# A Note on Hypertension Classification Scheme and Soft Computing Decision Making System

Authors: Pankaj Srivastava; Amit Srivastava; Anjali Burande; Amit Khandelwal
Journal: ISRN Biomathematics
 (2013)

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## Abstract

Nowadays young professionals are a soft target of hypertension due to the increased work pressure and poor tolerance. Many people have high blood pressure for years without knowing it. Most of the time, there are no symptoms, but when this condition goes untreated it damages arteries and vital organs throughout the body and that is why it is also termed as the silent killer. Complications arising from hypertension could lead to stroke and heart failure. Soft computing approach provides a sharper conclusion from vague, ambiguous, and imprecise data (generally found in medical field) using linguistic variables. In this study, a soft computing diagnostic support system for the risk assessment of hypertension is proposed.


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## Body

## 1. Introduction

A human body is a complex system and there are a number of variables that affect its functioning. The abnormality in its functioning causes a number of symptoms in the form of primary stages of different diseases although the recognition of these symptoms and their mapping with the diseases precisely is not an easy one. Sometimes compications in human body may be caused by improper diagnosis or improper management of the disease or due to the inaccessibility of medical personnel [1]. The quickening speed of change and adoption of western lifestyles by people in developing countries have led to a sharp rise in the incidence of hypertension [2]. Hypertension is a medical term for high blood pressure which is a condition that occurs when the pressure in the arteries is above the normal range. According to one of the studies “Recession has had an adverse impact on jobs in India and perhaps this is one of the reasons why cases of Hypertension have gone up in past two years among young IT professionals”. Recent analysis has predicted that more than 1.56 billon people will be living with hypertension worldwide by the year 2025. It has been declared by a survey report that one of four adults in India has high BP which kills 7.5 million people worldwide each year; moreover, AIDS, diabetes, road accidents, and tuberculosis are put together. In India 23.1% men and 22.6% women have high BP a notch lower than the global prevalence of one in three adults says the World Health statistics 2012 released, 16 May 2012. Jain [3] established a decision making process phenomenon in the presence of fuzzy variables. Poli et al. [4] developed a neural network expert system for diagnosing and treating hypertension. Degani [5] discussed computerized electrocardiogram diagnosis using fuzzy approach. Charbonnier et al. [6] proposed the statistical and fuzzy models of ambulatory systolic blood pressure for hypertension diagnosis. Jena et al. [7] discussed the application of soft computing in medical science. Pandey et al. [8] proposed a rule based system for cardiac analysis based on electrocardiography. Further, Allahverdi et al. [9] proposed a fuzzy expert system for the determination of coronary heart disease risk (CHD) of patient for the next ten years. Nalayini and Wahidabanu [10] were of the view that most of the cardiac diseases are characterized by varied degrees of intricacy and the conventional procedures are not capable of dealing with these intricacies very efficiently. Djam and Kimbi [1] developed a fuzzy expert system for the management of hypertension. Recently, P. Srivastava and A. Srivastava [11] proposed a soft computing diagnostic system to evaluate the risk factor for coronary heart disease (CHD). Srivastava and Sharma [12] designed a soft computing diagnostic system that classifies ECG beats in different phases and enables us to identify the status of cardiac health as per available ECG graphs. The present paper introduces a new soft computing model that measures risk factor on the basis of newly designed algorithm; a number of cases have been discussed as per available database.


## 2. Methodology

For complex systems, fuzzy tools are quite suitable because of its tolerance to some imprecision. In the present study, the inputs consist of age, systolic blood pressure (SBP), diastolic blood pressure (DBP), body mass index (BMI), heart rate, low density lipoprotein (LDL), high density lipoprotein (HDL), triglyceride, smoking, and exercise, while the output is the risk grade of hypertension.In order to design a user friendly informative system for evaluating risk percentage of hypertension, we propose fuzzy Algorithm1.Algorithm 1
(I) Initial fuzzification mechanism
BEGIN
(1) Input-Fuzzy system with suitable “n” parameters Ai
(2) Initialize i←1
DO UNTIL (i>n)
Categorize ni fuzzy sets in Xj linguistic variables
DO UNTIL (j>ni)
(1) Construction of suitable membership function µXj
(2) Increment j
END DO UNTIL
Increment i
END
(II)  Construction of Fuzzy Strings
BEGIN
(1) Input: “ni” fuzzy sets in linguistic variables
Xj; i=1,2,…, n and  j=1,2,…,ni
(2) Input: m output parameters Yo, o=1,2,…,m.
(3) Develop t=k1,k2,…,kr linguistic strings Jk; k=1,2,…,t
using AND operation on each linguistic term Xj; j=1,2,…,ni
(4) Initialize k←1
DO UNTIL (k>t)
Increment j
END DO UNTIL
Increment k
END
(III)   Output Evaluation
BEGIN
(1) Construct Utility matrix U of pxq order.
(2) Construct r utility fuzzy sets UI; I=1,2,…r
using x⊕y=x+y-xy  for each x,y∈U
(3) Initialize I←1
DO UNTIL (I>r)
(4) Construct r maximizing sets UMI, I=1,2…r
corresponding to each alternative.
(5) Develop r optimal fuzzy utility sets UOI, I=1,2…r.
Each optimal fuzzy set UOI is obtained by  fuzzy
intersection ⋀ on fuzzy utility set and maximizing
set such that μUOI(x)=μUI(x)⋂μUMI(x)=min(μUI(x),μUMI(x))
for each utility value x.
(6) Take maximum membership value from each optimal utility fuzzy set.
(7) The optimal alternative AO with corresponding maximum
membership grades obtained in step 10 such as
A
O
=
{
(
(
max
)
μ
U
O
I
(
x
)
,
B
I
)
:
⋁
x
∈
U
O
I
} for I=1,2…r.
END DO UNTIL
Increment I
END


