Design, Simulation and Testing of an Optimized Fuzzy Neural Network for Early Criticality Diagnosis Shubhajit Roy Chowdhury1, Arijit Biswas2, Rini Chowdhury3 IC Design and Fabrication Centre, Department of Electronics and Telecommunication Engineering, Jadavpur University, Kolkata, India 1 [email protected], [email protected], [email protected] Abstract— Current trends in the application of computational intelligent systems for cognitive health care applications have motivated the design of neuro-fuzzy systems that can signal the approaching critical condition of a patient at an early stage. This article proposes the design of an optimized fuzzy neural network that can predict the future patho-physiological state of a patient based on the previous data. The membership functions used for fuzzying the patient data is sigmoidal and has been suitably optimized for correctly diagnosing the patho-physiological trend of the patient. Using the trained network, the chance of approaching critical health condition of a patient has been predicted with confidence. The system has been suitably tested with height, weight, glucose, urea, creatinine, systolic blood pressure and diastolic blood pressure data of patients taken at 10 days interval of time. Finally we study the effect of slight variation in the center and width of the sigmoids , used for fuzzification, on the reliability and the time instants at which we can predict the criticality. Keywords- Criticality, fuzzy neural networks, medical diagnosis, pathophysiological, approximate inference

I. INTRODUCTION Medical diagnosis is a complicated and judgmental process, based not only on medical knowledge derived from books and literatures and data obtained from various pathological tests, but also is largely dependant on experience, judgment and reasoning which essentially are the functions of human brain []. During diagnosis the patients are forced to depend much on the decisions made by the medical experts. However, decision made by physicians is arbitrary and highly variable (within one physician and between physicians) and often lacking explanation or rationalization [1,9]. Problems in modern medicine are often very complex, but evidence for the best choice to be made is often lacking. Clinical examples of this phenomenon in diagnosis making are abundant and easy to understand. The body of potentially useful knowledge that is relevant to even a relatively narrow diagnostic area may be too large to make the optimal (diagnostic) decision on the spot. Ironically, modern information technology (especially through the Internet) increases the amount of available knowledge

even more, probably further complicating this situation. Moreover, individual patients need individualized decisions, because their characteristics differ from the average [2]. Apparently, individualizing the general results of research may be cumbersome and time consuming, while on the other hand modern medical practice demands efficiency, costeffectiveness and high technical quality. Recently extensive application of soft computing based intelligent techniques in medical diagnosis and health care inspires us to model some intelligent experts who will be able to detect the criticality related to renal system of human beings earlier and in a more accurate manner. The variation in decision-making is best simulated with the help of fuzzy logic [3]. Neural network is the most fitting tool when information about the patient is stored in the form of numerical data sets [4,5,6,7,8,10]. Thus an artificial neural network is apt for autonomous machine learning whereas fuzzy system has a significant potential of reasoning with inexact data and knowledge. So proper synergism of these two tools of soft computing may lead to develop some agent, which is intelligent, and handles difficulty related to medical diagnosis more efficiently[11,12]. In this article we propose a fuzzy neural network that is trained with a huge amount of fuzzy membership function values, and these membership values are obtained after properly fuzzying the patient’s data using sigmoidal membership functions. Proper sigmoidal fuzzy membership functions are optimized for diagnosing patient’s condition accurately. We are trying to detect the criticality of a patient at an earlier stage and the proposed system has been found to be performing with sufficient accuracy in absence of a physician. We have also studied the variation in the reliability and the time instants at which we can predict the criticality by changing the center and the width parameters of the sigmoidal membership functions. The paper is organized as follows. In section 2 a brief description of the stationary type-1 sigmoidal fuzzy expert systems has been presented. Section 3 describes the functional

architecture of the fuzzy neural smart agent based medical diagnostic system. Our method of fuzzyfying the patient’s data is described in detail in section 4. Section 5 focuses on the training of the neural network. In section 6 we have enlisted the results obtained which shows that this smart agent can legitimately replace human physicians. Finally we have concluded in section 7.

