioned characteristic behaviors [5 –16]. The fuzzy neural networks combine the low-level learning and computational power of neural networks into fuzzy systems and the high-level, human-like thinking and reasoning of fuzzy systems to neural networks.

Since the hepatitis is not only to bring health threat in the Taiwan, it is also a tremendous and threatening disease all over the world. With respect to health care attention and both the progress and the health care costs more and more attention, not only hospital is very concerned about this problem, the patient itself and the insurance companies are also concerned about this issue. It is critical to develop a forecasting model for medical cost. In addition, FNN has been widely used in various fields of research, and it can be established the prediction model with good accuracy. Therefore, the study refers the architecture of fuzzy neural network and proposes an improved method, which integrates the concept of intuitionistic fuzzy sets with the fuzzy neural network. Then, the proposed method is applied to establish the forecasting model for medical cost.

John Holland, from the University of Michigan, initiated his work on genetic algorithm (GA) at the beginning of the 1960s. His first achievement was the publication of adaptation in natural and artificial system [17]. He had two goals in mind: to improve the understanding of natural adaptation process, and to design artificial systems having properties similar to natural systems [18]. The basic idea is as follows: the genetic pool of a given population potentially contains the solution, or a better solution, to a given adaptive problem. This solution is not “active” because the genetic combination on which it relies is split between several subjects. Only the association of different genomes can lead to the solution. Holland’s method is especially effective because it not only considers the role of mutation, but it also uses genetic recombination (crossover) [19]. The crossover of partial solutions greatly improves the capability of the algorithm to approach, and eventually find, the optimal solution. The essence of the GA in both theoretical and practical domains has been well demonstrated [20]. However, despite the distinct advantages of a GA for solving complicated, constrained and multi-objective functions where other techniques may have failed, the full power of the GA in application is yet to be exploited [21, 22]. Kuo et al. [13] proposed a fuzzy neural network (FNN) that can process both fuzzy inputs and outputs. The continuous GA (CGA) was employed to enhance its performance. Kuo et al. [23] employed growing self-organizing map (GSOM) algorithm and CGA-based SOM to improve the performance of SOM.

According to aforementioned statements, this study will integrate the intuitionistic fuzzy logic (IFL) in the FNN to develop the intuitionistic fuzzy neural network (IFNN) and employ the genetic algorithm (GA) to optimize the parameters and weights which are in the proposed IFNN called genetic algorithm-based IFNN (GA-IFNN). Then, it is applied to medical cost forecasting problem.

The remainder of the paper is organized as follows. The intuitionistic fuzzy neural network (IFNN) and the genetic algorithm (GA) based learning algorithm, which is used to optimize the proposed IFNN, are described in Section 2. In Section 3, ten computational experiments, using benchmark functions, demonstrate the performance of the proposed GA-IFNN. The forecasting model of the medical cost is developed and the test results in Section 4. Finally, a brief conclusion is drawn in Section 5.

2 The intuitionistic fuzzy neural network

2.1 The intuitionistic fuzzy sets (IFSs)

The fuzzy set theory was proposed by Zadeh [24] and has been applied successfully in various fields [25, 26]. The theory states that the membership of an element to a fuzzy set is a single value between zero and one, and there is not certain that an element’s degree of non-membership in a fuzzy set is equal to one minus the degree of membership. However, there is some of uncertain degree. To explain the uncertain degree, the concept of IFS was introduced by Atanassov [27, 28], which added an additional attribute parameter called non-membership [29]. Bustince and Burillo [30] showed that vague sets (VS) are a kind of IFS. Generally, IFS is a useful means to describe and deal with vague and uncertain data. They have received wide attention in recent years. Many studies have applied IFS to solve complex problems such as data mining [31], decision-making [32 –39], clustering problem [40, 41], forecasting problem [42], pattern recognition [43 –45] and medical problems [46, 47]. IFSs were proposed as an extension of fuzzy sets. An IFS A in a fixed set E is an objective of the expression: $A = {x, μ_{A} (x), υ_{A} (x) 〉 x \in E},$ (1)

where the functions, μ_A : E → [0, 1] and υ_A : E → [0, 1] respectively denote the degree of the membership and the degree of non-membership of the element, and x ∈ E When μ_A (x) + υ_A (x) =1 for every x ∈ E, the fuzzy set with a membership function, μ_A (x) has the IFS expression: $A = {x, μ_{A} (x), 1 - μ_{A} (x) 〉 | x \in E},$ (2) under the condition that υ_A (x) =1 - μ_A (x) for every x ∈ E.

Furthermore, the uncertain degree must be considered for an IFS, A in E. The degree of hesitation for an element, x ∈ E in A is defined as: $π_{A} (x) = 1 - μ_{A} (x) - υ_{A} (x)$ (3)

π_A (x) is the degree of hesitation of x to A and 0 ⩽ π_A (x) ⩽1 for all x ∈ E.

According to [28, 29], to describe an IFSs completely, the model should be included the membership function, non-membership function, and hesitation degree. A concept of IFSs is that to consider the non-membership function, therefore, obtaining the hesitation degree. In order to demonstrate the IFSs completely, the Yager-generating functions [30] is employed in this study. Because the advantage of the Yager-generating function is that, in the functions for each value of α ∈ (0, ∞), a particular fuzzy complement can be well defined, which includes non-membership and hesitation degree. Thus, the intuitionistic fuzzy complement with Yager-generating functions is shown as: $\begin{matrix} N (x) = (1 - x^{α})^{1 / α}, α > 0 \\ where N (1) = 0 and α (0) = 1 \end{matrix}$ (4)

Therefore, using Atanassov’s intuitionistic fuzzy complement with Yager-generating functions, IFSs become: $A = {〈 x, μ_{A} (x), 1 - μ_{A} (x)^{α})^{1 / α} 〉 | x \in E},$ (5)

and the degree hesitation is as follows: $π_{A} (x) = 1 - μ_{A} (x) - (1 - μ_{A} (x)^{α})^{1 / α}$ (6)

where a > 0.

After defining the functions in IFSs, the degree of hesitation, the membership degree is calculated using a linear combination of μ_A (x) and π_A (x). Since the membership function, non-membership function, and hesitation degree are defined, therefore, the intuitionistic fuzzy neural network (IFNN) is developed with the concept of IFS. The model of the proposed IFNN and the learning algorithm are illustrated in the follow section.

2.2 The intuitionistic fuzzy neural network (IFNN)

The advantage of fuzzy neural network is that it combines the advantages of fuzzy control and artificial neural networks, and obtains the fuzzy IF-THEN rules. As the fuzzy neural network, the fuzzy IF-THEN rule is employed in IFNN. The k-th rule, which is instantiated as:

$\begin{matrix} Rulek : IF x_{1} is A_{1 k} and A_{2 k} and x_{n} is A_{nk} \\ THEN y_{k} is B_{k} \end{matrix}$ (7) where x₁, …, x_n are the input variables, n is the number of input variable, and y_k is the output variable, it means the value of forecasting. x₁, …, A_nk are the linguistic terms of the pre-condition with the Gaussian membership function. The architecture of IFNN is shown in Fig. 1 [48].

Fig.1

IFNN structure.

An integration function, f is associated with the fan-in of a unit and serves to combine information, activation, or evidence from other nodes. This function provides the net input for this node: $net - input = f (u_{1}^{k}, u_{2}^{k}, . . ., u_{p}^{k}; w_{1}^{k}, w_{2}^{k}, . . . w_{p}^{k})$ (8)

where the superscript shows the layer number.

A second action of each node is to output an activation value (act (f)) as a function of its net-input: $output = o_{i}^{k} = act (f)$ (9)

Next, the detailed computation of each layer is shown as follows:

Layer 1: The nodes in the layer only obtain an input value to the layer 2. $f = u_{i}^{1} and act = f$ (10)

The link weight of layer 1 $(w_{i}^{1})$ equal 1.