### 2.1. Input Variables

#### 2.1.1. Blood Pressure

In this field we use systolic BP (SBP) and diastolic BP (DBP). The input variables for SBP and DBP were classified into seven fuzzy sets (see Table1).Table 1
Systolic BP in mm Hg
Diastolic BP in mm Hg
Desirable
90–120
60–80
Above desirable
120–130
80–85
Moderate
130–140
85–90
Above moderate
140–150
90–95
Little high
150–160
95–100
High
160–170
100–110
Very high
>168
>108Systolic Blood Pressure (SBP).Consider
(1)μdesirable={1x≤90(x-9015)290≤x<1051-(x-10515)2105≤x<1200x≥120,μabovedesirable={0x≤120x-1203120<x≤1231123<x≤127130-x3127<x≤1300x≥130,μmoderate={0x≤130x-1303130<x≤1331133<x≤137140-x3137<x≤1400x≥140,μabovemoderate={0x≤140x-1403140<x≤1431143<x≤147150-x3147<x≤1500x≥150,μlittlehigh={0x≤150x-1503150<x≤1531153<x≤157160-x3157<x≤1600x≥160,μhigh={0x≤160x-1603160<x≤1631163<x≤167170-x3167<x<1700x≥170,μveryhigh={0x≤168(x-1686)2168≤x<1741-(x-1746)2174≤x<1801x≥180.Diastolic Blood Pressure (DBP)
(2)
μ
normal
=
{
1
x
≤
60
(
x
-
60
10
)
2
60
≤
x
<
70
1
-
(
x
-
70
10
)
2
70
≤
x
<
80
0
x
≥
80
,
μ
above
normal
=
{
0
x
≤
80
x
-
80
2
80
<
x
≤
82
85
-
x
3
82
<
x
≤
85
0
x
≥
85
,
μ
moderate
=
{
0
x
≤
85
x
-
85
2
85
<
x
≤
87
90
-
x
3
87
<
x
≤
90
0
x
≥
90
,
μ
above
moderate
=
{
0
x
≤
90
x
-
90
2
90
<
x
≤
92
95
-
x
3
92
<
x
≤
95
0
x
≥
95
,
μ
little
high
=
{
0
x
≤
95
x
-
95
2
95
<
x
≤
97
100
-
x
3
97
<
x
≤
100
0
x
≥
100
,
μ
high
=
{
0
x
≤
100
x
-
100
5
100
<
x
≤
105
110
-
x
5
105
<
x
≤
110
0
x
≥
110
,
μ
very
high
=
{
0
x
≤
108
(
x
-
108
6
)
2
108
≤
x
<
114
1
-
(
x
-
114
6
)
2
114
≤
x
<
120
1
x
≥
120
.


#### 2.1.2. Cholesterol

In this study we have classified total cholesterol into low density lipoprotein (LDL) cholesterol and high density lipoprotein (HDL). HDL cholesterol level has been classified into four fuzzy sets. LDL cholesterol level has been classified into five fuzzy sets. High levels of LDL are associated with coronary artery disease, whereas high levels of HDL appear to protect against coronary artery disease. These fuzzy sets have been shown in Table2.Table 2
Cholesterol (mg/dL)
LDL
HDL
Normal
≤100
Very high
≤30
Above normal
100–130
Borderline high
130–160
High
30–50
High
160–190
Nearly normal
50–60
Very high
≥180
Normal
≥58Low Density Lipoprotein (LDL). Consider
(3)μnormal={1x≤50(x-5025)250≤x<751-(x-7525)275≤x<1000x≥100,μabovenormal={0x≤100x-10010100<x≤1101110≤x≤120130-x10120<x≤1300x≥130,μborderlinehigh={0x≤130x-13010130<x≤1401140≤x≤150160-x10150<x≤1600x≥160,μhigh={0x≤160x-16010160<x≤1701170≤x≤180190-x10180<x≤1900x≥190,μveryhigh={0x≤180(x-19020)2180≤x<2001-(x-20020)2200≤x<2201x≥220.High Density Lipoprotein (HDL). Consider
(4)μveryhigh={0x≤0x-0100<x≤10110<x≤2030-x1020<x≤300x≥30,μhigh={0x≤30x-30530<x≤35135<x≤4550-x545<x≤500x≥50,μnearlynormal={0x≤50x-50350<x≤53153<x≤5760-x357<x≤600x≥60,μnormal={0x≤58(x-587)258≤x<651-(x-655)265≤x<701x≥70.


#### 2.1.3. Age

This input field is classified into six fuzzy sets. The fuzzy sets with their range are shown in Table3. Consider
(5)μyoung={1x≤0(x-015)20≤x<151-(x-1515)215≤x<300x≥30,μadult={0x<25x-25525≤x≤30130≤x≤4048-x840≤x≤480x≥48,μmidaged={0x<45x-45545≤x≤50150≤x≤5660-x456≤x≤600x≥60,μaged={0x<58x-58458≤x≤62162≤x≤6672-x666≤x≤720x≥72,μold={0x<70x-70470≤x≤74174≤x≤7886-x878≤x≤860x≥86,μveryold={0x≤80(x-807)280≤x<871-(x-878)287≤x<951x≥95.Table 3
Age (in years)
Young
<30
Adult
25–48
Midaged
45–60
Aged
58–72
Old
70–86
Very old
>80