II. STATIONARY TYPE-1 SIGMOIDAL FUZZY EXPERT SYSTEMS A fuzzy expert system (FES) normally consists of four main interconnected components: a fuzzifier, a set of rules, an interference engine, and an output processor (defuzzifier). Once the rules are established, an FES can be viewed as a (nonlinear) mapping from input to output. Many different types of functions can be used to generate type-1 fuzzy sets, with gaussians, for example, being a common choice. In this work sigmoids and products of sigmoids have been used. Left edge fuzzy sets (decreasing sigmoids) represented by:

1

µ ( x) = 1+ e

( x − c1 )

w1

Right edge fuzzy sets (increasing sigmoids) represented by:

1

µ ( x) = 1+ e

( x −c2 )

w2

Middle edge fuzzy sets represented by:

µ ( x) = 1+ e

1

1

( x − c3 )

( x −c4 )

w3

1+ e

w4

Where, c’s are the centers of the sigmoids and w’s are arbitrary values, which determine the steepness of the slope, or width of the sigmoid

III. FUNCTIONAL ARCHITECTURE OF FUZZY NEURAL SMART AGENT BASED MEDICAL DIAGNOSTIC SYSTEM Figure 1 shows the functional architecture of the fuzzy neural smart agent based medical diagnostic system.

Fig.1. Functional Architecture of the fuzzy neural smart agent based medical diagnostic system.

At least two entities, viz. patient and smart agent are required in this concept of smart agent based diagnostic system. The patients are the providers of data under the assistance of health care professionals who need not be physicians. The smart agent is represented by a weakly coupled fuzzy neural system that can predict the future pathophysiological state of a patient in presence of past pathophysiological data. The weakly coupled fuzzy neural network is basically a two unit composite system comprising of a fuzzy system placed before a neural network. The fuzzy interface makes an approximate inference about the current state of the patient from the current patient data being entered into the smart agent. The membership values obtained from the output of the fuzzy interface are supplied to the input of. IV. FUZZIFICATION OF PATIENT’S DATA The fuzzy interface discussed in section 2 performs fuzzification of patient data. Since data from the patient are nothing but physiological measures, they are subjected to noise and uncertainty. The data from the patient such as height or weight data cannot always be trusted as they are subjected to the quality and accuracy of measuring units and the skill of the technician. Moreover, based on a single data, it would be highly uncertain to make an accurate decision about the future physiological state of the patient [13]. So the patient data has been fuzzified with the objective of transformation of periodic measures into likelihoods that the Body Mass Index, blood glucose, urea, creatinine, systolic and diastolic blood pressure of the patient is high, low or moderate. The present work comprises of analyzing the pathological data of patient and predicting the future physiological state of a patient. From the height in feet and weight in kilograms, the B.M.I. of a patient is computed using the methodology discussed in [14].

The patient data has been fuzzified in a frame of cognition with the objective of transformation of periodic measures into likelihoods that the physiological parameter of the patient is high, low or moderate. In this paper we have considered six different pathophysiological parameters, which are required to predict any criticality in the renal system. From the following figures, we can obtain the optimal values of membership functions. 1

1 0 .9 0 .8 membership function v alues

Since physicians are more interested in knowing whether the pathological data of patients are high, moderate or low, and also the trend of patient parameters, it would be more useful, to represent the parameters of patients as linguistic variable rather than ordinary variable and use fuzzy logic to build a predictive model, to predict the fuzzy set in which the parameter of a patient is to lie in the next reading of patient data.