Layer 2: In the proposed IFNN, the Gaussian function is employed for the membership function, it shows in Equation (11), $f = M_{xi}^{j} (m_{ij}, σ_{ij}) = exp {- \frac{(u_{i}^{2} - m_{ij})^{2}}{σ_{ij}^{2}}}$ (11)

where m_ij is the center (mean) and σ_ij is the width (variance) of the Gaussian function of the jth term of the ith input linguistic variable x_i.

According to Equation (6), $act = 1 - (1 - f^{α})^{1 / α}$ (12)

The link weight of layer 2 $(w_{ij}^{2})$ can be interpreted as m_ij.

Layer 3: Using the fuzzy intersection operator, AND, to translate the degree of accommodation into firing strength, $f = min (u_{1}^{3}, u_{2}^{3}, \dots u_{p}^{3}) and act = f$ (13)

The link weight of layer 3 $(w_{i}^{3})$ is 1.

Layer 4: This structure uses the inference model of Mamdani. According to this inference model, this layer drives the OR operation of fuzzy inference: $f = \sum_{i = 1}^{p} u_{i}^{4} and act = (1, f)$ (14)

The link weight of layer 4 $(w_{i}^{4})$ equal 1.

Layer 5: The final layer of the IFNN architecture, and operate the defuzzification process. $f = \sum m_{ij}^{5} σ_{ij}^{5} u_{i}^{5} and act = \frac{f}{\sum σ_{ij} u_{i}^{5}},$ (15) where $m_{ij}^{5}$ and $σ_{ij}^{5}$ are the mean and the variance of the membership functions, respectively. The link weight at layer five $(w_{ij}^{5})$ is $m_{ij}^{5} σ_{ij}^{5}$ .

2.3 Genetic algorithm-based intuitionistic fuzzy neural network (GA-IFNN)

Other than the back-propagation learning algorithm of the IFNN, this study also integrates the GA with IFNN to provide a better initial parameters, including the u_ij, σ_ij, α_ij of the membership function in Layer 2 and the weight for the IFNN. This can avoid the local minimum. The procedures of GA in this study are as follows:

Step 1. Initialization

Setup the parameters, crossover rate (CR) and mutation rate (MR). Therefore, generate n structures of population randomly and set up the number of generation and fitness function. In this study, every gene in the chromosome is encoded with a continuous number, which is between 0 and 1. The chromosome is represented in Fig. 2, where m is the number of nodes in Layer 2, n is the number of nodes in Layer 3, i is the number of input variables, and j is the membership function.

Fig.2

The representation of chromosome.

Step 2. Evaluate the chromosomes

Calculate the fitness function value for each chromosome using Equation (16): $f_{p} = \frac{1}{\sum_{i = 1}^{N} (Y_{i} - T_{i})^{2}}$ (16) where p = 1,2, ... ,k, and k is the population size. T_i is the actual value, Y_i is the forecast value, i = 1,2, ... , number of data, and N is the total number of data.

Step 3. Selection

The tournament selection is used in the selection process [49, 50]. Tournament selection involves running several “tournaments” among a few individuals chosen at random from the population. The winner of each tournament (the one with the best fitness) is selected for crossover. Selection pressure is easily adjusted by changing the tournament size. If the tournament size is larger, weak individuals have a smaller chance to be selected. The chromosomes would be ranked and evaluated. The number of chromosomes to crossover is decided by CR. If CR equals 0.9, there are 90% chromosomes of population to crossover.

Step 4. Crossover

Randomly generate an integer K within 0 to the dimension of chromosomes, then use K as the middle point. The parameter before K will remain the same while the parameter after K will exchange with each other. Assume the parameter of the two chromosomes located on K is x (i) and y (i) respectively, the operation processes are:

Randomly generate an integer M between 1 and 1000, then calculate the $△ x = \frac{△ x}{M} and △ y$ through Equation (19) [51]: $△ x = \frac{△ x}{M} and △ y = \frac{△ y}{M}$ (17)

Calculate the value of x′ (i) and y′ (i) through Equation (20): $x^{'} (i) = x^{'} (i) + △ y - △ x and y^{'} (i) = y^{'} (i) + △ x - △ y$ (18)

Using the processes above to update the parameter values between paired chromosomes, of which can generate the population with diversity.

Step 5. Mutation

The chromosomes which are not selected to crossover, it means that these chromosomes have worse fitness, will have mutation process. The mutation rate (MR) control the number of gene on the chromosome to mutation. The selected genes would generate a random number between 0 and 1.

Step 6. Evaluate new chromosomes

Eliminate the chromosomes with lower fitness function values and add the new chromosomes with higher fitness function values.

Setp 7. If the stop criterion is satisfied, stop; otherwise, go back to Step 3.

In this study, there are fifty chromosomes in the population, and there are five hundred iterations. These settings are fixed in all experiments conducted in this study.

2.4 Performance criteria

In order to test the proposed IFNN, this study uses Matlab to program the code. Three different benchmark functions are used to verify the proposed model. This study compares the proposed IFNN with other algorithms, including a FNN, a SVR andan ANN.

Besides FNN, this study also uses artificial neural network (ANN) and support vector regression (SVR) to construct the forecasting models for comparison. The LIBSVM package developed by Chang and Lin [52] is used to construct the SVR model. The ANN, which is a feed forward neural network with back-propagation learning algorithm, is coded in C++programming language. The forecasting performance is evaluated using the performance measures, the mean square error (MSE) and the mean absolute difference (MAD). The definitions of the measures are shown as Equations (21) and (22): $MSE = \frac{1}{N} \sum_{i = 1}^{N} (Y_{i} - T_{i})^{2}$ (19)

and

$MAD = \frac{1}{N} \sum_{i = 1}^{N} | Y_{i} - T_{i} |$ (20) where T_i is the actual value, Y_i is the forecast value and n is the total number of data. The parameters for both algorithms are important, since they have a significant effect on the performance.

For the experiments, the K-fold cross-validation is employed to confirm the robustness of the developed models. The data set is divided into k subsets, and repeated k times. Each time, one of the k subsets is used as the test set and the other k-1 subsets are put together to form a training set. Then the average error (e.g. MSE) across all k trials is computed. In this study, there are 90% data is used to train samples and the subsequent 10% used to test sample. The goal is to determine whether the IFNN is significantly better than other algorithms.

3 Computational results

For testing the performance of the proposed GA-IFNN, this section will show the evaluation results using ten benchmark datasets

3.1 The simulation cases

The sources of the ten benchmark datasets are summarized in Table 1. The datasets 1 to 7 are generated from the functions, and datasets 8 to 10 are real world problems.

Table 1
The benchmark datasets

Dataset Source # of

Attributes

1 Ackley function 2

2 Lim et al. (2002) non-polynomial function 2

3 Hartmann function 3

4 Dette &Pepelyshev (2010) exponential function 3

5 Mackey-Glass time series 4

6 Gramacy &Lee (2009) function 4

7 Friedman (1991) function 5

8 Auto MPG6 prediction 5

9 Airfoil self-noise data 5

10 Yacht hydrodynamics data set 6

Dataset	Source	# of
1	Ackley function	2
2	Lim et al. (2002) non-polynomial function	2
3	Hartmann function	3
4	Dette &Pepelyshev (2010) exponential function	3
5	Mackey-Glass time series	4
6	Gramacy &Lee (2009) function	4
7	Friedman (1991) function	5
8	Auto MPG6 prediction	5
9	Airfoil self-noise data	5
10	Yacht hydrodynamics data set	6

3.2 Parameters determination

This study proposed two algorithms to optimize the parameters in IFNN. They are the back-propagation learning algorithm and GA. In the back-propagation learning algorithm, the learning rate (η) affects the learning efficiency significantly. There are two parameters, crossover rate (CR) and mutation rate (MR), in the GA. In order to reduce the required number of simulations, the Taguchi method which uses orthogonal parametric arrays, is employed [53]. The orthogonal arrays only identify the main effects and not the interactions between the parameters. The method implements the efficient screening of a large number of parameters and identifies the parameters that are more impact on the performance.