#### 2.1.4. BMI

Body mass index is defined as the individual’s body weight divided by square of his or her height. This input field is classified into four fuzzy sets. The fuzzy sets with their range are shown in Table4. Consider
(6)μlow={1x≤10(x-104)210≤x<141-(x-144)214≤x<180x≥18,μmedium={0x≤15x-15315<x≤18118<x≤2426-x224<x≤260x≥26,μabovemedium={0x≤25x-25225<x≤27127<x≤3034-x430<x≤340x≥34,μhigh={0x≤32x-32232<x≤34134<x≤3840-x238<x≤400x≥40,μveryhigh={0x≤38x-38238<x≤40140<x≤4446-x244<x≤460x≥46,μveryveryhigh={0x≤44(x-443)244≤x<471-(x-473)247≤x<501x≥50.Table 4
Body mass index (kg/m2)
Low (underweight)
10–18
Medium (normal weight)
15–26
Above medium (overweight)
25–34
High (obese)
32–40
Very high (severe obese)
38–46
Very very high (super obese)
44–50


#### 2.1.5. Heart Rate

This input field is classified into four linguistic variables.The fuzzy sets with their range are shown in Table5. Consider
(7)μlow={1x≤50(x-506)250≤x<561-(x-569)256≤x<650x≥65,μnormal={0x≤60x-601060<x≤70170<x≤7580-x575<x≤800x≥80,μhigh={0x≤78x-781278<x≤90190<x≤100110-x10100<x≤1100x≥110,μveryhigh={0x≤105(x-10510)2105≤x<1151-(x-11510)2115≤x<1251x≥125.Table 5
Heart rate (beats/min)
Low
50–65
Normal
60–80
High
78–110
Very high
105–125


#### 2.1.6. Triglyceride

Triglycerides have been identified to play a major role in heart disease and hypertension. This input field is classified into four fuzzy sets. The fuzzy sets with their range are shown in Table6. Consider
(8)μnormal={1x≤0(x-7575)20≤x<751-(x-7575)275≤x<1500x≥150,μalittlebithigh={0x≤150x-15015150<x≤1651165≤x≤185200-x15185<x≤2000x≥200,μhigh={0x≤200x-200100200<x≤3001300≤x≤400500-x100400<x≤5000x≥500,μveryhigh={0x≤500(x-500100)2500≤x<6001-(x-600100)2600≤x<7001x≥700.Table 6
Triglyceride (mg/dL)
Normal
<150
A little bit high
150–200
High
200–500
Very high
≥500


#### 2.1.7. Physical Exercise

This input field is classified into four fuzzy sets. The fuzzy sets with their range are shown in Table7. If a person is not doing exercise, then input value is zero. Consider
(9)μlow={1x≤5(x-512)25≤x<171-(x-1713)217≤x<300x≥30,μmedium={0x≤30x-301030<x≤40140≤x≤5060-x1050<x≤600x≥60,μhigh={0x≤60x-601060<x≤70170≤x≤90100-x1090<x≤1000x≥100,μveryhigh={0x≤90(x-9015)290≤x<1051-(x-10515)2105≤x<1201x≥120.Table 7
Exercise (in Min)
Low effective
5–30
medium effective
30–60
High effective
60–100
Very high effective
90–120


#### 2.1.8. Smoking

This input field is classified into four fuzzy sets. The fuzzy sets with their range are shown in Table8. If person is not smoking, then input value is zero. Consider
(10)μlow={1x≤5(x-52)25≤x<71-(x-73)27≤x<100x≥10,μmedium={0x≤8x-868<x≤1420-x614<x≤200x≥20,μhigh={0x≤18x-18618<x≤2430-x624<x≤300x≥30,μveryhigh={0x≤28(x-284)228≤x<321-(x-323)232≤x<351x≥35.Table 8
Smoking (per day)
Low smoker
5–10 cigarettes
Medium smoker
8–20 cigarettes
High smoker
18–30 cigarettes
Very high smoker
28–35 cigarettes


### 2.2. Output Variable

The output contains risk grade of hypertension which is classified in five linguistic variables, very low, low, moderate, high, and very high. The output optimal alternatives indicate patient’s present grade of hypertension. These optimal alternatives have been graphically shown in the form of Sugeno’s spikes.


## 2.1. Input Variables

### 2.1.1. Blood Pressure

In this field we use systolic BP (SBP) and diastolic BP (DBP). The input variables for SBP and DBP were classified into seven fuzzy sets (see Table1).Table 1
Systolic BP in mm Hg
Diastolic BP in mm Hg
Desirable
90–120
60–80
Above desirable
120–130
80–85
Moderate
130–140
85–90
Above moderate
140–150
90–95
Little high
150–160
95–100
High
160–170
100–110
Very high
>168
>108Systolic Blood Pressure (SBP).Consider
(1)μdesirable={1x≤90(x-9015)290≤x<1051-(x-10515)2105≤x<1200x≥120,μabovedesirable={0x≤120x-1203120<x≤1231123<x≤127130-x3127<x≤1300x≥130,μmoderate={0x≤130x-1303130<x≤1331133<x≤137140-x3137<x≤1400x≥140,μabovemoderate={0x≤140x-1403140<x≤1431143<x≤147150-x3147<x≤1500x≥150,μlittlehigh={0x≤150x-1503150<x≤1531153<x≤157160-x3157<x≤1600x≥160,μhigh={0x≤160x-1603160<x≤1631163<x≤167170-x3167<x<1700x≥170,μveryhigh={0x≤168(x-1686)2168≤x<1741-(x-1746)2174≤x<1801x≥180.Diastolic Blood Pressure (DBP)
(2)
μ
normal
=
{
1
x
≤
60
(
x
-
60
10
)
2
60
≤
x
<
70
1
-
(
x
-
70
10
)
2
70
≤
x
<
80
0
x
≥
80
,
μ
above
normal
=
{
0
x
≤
80
x
-
80
2
80
<
x
≤
82
85
-
x
3
82
<
x
≤
85
0
x
≥
85
,
μ
moderate
=
{
0
x
≤
85
x
-
85
2
85
<
x
≤
87
90
-
x
3
87
<
x
≤
90
0
x
≥
90
,
μ
above
moderate
=
{
0
x
≤
90
x
-
90
2
90
<
x
≤
92
95
-
x
3
92
<
x
≤
95
0
x
≥
95
,
μ
little
high
=
{
0
x
≤
95
x
-
95
2
95
<
x
≤
97
100
-
x
3
97
<
x
≤
100
0
x
≥
100
,
μ
high
=
{
0
x
≤
100
x
-
100
5
100
<
x
≤
105
110
-
x
5
105
<
x
≤
110
0
x
≥
110
,
μ
very
high
=
{
0
x
≤
108
(
x
-
108
6
)
2
108
≤
x
<
114
1
-
(
x
-
114
6
)
2
114
≤
x
<
120
1
x
≥
120
.


