effective completion of typewriting ...effective completion of typewriting examination – using...

EFFECTIVE COMPLETION OF TYPEWRITING EXAMINATION – USING FUZZY

MATRIX

aVivehananthan. V*, bRajeswari. K, cAnbalagan. S a B.T. Assistant Panchayat Union Middle School, Puttur, Ammapet-614402, Thanjavur, Tamilnadu, India.

bAssistant Professor, Department of Mathematics, Periyar Maniammai Institute of Science & Technology, Vallam, Thanjavur, Tamilnadu, India

cAssistant Professor, Department of Mathematics, Rajah Serfoji Government College (Autonomous), Thanjavur, Tamilnadu, India

Abstract

Type writing is one of the extra-curricular for both school students and college students. Type writing plays a main role getting jobs in government (TNPSC) and in private sector also. Some working peoples came to learn typewriting for their promotion, hike in salary etc., so we have interested the study which age group of people complete the type writing examination in their first attempt. We investigated the effective completion and suggest some ideas for their effective completion by using CETD matrix those who are trying to complete.

Mathematics Subject Classification: 15A60, 15B15

Keywords: Fuzzy matrix, RTD matrix, CETD matrix.

1. Introduction

VasanthaKandasamy and Indira [8] presented the Combined Effective Time Dependent data (CETD) matrix in 1998 for the study of passenger transportation problem. In that study the data was divided into four types of matrices in some manner and defined as Initial Raw Data Matrix, Average Time Dependent Data (ATD) matrix, Refined Time Dependent Data (RTD) matrix and Combined Effective Time Dependent Data (CETD) matrix. The same methodology was used by VasanthaKandasamy [6] to study the migrant laborers who were affected by HIV/AIDS and for agriculture labourers studied by VasanthaKandasamyand Victor Devadoss[9].

After that, a number of authors [2, 5, 7, 10, 11] studied the CETD matrix to find solution for various real life problems. Recently one of our authors co-authored with George [3] investigated for examination result analysis using fuzzy matrices and in [4] the impact of prerequisites in engineering mathematics.

In this paper we use the same CETD matrix methodology, to examine the effective completion of typewriting examination in the duration. We gave suggestions that continuous practice may useful to complete the examination on the particular duration.

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

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2. Preliminaries and Procedure

Average Time Dependent (ATD) matrix

Raw data transform it into a raw time dependent data matrix by taking along the rows the age group and along the columns problems facing by the candidates in type writing exams. Using the raw data matrix we make it into the Average Time Dependent Data (ATD) matrix (aij) by dividing each entry of the raw data matrix by the number of years i.e., the time period.

We found the average and Standard Deviation (S.D) of every column in the ATD matrix.

Refined Time Dependent (RTD) matrix

Using the average μj, the Standard Deviation σj of the each jth column we chose a parameter α in [0, 1] (in [8]), the Refined Time Dependent (RTD) Matrix is defined by the following formula:

aij ≤ (μj – α × σj) then eij = -1

else

if aij ∈ (μj – α × σj, μj + α × σj) then eij = 0 (2.1)

else

if aij ≥ (μj + α × σj) then eij= 1

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

belong to the set {-1, 0, 1}.

Combined Effective Time Dependent Data (CETD) matrix

Combine the RTD matrices for the various α [0, 1], so that we get the Combined Effective Time Dependent Data (CETD) matrix. The row sum is obtained for CETD matrix and conclusions are derived based on the row sums.

All these are represented by graphs and it plays a vital role in exhibiting the data by the simplest means, which can even be understood by a layman.

The methodology using CETD matrix is as follows:

Step 1: Construct the raw data matrix by taking along the rows the age group and along the columns Candidates facing problems in type writing examination.

Step 2: Average Time Dependent (ATD) matrix. Transform the raw data into a Average Time Dependent data Matrix (aij) by dividing each entry of the raw data matrix by the number of years (length of the interval).


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Step 3: Refined Time Dependent (RTD) matrix Find the average µj and S.D σj of each jth column, chose a parameter α from the interval

[0, 1]. Using the formula (2.1) form the RTD Matrix. Step 4: Obtain the row sum which gives the maximum age group. Step 5: Obtained the Combined Effective Time Dependent Data (CETD) matrix.

Combine the above RTD matrices for various α [0, 1].Obtain the row sum of the CETD matrix.

Step 6: Represent age group vs. row sum of the CETD matrix everything in graphs, since graphs play a vital role in exhibiting the data by the simplest way.

3. Effective Completion of Type Writing Examination Using5×5 Matrix

To complete the type writing examination the candidates facing many problems among them we categorized five most important attributes by interviewing and collecting the data from typewriting candidates and typewriting trainers in typing institute at Thanjavur Town. X1: Lack of English Knowledge. X2: Lack of attendance. X3: Lack of concentration. X4: Lack of Practicing. X5: Lack of Timing

Table 1: Initial Raw data matrix of order 5 × 5 X1 X2 X3 X4 X5

16-20 3 5 2 6 2

21-25 4 2 4 6 1

26-30 3 3 3 4 2

31-35 2 4 2 5 3

36-40 5 6 7 6 2

Table 2: Average Time Dependent Matrix (ATD) for 5 × 5 X1 X2 X3 X4 X5

16-20 0.6 1 0.4 0.6 0.4

21-25 0.8 0.4 0.8 1.2 0.2

26-30 0.6 0.6 0.6 0.8 0.4

31-35 0.4 0.8 0.4 1 0.6

36-40 1 1.2 1.4 1.2 0.4


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Table 3: Average (µ) and Standard Deviation (σ) of ATD Matrix