Five factors with three levels are used to design the parameters for the back-propagation learning algorithm. The notations of the factors are as follows: the learning rate of mean (η_m), the learning rate of standard deviation (η_s), the learning rate of Yager-parameter (η_α), the learning rate of weight (η_w), and the momentum (ρ). The levels of the parameters are as follows: η_m, η_s ∈ (0.0005, 0.001, 0.005) , η_α ∈ (0.001, 0.005, 0.009), and. Therefore, a L₂₇ (3⁵) orthogonal array is used for the experiment. The generated orthogonal array has 27 types of combinations. There are two parameters, CR and MR, in the genetic algorithm. For the simulations, three levels of both parameters are used, CR ∈ (0.7, 0.8, 0.9) and MR ∈ (0.1, 0.2, 0.3). Because there are nine combinations of the parameters, all of them are used in the experiments, without Taguchi method.

The test for each combination is performed ten times and five hundred iterations are used, to allow the optimal training parameters to be determined. This experiment determines the lowest MSE, so the-lower-the-better criterion is used for the calculation. The software package, MINITAB, is used to perform the Taguchi experiment. This study sets the MSE as the objective. The smaller MSE is better, so this experiment features the-lower-the-best characteristics. Table 2 shows the parameters of back-propagation learning algorithm, and

Table 2
The parameters of back-propagation learning algorithm

η _m η _s η _α η _w ρ

Dataset 1. 0.005 0.005 0.009 0.05 0.01

Dataset 2. 0.005 0.001 0.001 0.05 0.01

Dataset 3. 0.0005 0.0005 0.001 0.01 0.05

Dataset 4. 0.001 0.001 0.005 0.05 0.01

Dataset 5. 0.0005 0.0005 0.001 0.05 0.01

Dataset 6. 0.0005 0.001 0.009 0.1 0.01

Dataset 7. 0.001 0.005 0.005 0.05 0.01

Dataset 8. 0.005 0.005 0.001 0.01 0.05

Dataset 9. 0.001 0.001 0.001 0.05 0.05

Dataset 10. 0.001 0.001 0.005 0.05 0.01

	η _m	η _s	η _α	η _w	ρ
Dataset 1.	0.005	0.005	0.009	0.05	0.01
Dataset 2.	0.005	0.001	0.001	0.05	0.01
Dataset 3.	0.0005	0.0005	0.001	0.01	0.05
Dataset 4.	0.001	0.001	0.005	0.05	0.01
Dataset 5.	0.0005	0.0005	0.001	0.05	0.01
Dataset 6.	0.0005	0.001	0.009	0.1	0.01
Dataset 7.	0.001	0.005	0.005	0.05	0.01
Dataset 8.	0.005	0.005	0.001	0.01	0.05
Dataset 9.	0.001	0.001	0.001	0.05	0.05
Dataset 10.	0.001	0.001	0.005	0.05	0.01

Table 3 shows the parameters of GA-IFNN after the Taguchi experiments.

Table 3

The parameters of GA-IFNN

	CR	MR
Dataset 1.	0.8	0.2
Dataset 2.	0.8	0.3
Dataset 3.	0.9	0.2
Dataset 4.	0.9	0.3
Dataset 5.	0.9	0.3
Dataset 6.	0.8	0.3
Dataset 7.	0.8	0.3
Dataset 8.	0.8	0.2
Dataset 9.	0.8	0.3
Dataset 10.	0.9	0.3

3.3 Computational results

The simulation results (MSE) are shown in Tables 4 and 5, including the training data and testing data, respectively. Furthermore, the results of MAD are shown in Tables 6 and 7. The computational time of all compared algorithms are shown in Table 8. The results are obtained by running 500 iterations for each algorithm. We can see that the proposed GA-based IFNN needs longer computational time. But, it can offer the better results.

Table 4
Computational results (MSE) of training data

GA-IFNN IFNN FNN ANN SVR

Dataset 1. mean 0.003256 0.005050 0.005260 0.042325 0.005109

best 0.002193 0.004963 0.005139 0.042000 0.005109

Dataset 2. mean 0.000147 0.000410 0.000307 0.002633 0.008128

best 0.000129 0.000387 0.000146 0.002347 0.008128

Dataset 3. mean 0.007290 0.017032 0.020527 0.025788 0.048970

best 0.007028 0.007588 0.003158 0.025745 0.048970

Dataset 4. mean 0.000154 0.001459 0.004118 0.000729 0.003369

best 0.000141 0.000677 0.004081 0.000717 0.003369

Dataset 5. mean 0.001683 0.004753 0.008993 0.004398 0.006797

best 0.001413 0.001953 0.000378 0.004372 0.006797

Dataset 6. mean 0.002527 0.013156 0.016594 0.018428 0.007058

best 0.002059 0.012392 0.013471 0.016727 0.007058

Dataset 7. mean 0.000258 0.000012 0.023053 0.001716 0.004828

best 0.000245 0.000004 0.003908 0.001713 0.004828

Dataset 8. mean 0.003395 0.004840 0.005049 0.007061 0.007058

best 0.002920 0.004793 0.005026 0.007036 0.007058

Dataset 9. mean 0.011630 0.011695 0.030777 0.015668 0.015156

best 0.008077 0.009029 0.021855 0.015388 0.015153

Dataset 10. mean 0.001293 0.001634 0.052973 0.002092 0.003836

best 0.000590 0.001391 0.043681 0.001201 0.003836

		GA-IFNN	IFNN	FNN	ANN	SVR
Dataset 1.	mean	0.003256	0.005050	0.005260	0.042325	0.005109
	best	0.002193	0.004963	0.005139	0.042000	0.005109
Dataset 2.	mean	0.000147	0.000410	0.000307	0.002633	0.008128
	best	0.000129	0.000387	0.000146	0.002347	0.008128
Dataset 3.	mean	0.007290	0.017032	0.020527	0.025788	0.048970
	best	0.007028	0.007588	0.003158	0.025745	0.048970
Dataset 4.	mean	0.000154	0.001459	0.004118	0.000729	0.003369
	best	0.000141	0.000677	0.004081	0.000717	0.003369
Dataset 5.	mean	0.001683	0.004753	0.008993	0.004398	0.006797
	best	0.001413	0.001953	0.000378	0.004372	0.006797
Dataset 6.	mean	0.002527	0.013156	0.016594	0.018428	0.007058
	best	0.002059	0.012392	0.013471	0.016727	0.007058
Dataset 7.	mean	0.000258	0.000012	0.023053	0.001716	0.004828
	best	0.000245	0.000004	0.003908	0.001713	0.004828
Dataset 8.	mean	0.003395	0.004840	0.005049	0.007061	0.007058
	best	0.002920	0.004793	0.005026	0.007036	0.007058
Dataset 9.	mean	0.011630	0.011695	0.030777	0.015668	0.015156
	best	0.008077	0.009029	0.021855	0.015388	0.015153
Dataset 10.	mean	0.001293	0.001634	0.052973	0.002092	0.003836
	best	0.000590	0.001391	0.043681	0.001201	0.003836