### 2.1.2. Cholesterol

In this study we have classified total cholesterol into low density lipoprotein (LDL) cholesterol and high density lipoprotein (HDL). HDL cholesterol level has been classified into four fuzzy sets. LDL cholesterol level has been classified into five fuzzy sets. High levels of LDL are associated with coronary artery disease, whereas high levels of HDL appear to protect against coronary artery disease. These fuzzy sets have been shown in Table2.Table 2
Cholesterol (mg/dL)
LDL
HDL
Normal
≤100
Very high
≤30
Above normal
100–130
Borderline high
130–160
High
30–50
High
160–190
Nearly normal
50–60
Very high
≥180
Normal
≥58Low Density Lipoprotein (LDL). Consider
(3)μnormal={1x≤50(x-5025)250≤x<751-(x-7525)275≤x<1000x≥100,μabovenormal={0x≤100x-10010100<x≤1101110≤x≤120130-x10120<x≤1300x≥130,μborderlinehigh={0x≤130x-13010130<x≤1401140≤x≤150160-x10150<x≤1600x≥160,μhigh={0x≤160x-16010160<x≤1701170≤x≤180190-x10180<x≤1900x≥190,μveryhigh={0x≤180(x-19020)2180≤x<2001-(x-20020)2200≤x<2201x≥220.High Density Lipoprotein (HDL). Consider
(4)μveryhigh={0x≤0x-0100<x≤10110<x≤2030-x1020<x≤300x≥30,μhigh={0x≤30x-30530<x≤35135<x≤4550-x545<x≤500x≥50,μnearlynormal={0x≤50x-50350<x≤53153<x≤5760-x357<x≤600x≥60,μnormal={0x≤58(x-587)258≤x<651-(x-655)265≤x<701x≥70.


### 2.1.3. Age

This input field is classified into six fuzzy sets. The fuzzy sets with their range are shown in Table3. Consider
(5)μyoung={1x≤0(x-015)20≤x<151-(x-1515)215≤x<300x≥30,μadult={0x<25x-25525≤x≤30130≤x≤4048-x840≤x≤480x≥48,μmidaged={0x<45x-45545≤x≤50150≤x≤5660-x456≤x≤600x≥60,μaged={0x<58x-58458≤x≤62162≤x≤6672-x666≤x≤720x≥72,μold={0x<70x-70470≤x≤74174≤x≤7886-x878≤x≤860x≥86,μveryold={0x≤80(x-807)280≤x<871-(x-878)287≤x<951x≥95.Table 3
Age (in years)
Young
<30
Adult
25–48
Midaged
45–60
Aged
58–72
Old
70–86
Very old
>80


### 2.1.4. BMI

Body mass index is defined as the individual’s body weight divided by square of his or her height. This input field is classified into four fuzzy sets. The fuzzy sets with their range are shown in Table4. Consider
(6)μlow={1x≤10(x-104)210≤x<141-(x-144)214≤x<180x≥18,μmedium={0x≤15x-15315<x≤18118<x≤2426-x224<x≤260x≥26,μabovemedium={0x≤25x-25225<x≤27127<x≤3034-x430<x≤340x≥34,μhigh={0x≤32x-32232<x≤34134<x≤3840-x238<x≤400x≥40,μveryhigh={0x≤38x-38238<x≤40140<x≤4446-x244<x≤460x≥46,μveryveryhigh={0x≤44(x-443)244≤x<471-(x-473)247≤x<501x≥50.Table 4
Body mass index (kg/m2)
Low (underweight)
10–18
Medium (normal weight)
15–26
Above medium (overweight)
25–34
High (obese)
32–40
Very high (severe obese)
38–46
Very very high (super obese)
44–50


### 2.1.5. Heart Rate

This input field is classified into four linguistic variables.The fuzzy sets with their range are shown in Table5. Consider
(7)μlow={1x≤50(x-506)250≤x<561-(x-569)256≤x<650x≥65,μnormal={0x≤60x-601060<x≤70170<x≤7580-x575<x≤800x≥80,μhigh={0x≤78x-781278<x≤90190<x≤100110-x10100<x≤1100x≥110,μveryhigh={0x≤105(x-10510)2105≤x<1151-(x-11510)2115≤x<1251x≥125.Table 5
Heart rate (beats/min)
Low
50–65
Normal
60–80
High
78–110
Very high
105–125


### 2.1.6. Triglyceride

Triglycerides have been identified to play a major role in heart disease and hypertension. This input field is classified into four fuzzy sets. The fuzzy sets with their range are shown in Table6. Consider
(8)μnormal={1x≤0(x-7575)20≤x<751-(x-7575)275≤x<1500x≥150,μalittlebithigh={0x≤150x-15015150<x≤1651165≤x≤185200-x15185<x≤2000x≥200,μhigh={0x≤200x-200100200<x≤3001300≤x≤400500-x100400<x≤5000x≥500,μveryhigh={0x≤500(x-500100)2500≤x<6001-(x-600100)2600≤x<7001x≥700.Table 6
Triglyceride (mg/dL)
Normal
<150
A little bit high
150–200
High
200–500
Very high
≥500