0 .7 0 .6 0 .5 0 .4 0 .3 0 .2 0 .1 0

5 0

(a)

6 0

7 0

8 0 D ia s t o lic

B lo o d

9 0 P re s s u re

1 0 0

1 1 0

1 2 0

Fig. 2(f) Fig. 2. Plots of the membership functions: B.M.I. (b) Glucose (c) Creatinine (d) Urea (e) Systolic Blood Pressure (f) Diastolic Blood Pressure

V. DESIGN AND TRAINING OF THE FUZZY NEURAL NETWORK The architecture of the fuzzy neural network is shown in figure 3.

0 . 9

membership function values

0 . 8 0 . 7 0 . 6 0 . 5 0 . 4 0 . 3 0 . 2 0 . 1 0

0

5

1 0

1 5 B

o d y

M

2 0 a s s

2 5

3 0

3 5

4 0

In d e x

Fig. 2(a) 1 0 . 9

membership function val ues

0 . 8 0 . 7 0 . 6 0 . 5 0 . 4 0 . 3 0 . 2 0 . 1 0

5 0

6 0

7 0

8 0

9 0 G

1 0 0 l u c o s e

1 1 0

1 2 0

1 3 0

1 4 0

1 5 0

Fig. 2(b) 1 0 . 9

membership func tion values

0 . 8 0 . 7 0 . 6 0 . 5 0 . 4 0 . 3 0 . 2 0 . 1 0

0

5

1 0

1 5

2 0

2 5

U re a

Fig. 2(c) 1 0 .9

membership function values

0 .8 0 .7 0 .6 0 .5 0 .4 0 .3 0 .2 0 .1 0 0 .2

0 .4

0 .6

0 .8

1 c r e a t i n in e

1 .2

1 .4

1 .6

1 .8

Fig. 3 Design of the fuzzy neural network for diagnosing criticality of patients

Fig. 2(d) 1 0 .9

membership funct ion values

0 .8 0 .7 0 .6 0 .5 0 .4 0 .3 0 .2 0 .1 0

8 0

9 0

1 0 0

1 1 0 S y s t o li c

1 2 0 B lo o d

1 3 0 P re s s u re

Fig. 2(e)

1 4 0

1 5 0

1 6 0

The leftmost layer is the input layer, which accepts the values of pathophysiological parameters over time and fuzzifies them to generate membership function values, which are presented to the hidden layer for calculating the possibilities of the pathophysiological parameters to be low, moderate or high at the next instant of time. The weighted sum of these possibility values from the hidden to the output layer indicates the criticality of the current condition of the patient. The inputs are presented to the input layer in the form of a 60 tuple (b(1), b(2) ……, b(10), g(1), g(2),….. g(10), c(1), c(2),…., c(10),

u(1), u(2),….., u(10), s(1), s(2),……, s(10), d(1), d(2), ……, d(10)). Initially only b(1), g(1), c(1), u(1), s(1) and d(1)have non zero values, while others have zero values. At the next instant of time (after 10 days), when a new set of data is entered, b(2), g(2), c(2), u(2), s(2) and d(2) are updated to non-zero values and so on. As new sets of data are entered, the old sets of data are updated. Thus after 10 sets of data collected at 10 days interval are entered, when the 11th set of data are entered, the new set of data goes to b(10), g(10), c(10), u(10), s(10) and d(10) and b(9), g(9), c(9), u(9), s(9) and d(9) are updated with the previous values of b(10), g(10), c(10), u(10), s(10) and d(10) respectively and so on. The training of the neural network is done with 40 sets of data and testing is done with another 40 sets of data. For training the network, backpropagation-learning algorithm is used. The weights of the dendrites between input and hidden layer are shown in table 1. In table 1, wbl(1) refers to the weight of the dendrite from b(1) to pbl and the weights of other dendrites from the input to the hidden layer are also named using the same convention. The weights of the dendrites from the hidden to the output layer are shown in table 2. In the following table, Wpbl refers to the weight of the dendrite from pbl to l and the weights of the other dendrites from the hidden to the output layers are named using the same convention.