Table 5

Computational results (MSE) of testing data

		GA-IFNN	IFNN	FNN	ANN	SVR
Dataset 1.	mean	0.003892	0.005450	0.005714	0.043050	0.018309
	best	0.002809	0.005221	0.005281	0.042602	0.018309
Dataset 2.	mean	0.000180	0.000518	0.000409	0.008395	0.000304
	best	0.000096	0.000477	0.000251	0.007492	0.000304
Dataset 3.	mean	0.008049	0.019916	0.089320	0.030330	0.064308
	best	0.007508	0.005988	0.043652	0.030259	0.064308
Dataset 4.	mean	0.000184	0.004136	0.005194	0.005487	0.000950
	best	0.000160	0.001324	0.005156	0.005346	0.000950
Dataset 5.	mean	0.002675	0.005627	0.011616	0.004469	0.017716
	best	0.002024	0.001340	0.000918	0.004419	0.017716
Dataset 6.	mean	0.008324	0.004563	0.018175	0.035277	0.017163
	best	0.007524	0.000350	0.012040	0.034770	0.017163
Dataset 7.	mean	0.000432	0.000159	0.022197	0.002351	0.000178
	best	0.000414	0.000015	0.002100	0.002314	0.000178
Dataset 8.	mean	0.004168	0.005439	0.007617	0.007336	0.007333
	best	0.003800	0.005298	0.007505	0.007290	0.007333
Dataset 9.	mean	0.075895	0.021346	0.031787	0.014794	0.017120
	best	0.032479	0.008760	0.019733	0.014403	0.017118
Dataset 10.	mean	0.001323	0.001885	0.058585	0.003091	0.008080
	best	0.000485	0.001517	0.047392	0.002532	0.008080

Table 6

Computational results (MAD) of training data

		GA-IFNN	IFNN	FNN	ANN	SVR
Dataset 1.	mean	0.043649	0.056001	0.054802	0.172499	0.156370
	best	0.037469	0.055884	0.052984	0.171663	0.156370
Dataset 2.	mean	0.000161	0.004707	0.004412	0.030322	0.013193
	best	0.000124	0.003638	0.003877	0.029608	0.013193
Dataset 3.	mean	0.072717	0.085036	0.102618	0.116048	0.160111
	best	0.065102	0.004462	0.051683	0.115783	0.160111
Dataset 4.	mean	0.001784	0.001247	0.014295	0.020772	0.049340
	best	0.001727	0.000942	0.011618	0.020539	0.049340
Dataset 5.	mean	0.047419	0.056802	0.064536	0.051335	0.080030
	best	0.042577	0.023730	0.026976	0.051053	0.080030
Dataset 6.	mean	0.068184	0.061784	0.079891	0.088757	0.076445
	best	0.055030	0.056713	0.068838	0.083184	0.076445
Dataset 7.	mean	0.000651	0.001959	0.085505	0.034425	0.062291
	best	0.000512	0.001247	0.046878	0.034393	0.062291
Dataset 8.	mean	0.016535	0.017613	0.116033	0.054811	0.083641
	best	0.015085	0.009070	0.008178	0.054770	0.083641
Dataset 9.	mean	0.069839	0.084433	0.137206	0.096193	0.056732
	best	0.055710	0.072777	0.116194	0.095121	0.056732
Dataset 10.	mean	0.043809	0.025648	0.171057	0.016714	0.053312
	best	0.039318	0.024163	0.149200	0.015938	0.053312

Table 7

Computational results (MAD) of testing data

		GA-IFNN	IFNN	FNN	ANN	SVR
Dataset 1.	mean	0.047599	0.057775	0.072152	0.174694	0.276160
	best	0.041804	0.057458	0.069468	0.173546	0.276160
Dataset 2.	mean	0.001652	0.013070	0.026682	0.056428	0.087627
	best	0.001452	0.009447	0.018665	0.050714	0.087627
Dataset 3.	mean	0.082628	0.094122	0.192674	0.124770	0.171074
	best	0.075151	0.005338	0.154557	0.124400	0.171074
Dataset 4.	mean	0.001814	0.003287	0.016126	0.071456	0.015776
	best	0.001637	0.001764	0.011036	0.070349	0.015776
Dataset 5.	mean	0.051218	0.063497	0.074139	0.060033	0.108020
	best	0.047016	0.044733	0.019574	0.058813	0.108020
Dataset 6.	mean	0.078538	0.050151	0.085149	0.166902	0.058513
	best	0.073122	0.016887	0.067908	0.166250	0.058513
Dataset 7.	mean	0.002804	0.007605	0.084775	0.045036	0.010650
	best	0.002642	0.002976	0.036696	0.044668	0.010650
Dataset 8.	mean	0.017932	0.019301	0.122281	0.056860	0.174086
	best	0.016066	0.009969	0.007245	0.056795	0.174086
Dataset 9.	mean	0.128555	0.115084	0.138990	0.094479	0.178533
	best	0.105449	0.074003	0.109901	0.093370	0.178533
Dataset 10.	mean	0.062103	0.026390	0.181116	0.016121	0.074304
	best	0.056262	0.024322	0.152585	0.015278	0.074304

Table 8

The computational time of all algorithms

Dataset	GA-IFNN	IFNN	FNN	ANN	SVR
1	552	72	44	30	14
2	552	72	44	30	14
3	833	110	60	34	16
4	832	111	61	35	16
5	1053	245	140	35	86
6	1468	205	194	35	95
7	3338	627	505	43	114
8	1338	316	297	18	101
9	4899	1295	1072	44	187
10	2747	719	657	52	196

Unit: second.

To verify the performance of the proposed algorithm, ANOVA is employed to compare the efficiency of GA-IFNN with other models, and the results are shown in Tables 9 to 12. Furthermore, the non-parametric Wilcoxon signed-rank test [54] is employed. It calculates differences of pairs. The absolute differences are ranked after discarding pairs with the difference of zero. When several pairs have absolute differences that are equal to the other, each of these several pairs is assigned as the average of ranks that would have otherwise been assigned. The hypothesis is that the differences have the mean of 0. This allows us to apply it over the means obtained by the algorithms in each data set, without any assumptions about the sample of results obtained.

Table 9

The ANOVA of training data (MSE)

Dataset	sum sq	F	p-value
1	0.034112	124990.4	2.42E–255
2	0.001441	71713.47	7.39E–238
3	0.028995	310.2702	5.48E–70
4	0.000485	13847.27	3.84E–186
5	0.000902	57.46678	5.63E–29
6	0.000298	3993.029	3.41E–147
7	0.004913	1821.936	7.92E–123
8	0.00415	90.4826	2.05E–38
9	0.011482	158.093	8.06E–52
10	0.070126	2225.27	5.19E–129

Table 10

The ANOVA of testing data (MSE)

Dataset	sum sq	F	p-value
1	0.034112	124990.4	2.42E–255
2	0.001441	71713.47	7.39E–238
3	0.028995	310.2702	5.48E–70
4	0.000485	13847.27	3.84E–186
5	0.000902	57.46678	5.63E–29
6	0.000298	3993.029	3.41E–147
7	0.004913	1821.936	7.92E–123
8	0.00415	90.4826	2.05E–38
9	0.011482	158.093	8.06E–52
10	0.070126	2225.27	5.19E–129

Table 11

The ANOVA of training data (MAD)

Dataset	sum sq	F	p-value
1	0.465966	38313.24	3.92E–218
2	0.017815	59089.57	9.16E–232
3	0.137372	60.9597	4.06E–30
4	0.046386	42812.56	1.26E–221
5	0.019961	27.36034	6.33E–17
6	0.22157	87.36624	1.24E–37
7	0.016378	121.6585	2.63E–45
8	0.114003	670.363	2.13E–92
9	0.128648	503.9376	5.98E–84
10	0.412536	1881.225	8.13E–124

Table 12

The ANOVA of testing data (MAD)

Dataset	sum sq	F	p-value
1	0.465966	38313.24	3.92E–218
2	0.017815	59089.57	9.16E–232
3	0.137372	60.9597	4.06E–30
4	0.046386	42812.56	1.26E–221
5	0.019961	27.36034	6.33E–17
6	0.22157	87.36624	1.24E–37
7	0.016378	121.6585	2.63E–45
8	0.114003	670.363	2.13E–92
9	0.128648	503.9376	5.98E–84
10	0.412536	1881.225	8.13E–124

The MSE for training data indicates that GA-IFNN can obtain better results than other compared algorithms, except for Dataset 7. In Dataset 7, the MSE obtained by IFNN is 0.000159, which outperforms GA-IFNN. In Datasets 9 and 10, the ANN obtains better MAD but the MSE results are not better than the proposed algorithm.

