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Volume 5, Issue 7, July 2017

International Journal of Advance Research in Computer Science and Management Studies

Research Article / Survey Paper / Case Study Available online at: www.ijarcsms.com

Fuzzy Linguistic Model for Estimating the Risk of Child

Mortality Debajyoti Bora

1

Research Scholar

Department of Statistics

Dibrugarh University, Dibrugarh, Assam – India

Manash Pratim Barman2

Assistant Professor

Department of Statistics

Dibrugarh University, Dibrugarh, Assam – India

Abstract: Fuzzy theory deals with linguistic terms which are uncertain; vague and indistinct in nature. Studied factors of

child mortality often comprises of inevitably vague linguistic terms, such as birth spacing, immunization, etc. In this context

fuzzy logic approach is used here to develop a predictive model to estimate the risk of child mortality on the basis of the

fuzziness of three variables viz. educational year of mother, wealth of the family to which the child belongs and birth order

of the child. The validation of the model is done in three stages; ROC curve, statistical test and individual observation by

taking real data from NFHS-III. Mamdani method is used for the inference and Centroid defuzzification method for risk of

child mortality. The model estimates low risk to the children who survived than those who had died. The accuracy of the

model is 0.837 (95% CI: 0.79-0.88) (p < 0.001). The accuracy is higher with risk below 78.8%, corresponding to 0.68 (95%

CI: 0.61-0.75) in respect to sensitivity, 0.98 (95% CI: 0.92-0.99) specificity, 0.98 positive predictive value and 0.64 negative

predictive value. Comparison of the fitted fuzzy linguistic model output i.e. risk of child mortality with the actual data is

indispensable and it determines the applicability of a model in practical situations.

Keywords: Fuzzy logic, Linguistic variable, Mamdani method, Centroid method, Child Mortality.

I. INTRODUCTION

The theory of fuzzy sets, introduced by Lotfi A. Zadeh in the 1960s and the resulting fuzzy logic have been regarded as

highly valuable tools that can be used to simplify and enhance the analysis and design of complex humanistic systems and

processes by employing the principles of approximate reasoning [1,2,3]. It modeled the uncertainty within natural language and

introduced the concept of vagueness. Fuzzy logic provides a unique and effective way to draw conclusions (system outputs)

from vague and imprecise information (system inputs). Fuzzy logic is based on the concept of fuzzy set. It is a logic in which

the truth values are fuzzy subsets of the unit interval with linguistic labels such as true, false, not true, very true, quite true, not

very true and not very false, etc. and they assume intermediate truth values represented by membership grades [4,5].

Fuzzy logic aims at modeling human thinking and reasoning and at applying the model to problems according to needs.

Fuzzy logic tries to adapt verbal rules and the human ability to make decisions. It uses verbal variables and terms together with

verbal rules [6]. Verbal rules and terms used in human decision-making process are fuzzy rather than precise. Verbal terms and

variables are, here, expressed mathematically as membership degrees and membership functions.

A fuzzy linguistic model is a rule base system which uses fuzzy theory and fuzzy logic to address the concern problem. It

contains four main components;

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A fuzzifier: It translates crisp input value(s) into fuzzy value(s).

A knowledge base: It includes both fuzzy rule sets and their membership functions representing the fuzzy sets of linguistic

variable.

An inference engine: It applies a fuzzy reasoning to obtain a fuzzy output(s).

A defuzzifier: It translates the fuzzy output value(s) into crisp value(s).

The fuzzy inference rules are usually expressed in the form “IF-THEN” that defines the connection between input and

output variable. The inference engine assesses all fuzzy rules in the rule base and combines the weighted consequents of all

relevant rules into a single output fuzzy set (Mamdani method). The fuzzy output set then replaced by a crisp value using

defuzzification process.