### 2.1.7. Physical Exercise

This input field is classified into four fuzzy sets. The fuzzy sets with their range are shown in Table7. If a person is not doing exercise, then input value is zero. Consider
(9)μlow={1x≤5(x-512)25≤x<171-(x-1713)217≤x<300x≥30,μmedium={0x≤30x-301030<x≤40140≤x≤5060-x1050<x≤600x≥60,μhigh={0x≤60x-601060<x≤70170≤x≤90100-x1090<x≤1000x≥100,μveryhigh={0x≤90(x-9015)290≤x<1051-(x-10515)2105≤x<1201x≥120.Table 7
Exercise (in Min)
Low effective
5–30
medium effective
30–60
High effective
60–100
Very high effective
90–120


### 2.1.8. Smoking

This input field is classified into four fuzzy sets. The fuzzy sets with their range are shown in Table8. If person is not smoking, then input value is zero. Consider
(10)μlow={1x≤5(x-52)25≤x<71-(x-73)27≤x<100x≥10,μmedium={0x≤8x-868<x≤1420-x614<x≤200x≥20,μhigh={0x≤18x-18618<x≤2430-x624<x≤300x≥30,μveryhigh={0x≤28(x-284)228≤x<321-(x-323)232≤x<351x≥35.Table 8
Smoking (per day)
Low smoker
5–10 cigarettes
Medium smoker
8–20 cigarettes
High smoker
18–30 cigarettes
Very high smoker
28–35 cigarettes


## 2.1.1. Blood Pressure

In this field we use systolic BP (SBP) and diastolic BP (DBP). The input variables for SBP and DBP were classified into seven fuzzy sets (see Table1).Table 1
Systolic BP in mm Hg
Diastolic BP in mm Hg
Desirable
90–120
60–80
Above desirable
120–130
80–85
Moderate
130–140
85–90
Above moderate
140–150
90–95
Little high
150–160
95–100
High
160–170
100–110
Very high
>168
>108Systolic Blood Pressure (SBP).Consider
(1)μdesirable={1x≤90(x-9015)290≤x<1051-(x-10515)2105≤x<1200x≥120,μabovedesirable={0x≤120x-1203120<x≤1231123<x≤127130-x3127<x≤1300x≥130,μmoderate={0x≤130x-1303130<x≤1331133<x≤137140-x3137<x≤1400x≥140,μabovemoderate={0x≤140x-1403140<x≤1431143<x≤147150-x3147<x≤1500x≥150,μlittlehigh={0x≤150x-1503150<x≤1531153<x≤157160-x3157<x≤1600x≥160,μhigh={0x≤160x-1603160<x≤1631163<x≤167170-x3167<x<1700x≥170,μveryhigh={0x≤168(x-1686)2168≤x<1741-(x-1746)2174≤x<1801x≥180.Diastolic Blood Pressure (DBP)
(2)
μ
normal
=
{
1
x
≤
60
(
x
-
60
10
)
2
60
≤
x
<
70
1
-
(
x
-
70
10
)
2
70
≤
x
<
80
0
x
≥
80
,
μ
above
normal
=
{
0
x
≤
80
x
-
80
2
80
<
x
≤
82
85
-
x
3
82
<
x
≤
85
0
x
≥
85
,
μ
moderate
=
{
0
x
≤
85
x
-
85
2
85
<
x
≤
87
90
-
x
3
87
<
x
≤
90
0
x
≥
90
,
μ
above
moderate
=
{
0
x
≤
90
x
-
90
2
90
<
x
≤
92
95
-
x
3
92
<
x
≤
95
0
x
≥
95
,
μ
little
high
=
{
0
x
≤
95
x
-
95
2
95
<
x
≤
97
100
-
x
3
97
<
x
≤
100
0
x
≥
100
,
μ
high
=
{
0
x
≤
100
x
-
100
5
100
<
x
≤
105
110
-
x
5
105
<
x
≤
110
0
x
≥
110
,
μ
very
high
=
{
0
x
≤
108
(
x
-
108
6
)
2
108
≤
x
<
114
1
-
(
x
-
114
6
)
2
114
≤
x
<
120
1
x
≥
120
.


## 2.1.2. Cholesterol

In this study we have classified total cholesterol into low density lipoprotein (LDL) cholesterol and high density lipoprotein (HDL). HDL cholesterol level has been classified into four fuzzy sets. LDL cholesterol level has been classified into five fuzzy sets. High levels of LDL are associated with coronary artery disease, whereas high levels of HDL appear to protect against coronary artery disease. These fuzzy sets have been shown in Table2.Table 2
Cholesterol (mg/dL)
LDL
HDL
Normal
≤100
Very high
≤30
Above normal
100–130
Borderline high
130–160
High
30–50
High
160–190
Nearly normal
50–60
Very high
≥180
Normal
≥58Low Density Lipoprotein (LDL). Consider
(3)μnormal={1x≤50(x-5025)250≤x<751-(x-7525)275≤x<1000x≥100,μabovenormal={0x≤100x-10010100<x≤1101110≤x≤120130-x10120<x≤1300x≥130,μborderlinehigh={0x≤130x-13010130<x≤1401140≤x≤150160-x10150<x≤1600x≥160,μhigh={0x≤160x-16010160<x≤1701170≤x≤180190-x10180<x≤1900x≥190,μveryhigh={0x≤180(x-19020)2180≤x<2001-(x-20020)2200≤x<2201x≥220.High Density Lipoprotein (HDL). Consider
(4)μveryhigh={0x≤0x-0100<x≤10110<x≤2030-x1020<x≤300x≥30,μhigh={0x≤30x-30530<x≤35135<x≤4550-x545<x≤500x≥50,μnearlynormal={0x≤50x-50350<x≤53153<x≤5760-x357<x≤600x≥60,μnormal={0x≤58(x-587)258≤x<651-(x-655)265≤x<701x≥70.