A further analysis is conducted through a statistic test applied to the testing data. The Wilcoxon signed-rank test results indicate that the proposed GA-IFNN is significantly superior to other algorithms tested in this study. Tables 13 to 22 demonstrate the results of the statistical test, and there are the p-values in the tables. The hypotheses of the statistical test are as follows: $\begin{matrix} H_{1} : μ_{GA - IFNN} ⩾ μ_{IFNN} \\ H_{2} : μ_{GA - IFNN} ⩾ μ_{IFNN} \\ H_{3} : μ_{GA - IFNN} ⩾ μ_{ANN} \\ H_{4} : μ_{GA - IFNN} ⩾ μ_{SVR} \end{matrix}$

Table 13

The statistical results of GA-IFNN (MSE)

Dataset	GA-IFNN	IFNN	FNN	ANN	SVR1
1	–	0.000	0.000	0.000	0.000
2	–	0.000	0.000	0.000	0.000
3	–	0.000	0.000	0.000	0.000
4	–	0.000	0.000	0.000	0.000
5	–	0.000	0.000	0.000	0.000
6	–	1.000	0.000	0.000	0.000
7	–	1.000	0.000	0.000	1.000
8	–	0.000	0.000	0.000	0.000
9	–	1.000	1.000	1.000	1.000
10	–	0.000	0.000	0.000	0.000

Table 14

The statistical results of IFNN (MSE)

Dataset	GA-IFNN	IFNN	FNN	ANN	SVR
1	1.000	–	0.000	0.000	0.000
2	1.000	–	0.000	0.000	1.000
3	1.000	–	0.000	0.000	0.000
4	1.000	–	0.000	0.000	1.000
5	1.000	–	0.000	1.000	0.000
6	0.000	–	0.000	0.000	0.000
7	0.000	–	0.000	0.000	0.102
8	1.000	–	0.000	0.000	0.000
9	0.000	–	0.000	1.000	1.000
10	1.000	–	0.000	0.000	0.000

Table 15

The statistical results of FNN (MSE)

Dataset	GA-IFNN	IFNN	FNN	ANN	SVR
1	1.000	1.000	–	0.000	0.000
2	1.000	0.000	–	0.000	1.000
3	1.000	1.000	–	1.000	1.000
4	1.000	1.000	–	0.000	1.000
5	1.000	1.000	–	1.000	0.000
6	1.000	1.000	–	0.000	1.000
7	1.000	1.000	–	1.000	1.000
8	1.000	1.000	–	1.000	1.000
9	0.000	1.000	–	1.000	1.000
10	1.000	1.000	–	1.000	1.000

Table 16

The statistical results of ANN (MSE)

Dataset	GA-IFNN	IFNN	FNN	ANN	SVR
1	1.000	1.000	1.000	–	1.000
2	1.000	1.000	1.000	–	1.000
3	1.000	1.000	0.000	–	0.000
4	1.000	1.000	1.000	–	1.000
5	1.000	0.000	0.000	–	0.000
6	1.000	1.000	0.000	–	0.000
7	1.000	1.000	0.000	–	1.000
8	1.000	1.000	0.000	–	0.465
9	0.000	0.000	0.000	–	0.000
10	1.000	1.000	0.000	–	1.000

Table 17

The statistical results of SVR (MSE)

Dataset	GA-IFNN	IFNN	FNN	ANN	SVR
1	1.000	1.000	1.000	0.000	–
2	1.000	0.000	0.000	0.000	–
3	1.000	1.000	0.000	1.000	–
4	1.000	0.000	0.000	0.000	–
5	1.000	1.000	1.000	1.000	–
6	0.000	0.000	0.000	0.000	–
7	0.000	1.000	0.000	0.000	–
8	1.000	1.000	0.000	0.465	–
9	0.000	0.000	0.000	1.000	–
10	1.000	1.000	0.000	1.000	–

Table 18

The statistical results of GA-IFNN (MAD)

Dataset	GA-IFNN	IFNN	FNN	ANN	SVR
1	–	0.000	0.000	0.000	0.000
2	–	0.000	0.000	0.000	0.000
3	–	0.000	0.000	0.000	0.000
4	–	0.000	0.000	0.000	0.000
5	–	0.000	0.000	0.000	0.000
6	–	1.000	0.000	0.000	1.000
7	–	0.000	0.000	0.000	0.000
8	–	0.000	0.000	0.000	0.000
9	–	1.000	0.041	1.000	0.000
10	–	1.000	0.000	1.000	0.040

Table 19

The statistical results of IFNN (MAD)

Dataset	GA-IFNN	IFNN	FNN	ANN	SVR
1	1.000	–	0.000	0.000	0.000
2	1.000	–	0.000	0.000	0.000
3	1.000	–	0.000	0.000	0.000
4	1.000	–	0.000	0.000	0.000
5	1.000	–	0.035	0.120	0.000
6	1.000	–	0.000	0.000	0.033
7	1.000	–	0.000	0.000	0.000
8	1.000	–	0.000	0.000	0.000
9	0.003	–	0.000	1.000	0.000
10	0.000	–	0.000	1.000	0.000

Table 20

The statistical results of FNN (MAD)

Dataset	GA-IFNN	IFNN	FNN	ANN	SVR
1	1.000	1.000	–	0.000	0.000
2	1.000	1.000	–	0.000	0.000
3	1.000	1.000	–	1.000	1.000
4	1.000	1.000	–	0.000	1.000
5	1.000	1.000	–	1.000	0.000
6	0.002	1.000	–	0.000	0.000
7	1.000	1.000	–	0.000	0.000
8	1.000	1.000	–	0.000	0.000
9	0.040	1.000	–	1.000	0.000
10	1.000	1.000	–	1.000	1.000

Table 21

The statistical results of ANN (MAD)

Dataset	GA-IFNN	IFNN	FNN	ANN	SVR
1	1.000	1.000	1.000	–	0.000
2	1.000	1.000	1.000	–	0.000
3	1.000	0.001	0.000	–	0.000
4	1.000	1.000	1.000	–	1.000
5	1.000	0.120	0.014	–	0.000
6	1.000	1.000	1.000	–	0.000
7	1.000	1.000	1.000	–	1.000
8	1.000	1.000	1.000	–	1.000
9	0.000	0.000	0.000	–	0.000
10	0.000	0.000	0.000	–	0.000

Tables 13 to 17 show the results of MSE values, and Tables 18 to 22 show the result of MAD values. According to the experiments results, we can summarize that the GA is able to train the network efficiently. Secondly, since the GA-IFNN incorporates the concept of IFL, the hesitation degree considers the membership degree and non-membership degree simultaneously. This can better define the degree of uncertainty. Due to the reduction of the uncertainty degree, the performance can be enhanced.