The real life events, death or mortality in demographic terminology has uncertainty, vagueness, and imprecision of its

occurrence. Also its occurrence depends on one or more factors involved. The best and most useful description of mortality

factors often comprise linguistic terms that are inevitably vague, such as age (early or late) and birth weight (high or low). Child

mortality, a core indicator for child health and well-being is the death of child of the age group 1-4 years. Studies showed that

different factors which may be responsible for child mortality comprises of linguistic terms that are inevitably vague, such as

birth spacing, immunization, family wealth, age of mother etc. Since the influencing factors of child mortality are uncertain,

vague and indistinct in nature, it is more suitable to use fuzzy theory and fuzzy logic to model the phenomenon. Thus an attempt

has been made to develop a fuzzy linguistic model for estimating risk of child mortality using fuzzy logic approach based on

educational year of mother, wealth of the family to which the child belongs and birth order of the child.

II. METHODOLOGY

A vast literature survey has been conducted for the identification of risk factors (i.e. inputs) associated with child mortality

(i.e. output). From the survey of literatures it has observed that no formal education, poor households and living in rural areas

increased the risk of child mortality [7]. Abir et al., 2015 found that child deaths decreased significantly among mothers who had

other children aged 3 years or older [8]. Becher et al., 2004 showed that birth spacing was one of the major factors responsible for

childhood mortality [9]. Schellenberg et al., 2002 showed that poor maternal education and low socio-economic status are

important factors influencing child mortality [10]. A positive association between birth order and childhood mortality had been

demonstrated for developing countries [11,12,13,14]. A large number of research studies have pointed out that children of high

birth order may be more exposed to death over the life-course than their earlier-born brothers and sisters

[15,16,17,18,19,20,21,22].

A. Input and Output Variable for the Model

Form the findings of literature survey three factors are taken as inputs variables for the construction of the fuzzy model for

estimating the risk of child mortality, viz.- Educational year of mother, wealth of the family to which the child belongs and birth

order of the child. To convert these selected input variables with crisp values into fuzzy sets, the values of the input variables

are categorized into different categories as described below.

The model includes three fuzzy sets to the variable educational attainment of mother; such as primary (≤ 5 years),

secondary (between 5 years and 10 years) and higher (10 years and above). Various researchers made different levels to

categorize the attainment of education by the mother [7,8,23,24,25,26,27,28]. A large number of countries developed and tested

wealth index in relation to inequalities in household income, use of health services and health outcomes [29]. Wealth index is

considered as an indicator of the level of wealth that is consistent with expenditure and income measures [30]. NFHS also used

wealth index to measure the economic status of households. NFHS categories households into five classes viz.- Poorest, Poor,

Middle, Richer, Richest. This index is based on the 33 assets and housing characteristics, which are household electrification;




type of windows; drinking water source; type of toilet facility; type of flooring; material of exterior walls; type of roofing;

cooking fuel; house ownership; number of household members per sleeping room; ownership of a bank or post-office account;

and ownership of a mattress, a pressure cooker, a chair, a cot/bed, a table, an electric fan, a radio/transistor, a black and white

television, a colour television, a sewing machine, a mobile telephone, any other telephone, a computer, a refrigerator, a watch

or clock, a bicycle, a motorcycle or scooter, an animal-drawn cart, a car, a water pump, a thresher and a tractor (NFHS-III,

2007). In the present study also wealth index is used to study the relation between wealth of a family and child mortality. Five

fuzzy sets are defined for the variable wealth of the family viz., poorest, poor, middle, richer and richest. The variable birth

order of the child is divided into two fuzzy sets as “proper” up to second birth order and “high” with birth order more than two

i.e. from third birth order. The output i.e. the death risk of child is divided in three labels viz.- low, middle and high.

Fuzzy Inference Processes

In this study trapezoidal fuzzy number and triangular fuzzy number is applied to convert the values of the input and output

variables respectively to fuzzy sets by calculating their respective membership degree. A stratified analysis is conducted using

NFHS-II data to study the relationship between the input variables and the output variable. The results of the analysis are

considered as the basis for setting up the rules in the fuzzy predictive model. After going through the results of the stratified

analysis and considering all categories of the input variables 22 fuzzy rules are constructed. The sequence of input variables in

the fuzzy rules is: birth order, wealth of the family; educational year and the output variables is risk of child death. Using these

22 fuzzy rules the risk of child death is determined by Mamdani inference methods which are in fuzzyfied form. To get the risk

of child death as crisp value Centroid defuzzification method is used which are estimated in percentage.