## 2.1.3. Age

This input field is classified into six fuzzy sets. The fuzzy sets with their range are shown in Table3. Consider
(5)μyoung={1x≤0(x-015)20≤x<151-(x-1515)215≤x<300x≥30,μadult={0x<25x-25525≤x≤30130≤x≤4048-x840≤x≤480x≥48,μmidaged={0x<45x-45545≤x≤50150≤x≤5660-x456≤x≤600x≥60,μaged={0x<58x-58458≤x≤62162≤x≤6672-x666≤x≤720x≥72,μold={0x<70x-70470≤x≤74174≤x≤7886-x878≤x≤860x≥86,μveryold={0x≤80(x-807)280≤x<871-(x-878)287≤x<951x≥95.Table 3
Age (in years)
Young
<30
Adult
25–48
Midaged
45–60
Aged
58–72
Old
70–86
Very old
>80


## 2.1.4. BMI

Body mass index is defined as the individual’s body weight divided by square of his or her height. This input field is classified into four fuzzy sets. The fuzzy sets with their range are shown in Table4. Consider
(6)μlow={1x≤10(x-104)210≤x<141-(x-144)214≤x<180x≥18,μmedium={0x≤15x-15315<x≤18118<x≤2426-x224<x≤260x≥26,μabovemedium={0x≤25x-25225<x≤27127<x≤3034-x430<x≤340x≥34,μhigh={0x≤32x-32232<x≤34134<x≤3840-x238<x≤400x≥40,μveryhigh={0x≤38x-38238<x≤40140<x≤4446-x244<x≤460x≥46,μveryveryhigh={0x≤44(x-443)244≤x<471-(x-473)247≤x<501x≥50.Table 4
Body mass index (kg/m2)
Low (underweight)
10–18
Medium (normal weight)
15–26
Above medium (overweight)
25–34
High (obese)
32–40
Very high (severe obese)
38–46
Very very high (super obese)
44–50


## 2.1.5. Heart Rate

This input field is classified into four linguistic variables.The fuzzy sets with their range are shown in Table5. Consider
(7)μlow={1x≤50(x-506)250≤x<561-(x-569)256≤x<650x≥65,μnormal={0x≤60x-601060<x≤70170<x≤7580-x575<x≤800x≥80,μhigh={0x≤78x-781278<x≤90190<x≤100110-x10100<x≤1100x≥110,μveryhigh={0x≤105(x-10510)2105≤x<1151-(x-11510)2115≤x<1251x≥125.Table 5
Heart rate (beats/min)
Low
50–65
Normal
60–80
High
78–110
Very high
105–125


## 2.1.6. Triglyceride

Triglycerides have been identified to play a major role in heart disease and hypertension. This input field is classified into four fuzzy sets. The fuzzy sets with their range are shown in Table6. Consider
(8)μnormal={1x≤0(x-7575)20≤x<751-(x-7575)275≤x<1500x≥150,μalittlebithigh={0x≤150x-15015150<x≤1651165≤x≤185200-x15185<x≤2000x≥200,μhigh={0x≤200x-200100200<x≤3001300≤x≤400500-x100400<x≤5000x≥500,μveryhigh={0x≤500(x-500100)2500≤x<6001-(x-600100)2600≤x<7001x≥700.Table 6
Triglyceride (mg/dL)
Normal
<150
A little bit high
150–200
High
200–500
Very high
≥500


## 2.1.7. Physical Exercise

This input field is classified into four fuzzy sets. The fuzzy sets with their range are shown in Table7. If a person is not doing exercise, then input value is zero. Consider
(9)μlow={1x≤5(x-512)25≤x<171-(x-1713)217≤x<300x≥30,μmedium={0x≤30x-301030<x≤40140≤x≤5060-x1050<x≤600x≥60,μhigh={0x≤60x-601060<x≤70170≤x≤90100-x1090<x≤1000x≥100,μveryhigh={0x≤90(x-9015)290≤x<1051-(x-10515)2105≤x<1201x≥120.Table 7
Exercise (in Min)
Low effective
5–30
medium effective
30–60
High effective
60–100
Very high effective
90–120


## 2.1.8. Smoking

This input field is classified into four fuzzy sets. The fuzzy sets with their range are shown in Table8. If person is not smoking, then input value is zero. Consider
(10)μlow={1x≤5(x-52)25≤x<71-(x-73)27≤x<100x≥10,μmedium={0x≤8x-868<x≤1420-x614<x≤200x≥20,μhigh={0x≤18x-18618<x≤2430-x624<x≤300x≥30,μveryhigh={0x≤28(x-284)228≤x<321-(x-323)232≤x<351x≥35.Table 8
Smoking (per day)
Low smoker
5–10 cigarettes
Medium smoker
8–20 cigarettes
High smoker
18–30 cigarettes
Very high smoker
28–35 cigarettes


## 2.2. Output Variable

The output contains risk grade of hypertension which is classified in five linguistic variables, very low, low, moderate, high, and very high. The output optimal alternatives indicate patient’s present grade of hypertension. These optimal alternatives have been graphically shown in the form of Sugeno’s spikes.