Table 22

The statistical results of SVR (MAD)

Dataset	GA-IFNN	IFNN	FNN	ANN	SVR
1	1.000	1.000	1.000	1.000	–
2	1.000	1.000	1.000	1.000	–
3	1.000	1.000	1.000	1.000	–
4	1.000	1.000	1.000	0.000	–
5	1.000	1.000	1.000	1.000	–
6	1.000	1.000	1.000	1.000	–
7	1.000	1.000	1.000	1.000	–
8	1.000	1.000	1.000	1.000	–
9	1.000	1.000	1.000	1.000	–
10	1.000	1.000	0.000	1.000	–

4 Case study

This section presents the application of the proposed algorithms in the real data. First, the descriptive statistics of the clinical data is shown in subsection 4.1. The next subsection describes the input variables. Subsection 4.3 shows the computational results. Finally, the discussion is presented in subsection 4.4.

4.1 Data collection

This study collects the real data which are used for medical resource cost forecasting of patients with acute hepatitis admitted to the Emergency Department (ED) from a well-known teaching-oriented hospital in Taipei, Taiwan. Table 23 shows the data demographic. Acute hepatitis lasts less than 6 months while chronic hepatitis lasts longer than 6 months. Acute hepatitis has several possible causes, such as Infectious viral hepatitis (hepatitis A, B, C, D, and E), other viral diseases (glandular fever and cytomegalovirus), severe bacterial infections, amoebic infections, medicines (acetaminophen and halothane), and toxins (alcohol and fungal toxins). The severity of illness in acute hepatitis ranges from asymptomatic to fulminant and fatal. Some patients are asymptomatic with abnormalities noted only by laboratory studies, while other patients might have symptoms and signs, such as nausea, vomiting, fatigue, weight loss, abdominal pain, jaundice, fever, splenomegaly, or ascites [55 –58].

Table 23
The descriptive statistics of the dataset

Features N Ratio

Gender Female 39 35.5%

Male 71 64.5%

Age 20–29 23 20.9%

30–39 28 25.5%

40–49 22 20.0%

50–59 24 21.8%

>60 13 11.8%

Features	N	Ratio
Gender	Female	39	35.5%
	Male	71	64.5%
Age	20–29	23	20.9%
	30–39	28	25.5%
	40–49	22	20.0%
	50–59	24	21.8%
	>60	13	11.8%

4.2 Input variable selection

According to the findings of Yang et al. [59], the result indicated that the Child-Pugh score and abdominal ultrasound finding can used to predict the medical resource in patients with acute hepatitis. The results of correlation analysis between medical cost and variables are shown in Table 24. The six variables are significant correlation to the medical cost. Therefore, in this study, six input variables, hepatic portal vein varicose (PV), Gallbladder wall thickening (GB wall), splenomegaly, Child-Pugh index (CP), total bilirubin (T-bil), and prothrombin (PT) are used for training the FNN model. The medical cost is the output of the forecasting model. The notations about all variables are shown in Table 25, and the demographic of the medical cost is shown in Table 26.

Table 24
Correlation between medical cost and variables

Variable p-value

Hepatic portal vein varicose (PV) 0.049*

Gallbladder wall thickening (GB wall) 0.024*

Splenomegaly 0.005

Child-Pugh index (CP) 0.000

Total bilirubin (T-bil) 0.000

Prothrombin (PT) 0.008

Variable	p-value
Hepatic portal vein varicose (PV)	0.049*
Gallbladder wall thickening (GB wall)	0.024*
Splenomegaly	0.005**
Child-Pugh index (CP)	0.000**
Total bilirubin (T-bil)	0.000**
Prothrombin (PT)	0.008**

**p-value<0.01, *p-value<0.05.

Table 25

The notation of variables

Notation	Variable
X ₁	Hepatic portal vein varicose (PV)
X ₂	Gallbladder wall thickening (GB wall)
X ₃	Splenomegaly
X ₄	Child-Pugh index (CP)
X ₅	Total bilirubin (T-bil)
X ₆	Prothrombin (PT)
Y	The medical cost

Table 26

The demographic of the medical cost

	Min	Max	Mean	STD.
Cost	2171	152464	29493.37	30401.87

4.3 Computational results

For developing the forecasting model, five algorithms, GA-IFNN, IFNN, FNN, ANN, and SVR are employed. Before constructing the forecasting model, there are parameters selection with Taguchi method in IFNN. The levels of the parameters are as follows: η_m, η_s ∈ (0.0005, 0.001, 0.005) , η_α ∈ (0.001, 0.005, 0.009) and η_w, ρ ∈ (0.01, 0.5, 0.1). In the GA, there levels of both parameters are used, CR ∈ (0.7, 0.8, 0.9) and MR ∈ (0.1, 0.2, 0.3). After the selection, the combination of the parameters is shown in Tables 27 and 28.

Table 27
The parameters of IFNN in clinical data

η _m η _s η _α η _w ρ

0.005 0.005 0.009 0.05 0.01

η _m	η _s	η _α	η _w	ρ
0.005	0.005	0.009	0.05	0.01

Table 28

The parameters of GA-IFNN in clinical data

CR	MR
0.8	0.2

Tables 29 and 30 show the results of MSE and MAD, respectively. For the IFNN, the average training MSE and the average test MSE are 0.006876 and 0.008752, respectively. For the GA-IFNN, the average training MSE and the average test MSE are 0.004787 and 0.006765. Therefore, in terms of the MSE criterion, the GA-IFNN can provide a better forecast. For the MAD criterion, the similar results are represented. For the IFNN, the average training MAD and the average test MAD are 0.065687 and 0.078988, respectively.

Table 29

Computational results (MSE) of clinical data

MSE		GA-IFNN	IFNN	FNN	ANN	SVR
Training	mean	0.004787	0.006876	0.008549	0.008634	0.009133
	STD.	0.000326	0.000110	0.000551	0.000321	0.000000
	best	0.004273	0.006653	0.007523	0.007936	0.009133
Testing	mean	0.006765	0.008752	0.010333	0.010832	0.011360
	STD.	0.000382	0.000366	0.000503	0.000401	0.000000
	best	0.006074	0.007981	0.009142	0.010275	0.011360
	p-value	–	0.000**	0.000**	0.000**	0.000**

Table 30

Computational results (MAD) of medical data

MAD		GA-IFNN	IFNN	FNN	ANN	SVR
Training	mean	0.055838	0.065687	0.078422	0.079958	0.081036
	STD.	0.003024	0.000610	0.000880	0.006903	0.000000
	best	0.052050	0.064442	0.076284	0.065709	0.081036
Testing	mean	0.066025	0.078988	0.081516	0.087430	0.094607
	STD.	0.003446	0.001449	0.000466	0.005674	0.000000
	best	0.060387	0.076441	0.080578	0.075490	0.094607
	p-value	–	0.000**	0.000**	0.000**	0.000**

The converge curves are shown in Fig. 3. After training the GA-IFNN model, the membership functions (e.g. the Gaussian function) are shown in Fig. 4.

Fig.3

The converge curves in clinical data.

Fig.4

The membership functions in clinical data. (x-axis: value of features; y-axis: degree of membership function).

4.4 Discussions

This study attempts to establish the medical cost forecasting model, and five forecasting techniques including the proposed GA-IFNN, IFNN, FNN, ANN and SVR, are employed to develop the forecasting models. As the limitations of the study, it is difficult to collect the many clinical data. Thus, we only can have 110 instances. The results indicate that the GA-IFNN have a better performance in MSE and MAD values. If more data can be collected, it is possible to improve the accuracy for the forecasting models. In addition, constructing the forecasting model by the proposed GA-IFNN does not only provide the accuracy, but also provides the fuzzy rules for users’ reference. The fuzzy rules of GA-IFNN are shown in Table 31. Some of the fuzzy rules are illustrated as follows:

Table 31
The fuzzy rules of GA-IFNN

PV GB wall Splenomegaly CP T-bil PT Y

Rule 1 L L H M H H 0.1342

Rule 2 H H M H M L 0.1473

Rule 3 L H H M H L 0.2135

	PV	GB wall	Splenomegaly	CP	T-bil	PT	Y
Rule 1	L	L	H	M	H	H	0.1342
Rule 2	H	H	M	H	M	L	0.1473
Rule 3	L	H	H	M	H	L	0.2135

Rule 1:

IF X₁ is Low ∧ X₂is Low ∧ X₃ is High ∧ X₄ is Medium ∧ X₅ is High ∧ X₆ is High

THEN Y = 0.1342 .