B. Checking Validity of the Model

The validity of the developed model is tested in three stages. At first a ROC curve is fitted to check the sensitivity and

specificity of the model. In the second and the third stage the estimated risk computed by the model is compared with real life

data. The real life data are taken from NFHS-III database having same input variables and output variable. A statistical test is

applied to compare the risk estimated by the model for those who experienced child mortality with those who survive. Lastly

individual cases from NFHS-III database are checked with the estimated risk. The MATLAB software (R2008b) and SPSS

(17.0) are used to perform the analysis.

III. RESULTS AND FINDINGS

A. Membership Functions of Input and Output Variables

The figures from 1a) to 1c) respectively shows the membership functions of inputs viz.-birth order, educational year of the

mother and wealth of the family and figure 2 shows the membership functions of output variables risk of child death.

Fig.1a): Membership function plots of input birth order




Fig.1b): Membership function plots of input mother’s education (in years)

Fig.1c): Membership function plots of input family wealth (as per NFHS-III)

Fig.2: Membership function plots of output risk of child mortality

B. Fuzzy Rules

Combing 3 inputs and one output variables the following 22 fuzzy rules are constructed.

1 If (BO is P) and (FW is PRT) and (EY is SE) then (Risk is M)

2 If (BO is P) and (FW is PRT) and (EY is PE) then (Risk is H)

3 If (BO is H) and (FW is PRT) and (EY is SE) then (Risk is H)

4 If (BO is P) and (FW is PR) and (EY is PE) then (Risk is M)

5 If (BO is P) and (FW is PR) and (EY is SE) then (Risk is M)

6 If (BO is H) and (FW is PR) and (EY is SE) then (Risk is H)

7 If (BO is P) and (FW is M) and (EY is PE) then (Risk is M)




8 If (BO is P) and (FW is M) and (EY is SE) then (Risk is L)

9 If (BO is H) and (FW is M) and (EY is SE) then (Risk is H)

10 If (BO is P) and (FW is M) and (EY is HE) then (Risk is L)

11 If (BO is P) and (FW is R) and (EY is PE) then (Risk is M)

12 If (BO is H) and (FW is R) and (EY is PE) then (Risk is H)

13 If (BO is H) and (FW is R) and (EY is SE) then (Risk is H)

14 If (BO is P) and (FW is RST) and (EY is PE) then (Risk is M)

15 If (BO is P) and (FW is RST) and (EY is SE) then (Risk is L)

16 If (BO is H) and (FW is RST) and (EY is PE) then (Risk is M)

17 If (BO is H) and (FW is PR) and (EY is PE) then (Risk is H)

18 If (BO is H) and (FW is M) and (EY is PE) then (Risk is H)

19 If (BO is H) and (FW is PRT) and (EY is PE) then (Risk is H)

20 If (BO is P) and (FW is R) and (EY is SE) then (Risk is L)

21 If (BO is H) and (FW is R) and (EY is HE) then (Risk is L)

22 If (BO is H) and (FW is RST) and (EY is HE) then (Risk is L)

Legend: BO: birth order (P: proper; H: high); FW: wealth of the family (PRT: poorest; PR: poor; M: middle; R: richer; RST: richest); EY: educational year (PE:

primary; SE: secondary; HE: higher); Risk in three labels: H; high; M: middle; L: low.

For example: Rule 1 indicates that when the birth order of the child is proper and wealth of the family is poorest and

mother’s educational year is secondary, then the risk of child death is medium.

C. Inference from the Model

The mean of the estimated risk value of child mortality is 67.7% (SD = 20.4), the range of these values is lies between

12.4% and 88.7%. The median and mode values are 63.85% and 50%.