## 3. Result

Now we have developed various linguistic strings to represent the state of the patient using the input variables such as age, LDL, HDL, SBP, DBP, triglyceride, BMI, HR, exercise, and smoking. Some of the linguistic strings are given as follows.J
1 = YoungAgeNormalLDLNormalHDLDesirableSBPDesirableDBPNormalTriglycerideMBMINormalHRNoExcerciseNoSmokingJ
2 = YoungAgeNormalLDLNormalHDLDesirableSBPDesirableDBPNormalTriglycerideMBMINormalHRLowExcerciseLowSmokingJ3 = YoungAgeNormalLDLNormalHDLDesirableSBPDesirableDBPNormalTriglycerideMBMINormalHRMediumExcerciseLowSmokingJ
400 = YoungAgeNormalLDLNormalHDLNormalSBPNormalDBPNormalTriglycerideAMBMINormalHRMediumExcerciseLowSmokingJ
401 = YoungAgeNormalLDLNormalHDLDesirableSBPDesirableDBPNormalTriglycerideAMBMIHighHRMediumExcerciseMedSmokingJ
2500 = AdultAgeNormalLDLNormalHDLDesirableSBPADesirableDBPNormalTriglycerideMBMINormalHRNoExcerciseNoSmokingJ
6500 = AdultAgeHighLDLHighHDLDesirableSBPModerateDBPNormalTriglycerideAMBMIHighHRLowExcerciseLowSmokingJ
10001 = AdultAgeHighLDLHighHDLDesirableSBPModerateDBPNormalTriglycerideAMBMIHighHRLowExcerciseMediumSmokingJ
17009 = MidagedAgeNormalLDLNormalHDLDesirableSBPDesirableDBPNormalTriglycerideMBMINormalHRNoExcerciseNoSmokingJ17010 = MidagedAgeNormalLDLNormalHDLDesirableSBPDesirableDBPNormalTriglycerideMBMIHighHRNoExcerciseLowSmokingJ
200080 = AgedAgeNormalLDLNormalHDLDesirableSBPADesirableDBPNormalTriglycerideMBMINormalHRNoExcerciseNoSmokingJ
405001 = AgedAgeHighLDLHighHDLModerateSBPModerateDBPNormalTriglycerideVHBMIVHHRLowExcerciseMediumSmokingJ
966080 = AgedAgeVeryHighLDLNVeryhighHDLVeryhighSBPVeryhighDBPVeryhighTriglycerideVHBMINormalHRLowExcercisehighSmokingJ
1200200 = OldAgeHighLDLNormalHDLAboveDesirableSBPModerateDBPNormalTriglycerideAMBMINormalHRLowExcercise NoSmokingJ
2344569 = OldAgeVeryHighLDLNVeryhighHDLVeryhighSBPhighDBPVeryhighTriglycerideAMBMIHighHRNoExcerciseVery highSmokingJ
5676880 = VeryOldAgeVeryhighLDLNormalHDLModerateSBPADesirableDBPNormalTriglycerideAMBMINormalHRLowExcercise LowSmokingJ
7566780 = VeryoldAgeHighLDLHighHDLVeryhighSBPVeryhighDBPVeryhighTriglycerideHighBMIVHHRNoExcerciseVeryhighSmokingJ
8545200 = VeryoldAgeVeryHighLDLVeryhighHDLVeryhighSBPHighDBPV.highTriglycerideVHBMIHighHRNoExcercisehighSmokingJ
9031678 = VeryoldAgeVeryHighLDLVeryhighHDLVeryhighSBPVeryhighDBPVeryhighTriglycerideVHBMIVHHRLowExcerciseVery highSmokingJ
9031680 = VeryoldAgeVeryHighLDLVeryhighHDLVeryhighSBPVeryhighDBPVeryhighTriglycerideMVVHBMIVHHRNoExcerciseVery highSmoking.On the basis of our proposed technique to investigate the health status of a person whose medical data is available, three different cases have been discussed as follows.Case 1.
The input variables of first patient are(1)
Age = {(0, young), (0.8, adult), (0, midaged), (0, aged), (0, old), (0, very old)}.(2)
LDL = {(0.71, normal), (0, above normal), (0, borderline high), (0, high), (0, very high)}.(3)
HDL = {(0, very high), (0, high), (0, nearly normal), (1, normal)}.(4)
SBP = {(0, desirable), (0.8, above desirable), (0, moderate), (0, above moderate), (0, little high), (0, high), (0, very high)}.(5)
DBP = {(0, desirable), (1, above desirable), (0, moderate), (0, above moderate), (0, little high), (0, high), (0, very high)}.(6)
Triglyceride = {(0.72, normal), (0, a little bit high), (0, high), (0, very high)}.(7)
BMI = {(0, low), (0.99, medium), (0, above medium), (0, high), (0, very high), (0, very very high)}.(8)
HR = {(0, low), (0.86, normal), (0, high), (0, very high)}.(9)
Exercise = {(1, low), (0, medium), (0, high), (0, very high)}.(10)
Smoking = {(1, low), (0, medium), (0, high), (0, very high)}.This is the fuzzy set which represents the state of concerned patient:(11)X={(0.71,JA,N,N,AD,AD,N,M,N,L,L)}.The utility matrixUof order 5x9031680 by using the fuzzy rule base designed is as follows:
(12)U=(9895⋯10⋯10⋯056880⋯20⋯30⋯103025⋯45⋯62⋯402020⋯92⋯90⋯861010⋯55⋯20⋯95).The five fuzzy utilities are(1)
U1 = {(0.71, 98)},(2)
U2 = {(0.71, 68)},(3)
U3 = {(0.71, 30)},(4)
U4 = {(0.71, 20)},(5)
U5 = {(0.71, 10)}.The maximum sets corresponding to each alternative are(1)
U1m = {(1, 98)},(2)
U2m = {(0.69, 68)},(3)
U3m = {(0.30, 30)},(4)
U4m = {(0.20, 20)},(5)
U5m = {(0.10, 10)}.Now, the optimal fuzzy utilities using fuzzy utilities and maximizing sets are(1)
U1o = {(0.71, 98)},(2)
U2o = {(0.69, 68)},(3)
U3o = {(0.30, 30)},(4)
U4o = {(0.20, 20)},(5)
U5o = {(0.10, 10)}.Using these utilities, the optimal alternatives are given by(13)Ao={(0.71,verylow),(0.69,low),(0.30,moderate),(0.20,high),and(0.10,veryhigh)}.This optimal alternative indicates that the patient presently is in very low grade of hypertension. The optimal alternatives have been graphically shown in Figure1 in the form of Sugeno’s spikes.Figure 1