Rule 2:

IF X₁ is High ∧ X₂is High ∧ X₃ is Low ∧ X₄ is Low ∧ X₅ is Medium ∧ X₆ is Low

THEN.Y = 0.1473 .

Rule 3:

IF X₁ is Low ∧ X₂is High ∧ X₃ is High ∧ X₄ is Medium ∧ X₅ is High ∧ X₆ is Low

THEN.Y = 0.2135

Rule 1 reveals when PV is low, GB wall is low, Splenomegaly is high, CP is medium, T-bil is high, and PT is high, then the estimated medical cost is around NT$22,340 according to the FNN model result. Thus, the hospital manager can evaluate the medical cost needed for the patient from the rules and arrange the necessary medical resources.

5 Conclusions

In the industry, the prediction is a very important issue. However, there are not many studying related the medical cost forecasting. For medical management, if hospital can accurately predict healthcare costs, then it can avoid unnecessary consumption and waste. For the healthcare personnel, he/she can save time and thus provide better quality of care. This study proposed the GA-based IFNN to develop the medical cost forecasting model. In the simulations, there are ten benchmark datasets reveal that the GA-IFNN has better performance than the other compared methods, including FNN, ANN, and SVR. Additionally, the GA-IFNN results, which are in the form of fuzzy IF-THEN rules, can be easily interpreted. The medical doctors or hospital managers can apply these rules to explain the cost structure. The medical resource waste can be reduced and enhances the operation efficiency.

In the future, other soft computing techniques should be integrated into the heuristics to provide better estimation. The IF-THEN rules pruning also can be considered. In addition, increasing the data size for model evaluation might increase the accuracy of the prediction for the medical cost. Since it is quite difficult to collect the acute hepatitis cases, it might be feasible to combine different hospitals’ acute hepatitis cases together for the current study.

References

Rumelhart ,

Hinton and

Williams , Learning internal representations by error propagation, Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Foundations, MIT Press, Cambridge, MA (1986), pp. 318–362.

W.G.

Baxt , Application of artificial neural networks to clinical medicine, The lancet, 346(8983) (1995), pp. 1135–1138.

Khan , et al., Classification and diagnostic prediction of cancers using gene expression profiling and artificial neural networks, Nature medicine 7(6) (2001), pp. 673–679.

Z.-H.

Zhou and

Jiang , Medical diagnosis with C4, 5 rule preceded by artificial neural network ensemble, Information Technology in Biomedicine, IEEE Transactions on 7(1) (2003), pp. 37–42.

L.A.

Zadeh , The concept of a linguistic variable and its application to approximate reasoning—I, Information Sciences 8(3) (1975), pp. 199–249.

C.-T.

Lin and

C.S.G.

Lee , Neural-network-based fuzzy logic control and decision system, Computers, IEEE Transactions on 40(12) (1991), pp. 1320–1336.

C.-F.

Juang and

C-T.

Lin , An online self-constructing neural fuzzy inference network and its applications, Fuzzy Systems, IEEE Transactions on 6(1) (1998), pp. 12–32.

R.-J.

Wai and

P-C.

Chen , Intelligent tracking control for robot manipulator including actuator dynamics via TSK-type fuzzy neural network, Fuzzy Systems, IEEE Transactions on 12(4) (2004), pp. 552–560.

C.-F.

Juang and

Lo , Zero-order TSK-type fuzzy system learning using a two-phase swarm intelligence algorithm, Fuzzy Sets and Systems 159(21) (2008), pp. 2910–2926.

10.

Hadavandi ,

Shavandi and

Ghanbari , Integration of genetic fuzzy systems and artificial neural networks for stock price forecasting, Knowledge-Based Systems 23(8) (2010), pp. 800–808.

11.

R.J.

Kuo ,

C.H.

Chen and

Y.C.

Hwang , An intelligent stock trading decision support system through integration of genetic algorithm based fuzzy neural network and artificial neural network, Fuzzy Sets and Systems 118(1) (2001), pp. 21–45.

12.

R.J.

Kuo ,

Wu and

C.P.

Wang , An intelligent sales forecasting system through integration of artificial neural networks and fuzzy neural networks with fuzzy weight elimination, Neural Networks 15(7) (2002), pp. 909–925.

13.

R.J.

Kuo ,

S.M.

Hong ,

Lin and

Y.C.

Huang , Continuous genetic algorithm-based fuzzy neural network for learning fuzzy IF-THEN rules, Neurocomputing 71(13-15) (2008), pp. 2893–2907.

14.

R.J.

Kuo ,

S.Y.

Hung and

W.C.

Cheng , Application of an optimization artificial immune network and particle swarm optimization-based fuzzy neural network to an RFID-based positioning system, Information Sciences 262 (2014), 78–98.

15.

Kazemipoor ,

Hajifaraji ,

C.w. J. B. w. M.

Radzi ,

Shamshirband ,

Petković and

M.L.

Mat Kiah , Appraisal of adaptive neuro-fuzzy computing technique for estimating anti-obesity properties of a medicinal plant, Computer Methods and Programs in Biomedicine 118(1) (2015), pp. 69–76.

16.

E.D.

Übeyli , Adaptive neuro-fuzzy inference system for classification of ECG signals using Lyapunov exponents, Computer Methods and Programs in Biomedicine 93(3) (2009), pp. 313–321.

17.

Holland , Adaption in natural and artificial systems, Ann Arbor MI: The University of Michigan Press, 1975.

18.

D.E.

Goldberg and

J.H.

Holland , Genetic algorithms and machine learning, Machine Learning 3(2) (1988), pp. 95–99.

19.

Emmeche , The garden in the machine: The emerging science of artificial life, Princeton University Press (1996).

20.

K.-F.

Man ,

K.S.

TANG and

Kwong , Genetic algorithms: Concepts and designs. Springer Science & Business Media, 2012.

21.

Castillo ,

Valdez and

Melin , Hierarchical Genetic Algorithms for topology optimization in fuzzy control systems, International Journal of General Systems 36(5), pp. 57 (2007), 5–591.

22.

Valdez ,

Melin , and

Castillo , Modular Neural Networks architecture optimization with a new nature inspired method using a fuzzy combination of Particle Swarm Optimization and Genetic Algorithms, Information Sciences 270, 143–153.

23.

R.J.

Kuo ,

C.F.

Wang and

Z.Y.

Chen , Integration of growing self-organizing map and continuous genetic algorithm for grading lithium-ion battery cells, Applied Soft Computing 12(8) (2012), pp. 2012–2022.

24.

L.A.

Zadeh , Fuzzy sets, Information and Control 8(3) (1965), pp. 338–353.

25.

L.A.

Zadeh , Similarity relations and fuzzy orderings, Information sciences 3(2, pp) 17 (1971), 7–200.

26.

L.A.

Zadeh , Is there a need for fuzzy logic? Information Sciences 178(13) (2008), pp. 2751–2779.

27.

Atanassov and

Gargov , Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems 31(3) (1989), pp. 343–349.

28.

K.T.

Atanassov , More on intuitionistic fuzzy sets, Fuzzy Sets and Systems 33(1) (1989), pp. 37–45.

29.

K.T.

Atanassov , Intuitionistic fuzzy sets, Springer (1999).

30.

Burillo and

Bustince , Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Sets and Systems 78(3) (1996), pp. 305–316.