VI. RESULTS AND DISCUSSIONS In order to find out the optimal values of the membership functions, the centers and widths of sigmoids are varied slightly, the changes, i.e. the time instants for prediction is shown in table 3. The first row from each table provides the best result as far as we are concerned with our results. We find that for some values we get results at an earlier instant of time but they lack reliability. So considering all these we choose the optimized set of values for our experiment. The system has been tested with the data of 40 patients and the results are compared with decisions being given by the medical practitioner. The data of a sample patient of 42 years has been analyzed and shown in the paper. The data of a sample patient of age 42 years and height 5.0 feet is provided in table 4. Table 5 shows the results of decision being by the smart agent AS refers to the actual pathophysiological state of the patient and PNS refers to the predicted next state. A value M in the AS columns indicate a moderate parameter value of patient, H* indicates the parameter of the patient is high, but falling within the tolerance limits of moderate value and H indicates, the parameter of the patient is strictly high. Cw indicates whether the system indicates a condition of approaching criticality. Although, the developed system gives a crisp decision regarding the future physiological state of the patient, the essence of the system lies in that the system predicts a state of criticality of the patient at time T6, much before the condition of criticality occurs (at time T10). This also

elucidates that such type of system when implemented in portable hardware can be deployed in telemedicine environments in rural areas, where the health care professionals often provide support services in absence of the physician. TABLE I. WEIGHTS OF THE DENDRITES BETWEEN INPUT AND HIDDEN LAYERS

Weight of dendrite Wbl(1) Wbl(2) Wbl(3) Wbl(4) Wbl(5) Wbl(6) Wbl(7) Wbl(8) Wbl(9) Wbl(10) Wgl(1) Wgl(2) Wgl(3) Wgl(4) Wgl(5) Wgl(6) Wgl(7)

Value 0.9760 1.9797 2.9839 3.9833 4.9872 5.9912 6.9965 7.9510 8.9522 9.9551 1.0001 1.9772 2.9633 3.9684 4.9635 5.9636 6.9637

Weight of dendrite Wbm(1) Wbm(2) Wbm(3) Wbm(4) Wbm(5) Wbm(6) Wbm(7) Wbm(8) Wbm(9) Wbm(10) Wgm(1) Wgm(2) Wgm(3) Wgm(4) Wgm(5) Wgm(6) Wgm(7)

Wgl(8) Wgl(9) Wgl(10) Wul(1) Wul(2) Wul(3)

7.9590 8.9590 9.9545 1.0000 2.0000 3.0000

Wul(4) Wul(5) Wul(6) Wul(7) Wul(8) Wul(9) Wul(10) Wcl(1) Wcl(2) Wcl(3) Wcl(4) Wcl(5) Wcl(6) Wcl(7) Wcl(8) Wcl(9) Wcl(10) Wsl(1) Wsl(2) Wsl(3) Wsl(4) Wsl(5) Wsl(6) Wsl(7) Wsl(8) Wsl(9) Wsl(10) Wdl(1) Wdl(2) Wdl(3) Wdl(4) Wdl(5) Wdl(6) Wdl(7) Wdl(8) Wdl(9) Wdl(10)

3.9950 4.9172 5.9220 6.9123 7.9074 8.9074 9.9025 1.0000 2.0000 3.0000 3.9703 4.9406 5.9407 6.9406 7.9406 8.9109 9.9107 1.0000 1.9927 2.9855 3.9568 4.9497 5.9424 6.9357 7.9281 8.9281 9.9281 1.0000 2.0000 3.0000 3.9652 4.9481 5.9307 6.9306 7.9395 8.9134 9.9132

Value 1.0131 2.0104 3.0092 4.0087 5.0068 6.0056 7.0011 8.0253 9.0258 10.0258 1.0000 2.0132 3.0205 4.0186 5.0204 6.0207 7.0207

Weight of dendrite Wbh(1) Wbh(2) Wbh(3) Wbh(4) Wbh(5) Wbl(6) Wbh(7) Wbh(8) Wbh(9) Wbh(10) Wgh(1) Wgh(2) Wgh(3) Wgh(4) Wgh(5) Wgl(6) Wgh(7)

Value 1.0331 2.0281 3.0236 4.0230 5.0165 6.0137 7.0044 8.0665 9.0665 10.0665 1.0000 2.0332 3.0536 4.0464 5.0536 6.0536 7.0536

