RISK FACTOR OF BREAST CANCER USING CETD MATRIX-AN … · School using CETD Matrix _, Indo-Bhutan International Conference on Gross National Happiness, Vol.2- 189-195. [9]Vasanthakandasamy

RISK FACTOR OF BREAST CANCER USING CETD MATRIX-AN ANALYSIS

aRadhika. K*, bAnbalagan, cAlexander and dSuganthi Mariyappan

a,b,d Assistant Professor, P.G and Research Department of Mathematics, Rajah Serfoji Govt.College

(Autonomous), Thanjavur, Tamil Nadu. India.

cAssistant Professor, Department of Mathematics, Raja Doraisingam Govt.Arts College, Sivagangai,

Tamil Nadu. India.

Abstract

Cancer begins when mutations takes place in genes that regulate cell growth. Breast

cancer forms in either lobules (or) ducts of the breast. Lobules are the glands which produce

milk, and ducts are the pathways from the glands to nipple. Breast Cancer can also develop in

the fatty tissue (or) fibrous connective tissue of the breast. By interviewing we have collected

the data from 322 Breast Cancer patients at Thanjavur cancer care and Research Centre.

Using this data we analysed by CETD methodology.

Keywords: Breast Cancer, ATD matrix, RTD matrix, CETD matrix. 1.Introduction:

Vasanthakandsamy and Indira[6] presented the Combined Effective Time

Dependent data (CETD) Matrix in 1998 to study of passenger transportation problem. In that

study the data was divided in to four types of matrices in some manner and defined as initial

Raw Matrix Average time Development Data (ATD) matrix, Refined Time Dependent Data

(RTD) matrix and combined Effect Time Dependent Data (CETD) matrix. The same

technique was used by Vasanthakandasamy and Florcntin Smarandache[7] to study the

migrant labourers who were affected by HIV/AIDS and for agriculture labourers studied by

Vasanthakandasamy and Victor Devadoss[9].

After that, a number of authors [1, 4, 8 and 5] studied the CETD matrix and found

solution for various real life problems. By interviewing we have collected the data’s from 322

patients in Thanjavur cancer care and Research Centre and used CETD matrix.

Breast cancer can grow in different parts of the breast. Breast cancer is the

malignant tumour that forms in the cells of the breast [3]. It occurs both in men and women

for men the breast cancer is very rare. The most common cancer all over cities in India is

breast cancer and second in the rural areas. Globally, there are about 10% of breast cancer is

due to genetic (or) inherited DNA mutation. Whereas recent studies show that there may be a

greater occurrence of genetically linked breast cancer among Indian women [2].

2. Preliminaries:

Definition 2.1[8]

The classical set Aα called alpha cut set of elements in which a fuzzy set A defined on and any number α ϵ [0,1 ] is given by Aα ={xϵX\µA(x)≥ α }.

Definition 2.2[8]

Average Time Dependent Data (ATD) matrix (aij) is obtained by dividing each entry of the raw data matrix by the number of year or the time period that is the difference of the class interval of each row. This matrix represents a data, which is totally uniform.

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 4, 2019 (Special Issue) © Research India Publications. http://www.ripublication.com

Page 67 of 73

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Definition2.3 [8]

The dependent matrix has been converted into matrix entries eij, where eij{-1,0,1}. Using simple average techniques and such a matrix is called as Refined Time Dependent matrix (RTD). µj and S.D of the each jth column and we chose a parameter from α the interval [0, 1] and form the Refined time dependent matrix (RTD) using the formula,

If aij≤(µj-α*σj) then eij=-1 else

If aijϵ(µj-α*σj,µj+α*σj) then eij=0 (1) else

If aij≥(µj+α*σj) then eij=1,

We redefine the ATD matrix into the Refined Time Dependent Matrix for here.

The entries are -1 0 & 1, now the row sum of this matrix gives the maximum Risk factor.

Definition2.4 [8]

Using the Refined Time Data Matrices we obtained the Combined Effective Time Dependent Data Matrix (CETD) which gives the cumulative effect of all those entries. This is done by finding the row sum matrix of the RTD matrix and also by combining these matrix by varying α [0, 1], so that we get a Combined Effective Time Dependent Data (CETD) matrix.

3. The Methodology using CETD matrix is as follows:

Step1

Construct the raw data matrix by taking along the rows the different Risk factor of

peoples and along the columns the different age groups of Breast cancer.

Step2 (Average Time Dependent (ATD) matrix)

Transform the raw data into an Average Time Dependent data Matrix (aij) by dividing

each entry of the raw data matrix by the time period (length of the interval).

Step3 (Refined Time Dependent (RTD) matrix)

Find the average (µj) and S.D ( j) of each column, chose a parameter α from the

interval [0, 1]. Using the formula (1) form the (RTD) matrix

Step4

The ATD matrix is refined into the RTD matrix whose entries are -1, 0 (or) 1. Now

we find for each RTD matrices with respect to α [0, 1] and combined all the RTD matrices

we have the CETD matrix.

Step5

We have the conclusion based on the row sum of CETD matrices and the

different risk factor, we plot the graph for the risk factor as x-axis and the Row sum of

the CETD matrix is y-axis. The graphs reflect the conclusion next manner.