Three surface graphs are constructed to plot the risks of infant death using the family wealth and mother’s educational years

(Fig. 3a); mother’s educational years and birth order (Fig. 3b); family wealth and birth order (Fig. 3c). The surface plot of risk

of child mortality using the family wealth and mother’s education (in years) shows that as the family wealth and mother’s

educational year increases, the risk of child mortality decreases. Similarly, From the surface plot of mother’s education (in

years) and birth order, it can be observed that risk of child death decreases with decrease of birth order and increase of

educational year. The surface plot of family wealth and birth order shows that the risk of child death decreases when family

wealth increases and birth order decreases.

Fig. 3a): Surface plot of family wealth and mother’s education (in years)




Fig. 3b): Surface plot of mother’s education (in years) and birth order

Fig. 3c): Surface plot of family wealth and birth order

D. Validity of the Model

Receiver Operating Characteristic (ROC) Curve: The ROC curve and the resulting table are given in Figure 4 and Table

1 below. From the above table it is observed that the area under the curve is significant at 95% confidence interval. Therefore it

can be say that the fitted model correctly specifies the risk of child mortality.

Table 1: Result of ROC analysis of child mortality risk.

Area under the curve Std. Error Sig. Asymptotic 95% Confidence Interval

Lower Bound Upper Bound

0.837 0.024 0.001 0.790 0.883

Fig.4: ROC curve of the estimated risks of child mortality

It can be observed that the accuracy of the ROC curve is higher when risk is below 78.8%, corresponding to 0.68 in respect

to sensitivity, 0.98 specificity, 0.98 positive predictive value and 0.64 negative predictive value. At 47.2% risk values,

sensitivity is 0.99, specificity is 0.14, negative predictive value is 0.92 and positive predictive value is 0.67.




Statistical Test: Before choosing proper statistical method for testing the estimated risk between those who died and

survived. The normality of the risk values are tested by using Kolmogorov-Smirnov and Shapiro-Wilk tests. The results are

given in Table 2 bellow.

Table 2: Normality test of the estimated risk values of child mortality

Kolmogorov-Smirnov Shapiro-Wilk

Statistic Df Sig. Statistic df Sig.

Risk of Child mortality .261 266 .001 .794 266 .001

From the above table it is clear that the estimated risk values of child mortality are not normally distributed as the p values

of both the tests is significant. It can also observe from the following Q-Q plot (Fig. 5).

Fig. 5: Normality plot of the risk values of child mortality

Since the risk values of child mortality does not follow normal distribution, Mann-Whitney test is applied to compare

whether the estimated risk of child mortality between those who died and survive are significantly different or not. The Mann-

Whitney test statistic value is 9.305 which is notably significant (p < 0.001). The mean rank of risk of child mortality among

those who died is 166.17; while the mean rank of risk among the survive children is 76.58. Therefore it can be inferred that the

developed fuzzy model estimate high risk value for those children who actually died and low risk for those who survive. It

justifies the accuracy of the fitted model in estimating child mortality.

Individual Observation of Cases: In this case, 12 cases are randomly selected from NFHS-III database which contains the

information on the input variables and their outcomes i.e. dead or alive of child and they are observed individually. The risk of

child mortality is estimated for these cases by using the developed model. The selected 12 cases with the information of input

variables and output variable together with estimated risk are presented in Table 3 below:

Table 3: Individual observation of cases

Sl. No. Birth

order

Family

wealth

Mother’s

Educational

year

Estimated

Risk (%)

Result

(Dead/ Alive)

1 2 (Proper) Richer 7 (Secondary) 12.4 Alive

2 2 (Proper) Richest 7 (Secondary) 13 Alive

3 1 (Proper) Richest 6 (Secondary) 38 Alive

4 1 (Proper) Richest 6 (Secondary) 43.4 Alive

5 2 (Proper) Richer 5 (Primary) 50 Alive

6 2 (Proper) Richest 5 (Primary) 50.2 Alive

7 1 (Proper) Poor 3 (Primary) 57.4 Dead

8 2 (Proper) Poorest 1 (Primary) 61.2 Dead

9 3 (High) Richest 2 (Primary) 74.3 Dead

10 6 (High) Middle 5 (Primary) 87.5 Dead

11 5 (High) Richest 0 (Primary) 87.6 Dead

12 3 (High) Richer 5 (Primary) 88.3 Dead




From this individually verification of selected cases it can be observed that the fitted model assign low risk values to the

children who survived than those who had died. The results of all the verifications justify that the fuzzy model developed in the

present research work is valid and can be used to estimate the risk of child mortality with specific input variables.