View of Sugeno’s spikes.Case 2.
The input variables of the second patient are as follows.(1)
Age = {(0, young), (0, adult), (1, midaged), (0, aged), (0, old), (0, very old)}.(2)
LDL = {(1, normal), (0, above normal), (0, borderline high), (0, high), (0, very high)}.(3)
HDL = {(0, very high), (0.6, high), (0, nearly normal), (0, normal)}.(4)
SBP = {(0, desirable), (0.8, above desirable), (0, moderate), (0, above moderate), (0, little high), (0, high), (0, very high)}.(5)
DBP = {(0, desirable), (0.66, above desirable), (0, moderate), (0, above moderate), (0, little high), (0, high), (0, very high)}.(6)
Triglyceride = {(0.66, normal), (0, a little bit high), (0, high), (0, very high)}.(7)
BMI = {(0, low), (0, medium), (0.86, above medium), (0, high), (0, very high), (0, very very high)}.(8)
HR = {(0, low), (0.76, normal), (0, high), (0, very high)}.(9)
Exercise = {(0, low), (0.79, medium), (0, high), (0, very high)}.(10)
Smoking = {(1, low), (0, medium), (0, high), (0, very high)}.This is the fuzzy set which represents the state of concerned patient:(14)X={(0.6,JMA,N,H,AD,AD,N,AM,N,M,L)}.The utility matrix is the same as in Case1.The five fuzzy utilities are(1)
U1 = {(0.6, 55)},(2)
U2 = {(0.6, 92)},(3)
U3 = {(0.6, 40)},(4)
U4 = {(0.6, 24)},(5)
U5 = {(0.6, 10)}.The maximum sets corresponding to each alternative are(1)
U1m = {(0.59, 55)},(2)
U2m = {(1, 92)},(3)
U3m = {(0.43, 35)},(4)
U4m = {(0.26, 24)},(5)
U5m = {(0.10, 10)}.Now, the optimal fuzzy utilities using fuzzy utilities and maximizing sets are(1)
U1o = {(0.59, 55)},(2)
U2o = {(0.6, 92)},(3)
U3o = {(0.43, 35)},(4)
U4o = {(0.26, 24)},(5)
U5o = {(0.10, 10)}.Using these utilities, the optimal alternatives are given by(15)Ao={(0.59,verylow),(0.60,low),(0.43,moderate),(0.26,high),and(0.10,veryhigh)}.This optimal alternative indicates that the patient presently is in low grade of hypertension. The optimal alternatives have been graphically shown in Figure2 in the form of Sugeno’s spikes.Figure 2
View of Sugeno’s spikes.Case 3.
The input variables of the third patient are as follows.(1)
Age = {(0, young), (0, adult), (0, midaged), (0, aged), (0.75, old), (0, very old)}.(2)
LDL = {(0, normal), (0, above normal), (0, borderline high), (0.8, high), (0, very high)}.(3)
HDL = {(0, very high), (1, high), (0, nearly normal), (0, normal)}.(4)
SBP = {(0, desirable), (0, above desirable), (0.8, moderate), (0, above moderate), (0, little high), (0, high), (0, very high)}.(5)
DBP = {(0, desirable), (1, above desirable), (0, moderate), (0, above moderate), (0, little high), (0, high), (0, very high)}.(6)
Triglyceride = {(1, normal), (0.66, a little bit high), (0, high), (0, very high)}.(7)
BMI = {(0, low), (0, medium), (0, above medium), (0.78, high), (0, very high), (0, very very high)}.(8)
HR = {(0, low), (0, normal), (0.96, high), (0, very high)}.(9)
Exercise = {(0, low), (1, medium), (0, high), (0, very high)}.(10)
Smoking = {(1, low), (0, medium), (0, high), (0, very high)}.This is the fuzzy set which represents the state of concerned patient:(16)X={(0.66,JO,H,H,M,AD,LH,H,H,M,L)}.The utility matrixUis the same as in Case 1.The five fuzzy utilities are(1)
U1 = {(0.66, 15)},(2)
U2 = {(0.66, 30)},(3)
U3 = {(0.66, 45)},(4)
U4 = {(0.66, 80)},(5)
U5 = {(0.66, 50)}.The maximum sets corresponding to each alternative are(1)
U1m = {(0.187, 15)},(2)
U2m = {(0.375, 30)},(3)
U3m = {(0.562, 45)},(4)
U4m = {(1, 80)},(5)
U5m = {(0.62, 50)}.Now, the optimal fuzzy utilities using fuzzy utilities and maximizing sets are(1)
U1o = {(0.187, 15)},(2)
U2o = {(0.375, 30)},(3)
U3o = {(0.562, 45)},(4)
U4o = {(0.66, 80)},(5)
U5o = {(0.62, 50)}.Using these utilities, the optimal alternatives are given by(17)Ao={(0.187,verylow),(0.375,low),(0.562,moderate),(0.66,high),and(0.62,veryhigh)}.This optimal alternative indicates that the patient is presently in high grade of hypertension.The optimal alternatives have been graphically shown in the form of Sugeno’s spikes in Figure3.Figure 3
View of Sugeno’s spikes.


## 4. Conclusion

The present research paper confirms that the soft computing diagnostic system can represent the expert’s thinking in an efficient manner to handle complex cases. The design and development of soft computing risk assessment system on the basis of the proposed technique will assist medical experts to measure grade classification of hypertension efficiently.



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*Source: 342970-2013-12-23.xml*