Wgm(8) Wgm(9) Wgm(10) Wum(1) Wum(2) Wum(3)

8.0232 9.0234 10.0261 1.0002 2.0000 3.0000

Wgh(8) Wgh(9) Wgh(10) Wuh(1) Wuh(2) Wuh(3)

8.0602 9.0604 10.067 1.0000 2.0000 3.0000

Wum(4) Wum(5) Wum(6) Wum(7) Wum(8) Wum(9) Wum(10) Wcm(1) Wcm(2) Wcm(3) Wcm(4) Wcm(5) Wcm(6) Wcm(7) Wcm(8) Wcm(9) Wcm(10) Wsm(1) Wsm(2) Wsm(3) Wsm(4) Wsm(5) Wsm(6) Wsm(7) Wsm(8) Wsm(9) Wsm(10) Wdm(1) Wdm(2) Wdm(3) Wdm(4) Wdm(5) Wdm(6) Wdm(7) Wdm(8) Wdm(9) Wdm(10)

4.0025 5.0365 6.0343 7.0381 8.0402 9.0403 10.0416 1.0000 2.0000 3.0000 4.0133 5.0271 6.0275 7.0275 8.0275 9.0406 10.0401 1.0000 2.0033 3.0074 4.0211 5.0253 6.0290 7.0329 8.0364 9.0361 10.0368 1.0000 2.0000 3.0000 4.0160 5.0245 6.0320 7.0321 8.0280 9.0401 10.0402

Wuh(4) Wuh(5) Wul(6) Wuh(7) Wuh(8) Wuh(9) Wuh(10) Wch(1) Wch(2) Wch(3) Wch(4) Wch(5) Wch(6) Wch(7) Wch(8) Wch(9) Wch(10) Wsh(1) Wsh(2) Wsh(3) Wsh(4) Wsh(5) Wsl(6) Wsh(7) Wsh(8) Wsh(9) Wsh(10) Wdh(1) Wdh(2) Wdh(3) Wdh(4) Wdh(5) Wdl(6) Wdh(7) Wdh(8) Wdh(9) Wdh(10)

4.0053 5.0976 6.0927 7.1033 8.1094 9.1095 10.1151 1.0000 2.0000 3.0000 4.0365 5.0723 6.0723 7.0723 8.0724 9.10911 10.1093 1.0000 2.0099 3.0192 4.0570 5.0665 6.0760 7.0854 8.0951 9.0950 10.0957 1.0000 2.0000 3.0000 4.0380 5.0573 6.0765 7.0765 8.0666 9.0953 10.0956

c) UREA

TABLE II. WEIGHT OF THE DENDRITE BETWEEN THE HIDDEN AND OUTPUT LAYERS

Weight of dendrite Wpbl Wpgl Wpcl Wpul Wpsl Wpdl

Value 7.2386 25.2680 52.5734 38.0779 26.0201 37.7542

Weight of dendrite Wpbm Wpgm Wpcm Wpum Wpsm Wpdm

Value 7.2582 24.9634 52.4827 38.9717 26.5323 36.8932

Weight of dendrite Wpbh Wpgh Wpch Wpuh Wpsh Wpdh

Value 7.2142 25.3232 53.1095 38.1981 26.1835 37.5777

Table III Time instant of prediction when center and width of the sigmoids are varied.

Cru (Center of right edge fuzzy set)

Wru (Width of right edge fuzzy set)

Time instant for prediction

0.2 0.2

Crmu (Center of the decreasin g sigmoid of the middle fuzzy set) 20 21

20 21

0.2 0.2

0.2 0.1 0.3 0.5 0.1

19 20 20 20 20

19 20 20 20 20

0.2 0.3 0.1 0.1 0.5

T6 Can’t be predicted T5 T6 T7 T7 T6

Wlu(width of the increasing and decreasing sigmoid of the middle fuzzy sets)

a)BMI Wlb(width of the increasing and decreasing sigmoid of the middle fuzzy sets) 1.25 1.25 1.5 1.15 1.25 1.25 1.25 1.15 1.35