IV. DISCUSSION CONCLUSION

In this paper fuzzy logic approach has been applied to develop a fuzzy linguistic model to estimate the risk of child

mortality. The proposed model includes three input variables viz.- Educational year of mother, wealth of the family to which the

child belongs and birth order of the child.

The validity tests of the fitted model i.e. ROC curve, Mann-Whitney test analysis shows that the developed predictive

model of child mortality provides good results. Again, indispensable comparison of outputs of fitted fuzzy linguistic model i.e.

risks of child mortality in various situations with the actual data from NFHS-III determines the applicability of the model in

practical situations.

The theory of Fuzzy Sets has become an important mathematical approach in diagnosis systems, treatment of medical

images and more recently, in epidemiology and public health [31]. Again fuzzy logic has become a powerful tool for dealing

with imprecision and uncertainty aiming at tractability, robustness and low-cost solutions for real-world problems. These

features and the ability to deal with linguistic terms increase the number of works applying Fuzzy Logic in every area. It is need

to be mention that the application of fuzzy sets theory and fuzzy logic in demography and human health is a new area of

research. However, the approach has provides promising way for analyzing various demographic and health characteristics.

References

1. L. A. Zadeh, “Fuzzy Logic and Approximate Reasoning,” Synthes, vol. 30, pp. 407-428, 1975.

2. L. A. Zadeh, “Toward a Theory of Fuzzy Systems,” Report No. ERL-69-2, Electronics Research Laboratory, University of California, Berkeley, 1969.

3. L. A. Zadeh, “Outline of a New Approach to the Analysis of Complex Systems and Decision Processes,” IEEE Transactions Systems, Man and

Cybernetics, SMC-3(1), pp. 28-44, 1973.

4. A. Khaliq, and A. Ahmad, Fuzzy Logic and Approximate Reasoning, Blekinge Institute of Technology, Sweden, 2010.

5. H. Diab, and J. Saade, “Fuzzy Inference Modeling Methodology for the Simulation of Population Growth”, International Arab Jou rnal of Information

Technology, vol.2, no. 1, pp. 75-86, 2005.

6. H. Ishibuchi, T. Nakashima, and T. Murata, “A fuzzy classifier system that generates fuzzy if-then rules for pattern classification problems”, IEEE

International Conference on Evolutionary Proceedings, vol. 2, pp. 759–764, 1995.

7. O. K. Ezeh, K. E. Agho, M. J. Dibley, J. J. Hall, and A. N. Page, “Risk factors for postneonatal, infant, child and under-5 mortality in Nigeria: a pooled

cross-sectional analysis” BMJ Open, vol. 5, 2015.

8. T. Abir, K.E. Agho, A.N. Page, A.H. Milton, and M. J. Dibley, “Risk factors for under-5 mortality: evidence from Bangladesh Demographic and Health

Survey, 2004–2011”, BMJ Open, vol. 5, pp.1-9, 2015.

9. H. Becher, O. Muller, A. Jahn, A. Gbangou, G. Kynast-Wolf, and B. Kouyate, “Risk factors of infant and child mortality in rural Burkina Faso”, Bulletin

of the World Health Organization, vol. 82, no. 4, pp. 265-273, 2004.

10. J. R. M. A. Schellenberg, R. Nathan, S. Abdulla, O. Mukasa, T. J. Marchant, M. Tanner, and C. Lengeler, “Risk factors for child mortality in rural

Tanzania”, Tropical Medicine and International Health, vol. 7, no. 6, pp 506–511, 2002.

11. J. A. Ballweg, and I. G. Pagtolunan, “Parental underinvestment: A link in the fertility-mortality continuum”, Population Research and Policy Review, vol.