31.

Atanassov , Intuitionistic fuzzy logics as tools for evaluation of Data Mining processes, Knowledge-Based Systems 80 (2015), 122–130.

32.

Atanassov ,

Pasi and

Yager , Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making, International Journal of Systems Science 36(14) (2005), pp. 9–868.

33.

H.-W.

Liu and

G-J.

Wang , Multi-criteria decision-making methods based on intuitionistic fuzzy sets, European Journal of Operational Research 179(1) (2007), pp. 220–233.

34.

Ye , Multicriteria fuzzy decision-making method using entropy weights-based correlation coefficients of interval-valued intuitionistic fuzzy sets, Applied Mathematical Modelling 34(12) (2010), pp. 3864–3870.

35.

Beliakov ,

Bustince ,

Goswami ,

Mukherjee and

N.R.

Pal , On averaging operators for Atanassov’s intuitionistic fuzzy sets, Information Sciences 181(6) (2011), pp. 1116–1124.

36.

T.-Y.

Chen , A comparative analysis of score functions for multiple criteria decision making in intuitionistic fuzzy settings, Information Sciences 181(17) (2011), pp. 3652–3676.

37.

Chen and

Yang , A new multiple attribute group decision making method in intuitionistic fuzzy setting, Applied Mathematical Modelling 35(9) (2011), pp. 4424–4437.

38.

Guo and

Li , An attitudinal-based method for constructing intuitionistic fuzzy information in hybrid MADM under uncertainty, Information Sciences 208 (2012), 28–38.

39.

Akram ,

Ashraf and

Sarwar , Novel applications of intuitionistic fuzzy digraphs in decision support systems, Scientific World Journal 2014 2014, Art no. 904606.

40.

K.P.

Lin , A Novel Evolutionary Kernel Intuitionistic Fuzzy C-means Clustering Algorithm, Fuzzy Systems, IEEE Transactions on PP(99) (2013), 1.

41.

Akram and

W.A.

Dudek , Intuitionistic fuzzy hypergraphs with applications, Information Sciences 218 (2013), 182–193.

42.

K.-C.

Hung and

K.-P.

Lin , Long-term business cycle forecasting through a potential intuitionistic fuzzy least-squares support vector regression approach, Information Sciences 224(0) (2013), pp. 37–48.

43.

Chaira and

Ray , A new measure using intuitionistic fuzzy set theory and its application to edge detection, Applied Soft Computing 8(2) (2008), pp. 919–927.

44.

Dengfeng and

Chuntian , New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions, Pattern Recognition Letters 23(1) (2002), pp. 221–225.

45.

C.-M.

Hwang ,

M.-S.

Yang ,

W.-L.

Hung and

M.-G.

Lee , A similarity measure of intuitionistic fuzzy sets based on the Sugeno integral with its application to pattern recognition, Information Sciences 189 (2012), 93–109.

46.

Chaira , A novel intuitionistic fuzzy C means clustering algorithm and its application to medical images, Applied Soft Computing 11(2) (2011), pp. 1711–1717.

47.

Kharal , Homeopathic drug selection using intuitionistic fuzzy sets, Homeopathy 98(1) (2009), pp. 35–39.

48.

R.J.

Kuo and

W.C.

Cheng , An intuitionistic fuzzy neural network with Gaussian membership function, Journal of Intelligent & Fuzzy Systems 36(6) (2019), pp. 6731–6741.

49.

K.-F.

Man ,

K-S.

Tang and

Kwong , Genetic algorithms: Concepts and applications, IEEE Transactions on Industrial Electronics 43(5) (1996), pp. 519–534.

50.

Srinivas and

L.M.

Patnaik , Genetic algorithms: A survey, Computer 27(6) (1994), pp. 17–26.

51.

Chelouah and

Siarry , A continuous genetic algorithm designed for the global optimization of multimodal functions, Journal of Heuristics 6(2) (2000), pp. 191–213.

52.

C.-C.

Chang and

C.-J.

Lin , LIBSVM: A library for support vector machines, ACM Transactions on Intelligent Systems and Technology (TIST) 2(3) (2011), pp. 1–27.

53.

Taguchi ,

Chowdhury and

Wu , Taguchi’s quality engineering handbook. Wiley, 2005.

54.

Demšar , Statistical comparisons of classifiers over multiple data sets, The Journal of Machine Learning Research 7 (2006), 1–30.

55.

Zauner , et al., Outcome prediction for patients with cirrhosis of the liver in a medical ICU: A comparison of the APACHE scores and liver-specific scoringsystems, Intensive Care Medicine 22(6) (1996), pp. 559–563.

56.

Li ,

G-Y.

Yuan ,

K-C.

Tang ,

G-W.

Liu ,

Wang and

W-K.

Cao , Prognostic factors for chronic severe hepatitis and construction of a prognostic model, Hepatobiliary Pancreat Dis Int 7(1) (2008), pp. 40–44.

57.

Sarin ,

Kumar and

Garg , Clinical profile of acute on chronic liver failure (ACLF) and predictors of mortality: A study of 64 patients, Hepatology 48 (2008), pp. 450A.

58.

S.K.

Sarin , et al., Acute-on-chronic liver failure: Consensus recommendations of the Asian Pacific Association for the study of the liver (APASL), Hepatology International 3(1) (2009), pp. 269–282.

59.

T.-J.

Yang , et al., Child–Pugh Score and Ascites for Predicting Economic Outcomes in Adult Patients with Acute Hepatitis, Journal of Medical Ultrasound 22(2) (2014), pp. 88–91.

Application of genetic algorithm-based intuitionistic fuzzy neural network to medical cost forecasting for acute hepatitis patients in emergency room

Abstract

Keywords

1 Introduction

2 The intuitionistic fuzzy neural network

2.1 The intuitionistic fuzzy sets (IFSs)

3.1 The simulation cases

4.1 Data collection

Table 23 The descriptive statistics of the dataset Features N Ratio Gender Female 39 35.5% Male 71 64.5% Age 20–29 23 20.9% 30–39 28 25.5% 40–49 22 20.0% 50–59 24 21.8% >60 13 11.8%

Table 24 Correlation between medical cost and variables Variable p-value Hepatic portal vein varicose (PV) 0.049* Gallbladder wall thickening (GB wall) 0.024* Splenomegaly 0.005** Child-Pugh index (CP) 0.000** Total bilirubin (T-bil) 0.000** Prothrombin (PT) 0.008**

Table 27 The parameters of IFNN in clinical data η m η s η α η w ρ 0.005 0.005 0.009 0.05 0.01

Table 31 The fuzzy rules of GA-IFNN PV GB wall Splenomegaly CP T-bil PT Y Rule 1 L L H M H H 0.1342 Rule 2 H H M H M L 0.1473 Rule 3 L H H M H L 0.2135

References

Table 23
The descriptive statistics of the dataset

Features N Ratio

Gender Female 39 35.5%

Male 71 64.5%

Age 20–29 23 20.9%

30–39 28 25.5%

40–49 22 20.0%

50–59 24 21.8%

>60 13 11.8%

Table 24
Correlation between medical cost and variables

Variable p-value

Hepatic portal vein varicose (PV) 0.049*

Gallbladder wall thickening (GB wall) 0.024*

Splenomegaly 0.005

Child-Pugh index (CP) 0.000

Total bilirubin (T-bil) 0.000

Prothrombin (PT) 0.008

Table 27
The parameters of IFNN in clinical data

η _m η _s η _α η _w ρ

0.005 0.005 0.009 0.05 0.01

Table 31
The fuzzy rules of GA-IFNN

PV GB wall Splenomegaly CP T-bil PT Y

Rule 1 L L H M H H 0.1342

Rule 2 H H M H M L 0.1473

Rule 3 L H H M H L 0.2135