Crmb (Center of the decreasing sigmoid of the middle fuzzy set)

Crb (Center of right edge fuzzy set)

Wrb (Width of right edge fuzzy set)

Time instant for prediction

26.5 27.5 26.5 26.5 25.5 25.5 27.5 26.5 26.5

31 30 31 31 32 30 32 31 31

1.7 1.7 1.5 1.8 1.7 1.7 1.7 1.5 1.9

T4 T4 T7 T3 T3 T1 T10 T4 T3

b) GLUCOSE Wlg (Width of the increasing and decreasing sigmoid of the middle fuzzy sets) 1.2 1.2 1.2 1.2 1.2 1.3 1.1 1.3 1 1

Crmg (Center of the decreasing sigmoid of the middle fuzzy set)

Crg (Center of right edge fuzzy set)

Wrg (Width of right edge fuzzy set)

Time instant for prediction

125 127 127 123 123 125 125 125 125 135

125 127 123 127 123 125 125 125 125 115

1.2 1.2 1.2 1.2 1.2 1.3 1.4 1.5 1 1

T3 T5 T3 T3 T2 T3 T2 T3 T3 Cant be predicted

d) CREATININE Wlc (Width of the increasing and decreasing sigmoid of the middle fuzzy sets) 0.035 0.035 0.035 0.025 0.045 0.045 0.035 0.035 0.035

Crmc (Center of the decreasing sigmoid of the middle fuzzy set) 1.3 1.4 1.2 1.3 1.3 1.3 1.3 1.6 1.1

Crc (Center of right edge fuzzy set)

Wrc (Width of right edge fuzzy set)

Time instant for prediction

1.3 1.4 1.2 1.3 1.3 1.3 1.3 1.1 1.6

0.035 0.035 0.035 0.025 0.045 0.035 0.045 0.035 0.035

T6 T10 T4 T6 T6 T6 T6 T9 T9

e) SYSTOLIC BLOOD PRESSURE Wls (Width of the increasing and decreasing sigmoid of the middle fuzzy sets) 1.35 1.35 1.35 1.35 1.35 1.25 1.45 1.25 1.55

Crms (Center of the decreasin g sigmoid of the middle fuzzy set)

Crs (Center of right edge fuzzy set)

Wrs (Width of right edge fuzzy set)

Time instant for prediction

135 137 133 137 130 135 135 135 135

135 137 137 133 130 135 135 135 135

1.35 1.35 1.35 1.35 1.35 1.25 1.25 1.45 1.55

T6 T8 T6 T6 T2 T6 T6 T6 T6

f) DIASTOLIC BLOOD PRESSURE TABLE IV. RESULT OF A SAMPLE PATIENT OF AGE 42 YEARS, Wld (Width of the increasing and decreasing sigmoid of the middle fuzzy sets) 1.45 1.65 1.45 1.65 1.25 1.45 1.45 1.45 1.45

Crmd (Center of the decreasing sigmoid of the middle fuzzy set) 93 93 93 93 93 90 97 90 96

Crd (Center of right edge fuzzy set)

Wrd (Width of right edge fuzzy set)

95 95 95 95 95 100 93 92 100

1.45 1.65 1.65 1.65 1.25 1.45 1.45 1.45 1.45

Time instant for prediction

HEIGHT OF PATIENT: 5.0 FT

T6 T5 T6 T6 T6 T9 T7 T5 Cant be predicted

Time

Weight

B.M.I.

Glucose

Creatinine

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10

64.1 66.2 66.8 67.5 66.9 67.8 68.2 69.5 70.5 70.6

27.97 28.31 28.57 28.87 28.61 29.00 29.17 29.73 30.15 30.62

120 125 128 127 128 128 128 129 129 131

1.0 1.1 1.2 1.3 1.4 1.4 1.4 1.4 1.8 2.4

Systolic Blood Pressure 128 131 132 136 137 138 139 140 140 143

ASS M H* H* H* H* H* H* H H H

PNSS M M M M M H H H H H

Diastolic Blood Pressure 87 88 90 94 96 98 98 97 100 101

.