Average 0.68 0.8 0.72 0.96 0.4

SD 0.2280 0.3162 0.414 0.260 0.141

For the various value of α {0.25, 0.5, 0.75,0.9} andby the formula (2.1) we have the RTD matrices as follows:

RTD matrix for 𝜶 = 𝟎. 𝟐𝟓

Row sum

[ −1 1 −1 −1 0 1 −1 0 1 −1−1 −1 −1 −1 0−1 0 −1 0 1 1 1 1 1 0]

[ −2 0−4−1 4]

Table 4 Age Group 16-20 21-25 26-30 31-35 36-40

Row Sum -2 0 -4 -1 4

Graph 1: Depicting the impact for α = 0.25

-6

-4

-2

0

2

4

6

16-20 21-25 26-30 31-35 36-40 Datenreihen1


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RTD matrix for 𝜶 = 𝟎. 𝟓

Row sum

[

0 1 −1 −1 0 1 −1 0 1 −10 −1 0 −1 0

−1 0 −1 0 1 1 1 1 1 0]

[ −1 0−2−1 4]

Table 5

Age Group 16-20 21-25 26-30 31-35 36-40 RTD -1 0 -2 -1 4


-6

-4

-2

0

2

4

6

16-20 21-25 31-35 36-40 26-30 Datenreihen1


0 of 54

RTD matrix for 𝜶 = 𝟎. 𝟕𝟓

Row sum

[ 0 0 −1 −1 0 0 −1 0 1 −1 0 0 0 0 0−1 0 −1 0 1 1 1 1 1 0]

[ −2−1 0−1 4]

Table 6

Age Group 16-20 21-25 26-30 31-35 36-40

Row Sum -2 -1 0 -1 4 Graph 3: Depicting the impact for α = 0.75

-6

-4

-2

0

2

4

6

16-20 21-25 31-35 36-40 26-30 Datenreihen1


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RTD matrix for 𝜶 = 𝟎. 𝟗

Row sum

[ 0 0 0 −1 0 0 −1 0 1 −1 0 0 0 0 0−1 0 0 0 1 1 1 1 1 0]

[ −1−1 0 0 4]

Table 7

Age Group 16-20 21-25 26-30 31-35 36-40

Row Sum -1 -1 0 0 4


-6

-4

-2

0

2

4

6

16-20 21-25 31-35 36-40 26-30 Datenreihen1


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Combined Effective Time Dependent Data matrix (CETD):

Row sum

[ −1 2 −3 −4 0 2 −4 0 4 −4−1 −2 −1 −2 0−4 0 −3 0 4 4 4 4 4 0]

[ −6−2−6−3 16]

Table 8

Age Group 16-20 21-25 26-30 31-35 36-40 CETD -6 -2 -6 -3 16

Graph 5: CETD Matrix

4. Conclusion

By using CETD matrix (Graph 5) we conclude that, the age group 16–20and 26–30got passing the typewriting examination is the particular duration and huge in number. And it shows that the age group 36 – 40 scored a very big score in the lacking performance so we strongly suggest, for that group to take continuous practice to perform well and clear the type writing examination in the particular period of time.

-10

0

10

20

16-20 21-25 26-30 31-35 36-40

Datenreihen1


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References

[1] G.J.Klir, and N.J. Folger, Fuzzy Sets Uncertainty and Information, Prentice Hall Englewood, Cliffs (1998).

[2] A.Praveenprakash and Kanimozhiraman, “Estimation of Maximum Age Group of Old

Age People affected by the Psychological Problems using CETD Matrix”, Int. J. Engg.

Res. and General Sci., Vol-3(1) (2015) 544-550. [3] K. Rajeshwari and A. George, “Examination Result Analysis Using Fuzzy Matrix”, Int. J.

of Innovative Research in Computer and Communication Engineering, vol-4(5), (2016).

[4] K. Rajeshwari and A. George, “Impact of Prerequisites in Engineering Mathematics – A Fuzzy Approach”, Indian J. Sci. Res. 14 (1), (2017) 340-343.

[5] W.B.VasanthaKandasamy, Public. Pity.Patients.Peace.,Public opinion on HIV/AIDS,

Tamil Nadu State AIDS ControlSociety, Chennai, 2006.

[6] W.B. VasanthaKandasamy and FlorentinSmarandache, 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, Phoenix, USA (2004).

[7] W.B.VasanthaKandasamy,FlorentinSmarandache and K.Ilanthenral, Elementary Fuzzy MatrixTheory and Fuzzy Models for Social Scientistis Published by Automaton, Los Angeles, USA (2007).

[8] W.B.VasanthaKandasamy, and V.Indra, Maximizing thepassengers comfort in the madras transport corporation usingfuzzy programming, Progress of Mat., Banaras Hindu Univ., 32, (1998)91-134.

[9] W.B.VasanthaKandasamy and Victor Devadoss,Identification of the maximum age group in which theagricultural labourers suffer health hazards due to chemicalPollution using fuzzy matrix,Dimension of pollution, 3 (2005)1-55.

[10] A. Victor Devadoss and A. Felix,Woman Teacher affected by Stress in Chennai School using CETD Matrix, Indo-Bhutan International Conference on Gross National Happiness, Vo1.2,(2013)189- 195.

[11] A.VictorDevadoss and S.M.A. ShahulHameed VulnerableAttitude of Road user using

Fuzzy Matrix Technique, International Journal of Engineering and Computer Science ISSN:2319-7242 Vol.-4 (3), (2015) 10787-10790.


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