Page 68 of 73

4. Estimation of maximum Risk factor of women affected by Breast cancer disease by

using 6x4 matrixes:

In this section we apply main factor that is

R1- Genetics R2-Hormone

R3- Over weight R4- Age

R5-Diet R6-Stress

Table 4.1: Initial Raw data Matrix of order 6x4.

Age groups

Risk factor

15-35 36-50 51-60 61-80

R1 30 12 18 11

R2 10 30 8 9

R3 10 15 10 8

R4 13 10 9 15

R5 20 9 15 10

R6 10 20 9 11

Table 4.2: ATD Matrix of order 6x4.

Age Groups

Risk factor

15-35 36-50 51-60 61-80

R1 0.323 0.125 0.261 0.172

R2 0.108 0.313 0.116 0.141

R3 0.108 0.156 0.145 0.125

R4 0.139 0.104 0.130 0.234

R5 0.215 0.094 0.217 0.156

R6 0.108 0.208 0.130 0.172

The RTD Matrix for α=0.1 Row sum Matrix

(

1 −1−1 1−1 −1

1 1−1 −1−1 −1

−1 −11 −1−1 1

−1 11 −1−1 1 )

(

2−2−4−200 )


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Graph4.1

The RTD Matrix for α=0.3 Row sum Matrix

(

1 −1−1 1−1 0

1 0−1 −11 −1

−1 −11 −1−1 1

−1 11 0−1 0 )

(

1−2−1−2

1−1)

Graph4.2:

-5

-4

-3

-2

-1

0

1

2

3

S1 S2 S3 S4 S5 S6

The

row

su

m o

f th

e m

atri

x

Risk Factor

The graph depicting maximum risk factor of women

affected by Breast cancer Disease for =0.1

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

S1 S2 S3 S4 S5 S6

The

row

sum

of

the

mat

rix

Risk Factor


affected by Breast Cancer Disease for =0.3


Page 70 of 73

The RTD matrix for=0.9 Row sum Matrix

(

1 00 10 0

1 00 00 −1

0 00 −10 0

0 10 00 0 )

(

21−11−10 )

Graph4.3:

The CETD matrix Row sum Matrix

(

3 −2−2 3−2 −1

3 1−2 −20 −3

−2 −22 −3−2 2

−2 32 −1−2 1 )

(

5−3−6−30−1)

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

S1 S2 S3 S4 S5 S6

The

ro

w s

um

of

the

mat

rix

Risk Factor


affected by Breast Cancer Disease for =0.9


Page 71 of 73

Graph 4.4:

CONCLUSION:

In this above study, the graph4.4 shows that the genetic risk factor affects mostly

other from all rise factors. By adopting the following life style, we can prevent breast cancer.

Control of weight, doing physical exercise, limited dose and duration of hormone therapy,

avoiding exposure to radiation and environmental pollution.

REFERENCES

[1] Albert William.M, Victor Devadoss.A and Janet Sheeba.J 2013, “Study of Breast Cancer

using Fuzzy matrix theory”,Int.J.Data mining Tech.&appl.vol.(2)20-23.

[2]Breast Cancer in women – Prevention-NHS.U.K https-//www.nhs uk>….>Breast Cancer.

[3]http//www.breastcancer.org>what is breast cancer. [4]Clement Joe.M Anand and Lathamaheswari.M., 2015, “A CETD matrix Approach to

Analyze the men Affected by Cardiovascular Disease matrix in Chennai”, Int.J.of

Engg.comp.sci.vol.(4)10469-10474.

[5] Lookman.H Sithic., Uma Rani, R.,2015, “Fuzzy matrix theory as a Knowledge Discovery in

health Care Domain”, Computer science vol. (47)-282.

[6]Vasanthakandasamy W.B, Indra.V, 1998, “Maximizing the passengers comfort in the

Madras transport corporation” using fuzzy programming progress of mat.Banaras Hindu

unit3, 2-91-134

-8

-6

-4

-2

0

2

4

6

S1 S2 S3 S4 S5 S6

The

ro

w s

um

of

the

mat

rix

Risk Factor

The graph depicting maximum risk factor of women affected by Breast Cancer Disease for CETD matrix


Page 72 of 73

[7]Vasanthakandasamy W.B. and Florentin Smarandache, 2004, “Analysis of social Aspects

of Migrant Labourers Living with HIV/AIDS” using Fuzzy theory and Neutrosophic Cognitive

Maps” with Special Reference to Rural Tamilnadu in India. Published by Xiquan,phonix,USA.

[8]Vector Devadoss.A and Felix, A., 2013, “Women Teacher affected by Stress in Chennai

School using CETD Matrix”, Indo-Bhutan International Conference on Gross National

Happiness, Vol.2- 189-195.

[9]Vasanthakandasamy W.B and Vector Devadoss.A,2005, “ Identification of the maximum

age group in which the agricultural labourers suffer health hazards due to chemical

pollution” using fuzzy matrix, Dimension of Pollution,vol.3 -1-55.


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RISK FACTOR OF BREAST CANCER USING CETD MATRIX-AN … · School using CETD Matrix _, Indo-Bhutan International Conference on Gross National Happiness, Vol.2- 189-195. [9]Vasanthakandasamy

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