TABLE V

Results of decision being given by the smart agent Time T1 T2 T3 T4 T5 T6 T7 T8 T9 T10

ASB M H* H* H* H* H* H* H* H H

PNSB M M M M H H H H H H

ASG M M H* H* H* H* H* H* H* H

PNSG M M M H H H H H H H

ASU M M M H* H* H* H* H* H* H

VII. CONCLUSION The present work proposes an intelligent model with a fuzzy neural network, which can predict the future condition of a patient on the basis of past pathophysiological parameters. It explains the usage of fuzzy neural networks in medical diagnosis systems and the extended example on the problem of early detection of approaching critical renal condition of patients. For diagnosis purposes, body mass index (B.M.I.), glucose, urea, creatinine, systolic and diastolic blood pressures are considered as pathophysiological parameters. The fuzzy neural network has been suitably trained and tested with real patient data to find out the correspondence with the decision being given by the fuzzy neural network and the actual pathophysiological state of the patient. The results show that the model developed can predict the critical condition of a patient much earlier than the critical condition actually occurs. REFERENCES [1] D. M. Eddy, “The challenge”, Journal of American Medical Association, Vol. 263 pp. 287–290, 1990. [2] R.J. Lilford, S.G. Pauker, D.A. Braunholz, and J. Chard, “Decision analysis and the implementation of research findings”, Biomedical Journal, Vol. 317 pp. 405–409, 1998.

PNSU M M M M M M H H H H

ASC M M M H* H* H* H* H* H H

PNSC M M M M M M H H H H

ASD M M H* H* H* H* H* H* H H

PNSD M M M M M M H H H H

CW 0 0 0 0 0 0 1 1 1 1

[3] L.A. Zadeh, “Fuzzy Sets”, Information and Control, Vol. 8, pp. 338-353, 1965. [4] D.R. Hush, B.G. Horne, “Progress in Supervised Neural Networks”, IEEE Signal Processing Magazine, Vol. 10, pp. 8-39, 1993. [5] R.P. R.P. Lippmann, “An Introduction of Computing with Neural Nets”, IEEE ASSP Magazine, pp. 4-22, 1992. [6] R.S. Scalero, N. Tepedelenlioglu, “A Fast New Algorithm for training Feedforward NN”, IEEE Transactions on Signal Processing, Vol. 40, pp. 202210, 1992. [7] B. Widrow, MA. Lehr, “30 years of Adaptive Neural Networks: Perceptron, Madaline and Backpropagation”, Proceedings of the IEEE Neural Networks Conference, Vol. 78, pp.1415-1442, 1990 [8] G.P.K. Economou, C. Spiropoulos, N.M. Economopoulos, N. Charokopos, D. Lymberopoulos, M. Spiliopoulou, E. Haaralambopulu, C.E. Goutis, “Medical Decision making systems in Pulmonology: A creative environment based on Artificial Neural Networks”, IEEE Workshop on Neural Networks for Signal Processing, 1994. [9] M. Berg, “Rationalizing Medical Work, Decision-support Techniques and Medical Practices”, MIT press, 1997. [10] A. Kaufmann, M.M. Gupta, “Introduction to fuzzy arithmetic, theory and applications”, Van Nostrand Reinhold Co., 1985. [11] A. Abraham, M. Koppen, “Hybrid Information Systems”, Physica Verlag, Heidelberg, 2002. [12] A. Konar, S. Pal, “Modeling Cognition with Fuzzy Neural Nets”, Fuzzy Theory Systems: Techniques and Applications, Vol. 3, Academic Press, 1999. (Editor: C.T. Leondes) [13] M. Gott, “Telematics for Health: The Role of Telemedicine in Homes and Communities”, Oxford, U.K.: Radcliffe Med. Press, 1995. [14] A.L. Gibbs, E. Braunwald, “Primary Cardiology”, W.B. Saunders Company, Philadelphia, Pennsylavania, 1998.