11, pp. 73–89, 1992.

12. V. C. Chidambaram, J. W. McDonald, and M. D. Bracher, Childhood mortality, The world fertility survey: An assessment, Oxford: Oxford University

Press, 1987.

13. S. O. Rutstein, Infant and child mortality: Levels, trends and demographic differentials, revised ed., World fertility survey, comparative studies, no. 43.

Voorburg: International Statistical Institute, 1984.

14. H. B. Newcombe, “Environmental versus genetic interpretations of birth order effects”, Eugenics Quarterly, vol. 12, no. 2, pp. 90–101, 1965.

15. J. Nixon, and J. Pearn, “An investigation of socio-demographic factors surrounding childhood drowning accidents”, Social Science & Medicine, vol. 12,

pp. 387–390, 1978.

16. B. A. Elliot, “Birth order and health: Major issues”, Social Science and Medicine, vol. 35, no. 4, pp. 443–452, 1992.

17. M. Wallden, Sibling position and mental capacity-reconsidered project metropolitan. A longitudinal study of a Stockholm cohort, Research report no.31,

University of Stockholm, Stockholm, 1990.




18. M. Wallden, Sibling position and the educational career. Project metropolitan. A longitudinal study of a Stockholm cohort, Research report no. 37,

University of Stockholm, Stockholm, 1992.

19. B. A. Kaplan, C. G. Mascie-Taylor, and J. Boldsen, “Birth order and the health status in a British national sample”, Journal of Biosocial Science, vol. 24,

pp. 25–33, 1992.

20. L. Belmont, and F. A. Marolla, “Birth order, family size, and intelligence”, Science, vol. 182, pp. 1096–1101, 1973.

21. H. M. Breland “Birth order, family size, and intelligence”, Science, vol. 184, 149, 1973.

22. H. M. Breland, “Birth order, family configuration and verbal achievement”, Child Development, vol. 45, pp. 1011–1019, 1974.

23. G. A. Kayode, V. T. Adekanmbi, and O. A. Uthman, “Risk factors and a predictive model for under-five mortality in Nigeria: evidence from Nigeria

demographic and health survey”, BMC Pregnancy and Childbirth, vol. 12, no. 10, pp. 1 -11, 2012.

24. F. Tabassum, A. Rizvi, S. Ariff, S. Soofi, and Z. A. Bhutta, “Risk Factors Associated with Birth Asphyxia in Rural District Matiari, Pakistan: A Case

Control Study”, International Journal of Clinical Medicine, vol. 5, pp. 1430-1441, 2014.

25. A. I. Benjamin, P. Sengupta, and S. Singh, “Perinatal Mortality and its Risk Factors in Ludhiana: A Population-Based Prospective Cohort Study”, Health

and Population: Perspectives and Issues, vol. 32, no. 1, pp. 12-20, 2009.

26. R. M. Joanna, A. Schellenberg, R., S. Abdulla, O. Mukasa, T. J. Marchant, M. Tanner, and C. Lengeler, “Risk factors for child mortality in rural

Tanzania”, Tropical Medicine and International Health, vol. 7, no. 6, pp. 506-511, 2002.

27. A. Mercer, F. Haseen, N. L. Huq, N. Uddin, M. H. Khan, and C. P. Larson, Risk factors for neonatal mortality in rural areas of Bangladesh served by a

large NGO programme, Advance Access publication, Oxford University, pp. 432-443, 2006.

28. A.L. Silva, and T.A. Mathias, “Independent risk factors associated with infant deaths”, Acta Paul Enferm, vol. 27, no. 1, pp.48-55, 2014.

29. S. Rutstein, K. Johnson, and D. Gwatkin, Poverty, health inequality, and its health and demographic effects, paper presented at the 2000 Annual Meeting

of the Population Association of America, Los Angeles, California in 2000.

30. S. Rutstein, Wealth versus expenditure: Comparison between the DHS wealth index and household expenditures in four departments of Guatemala,

Calverton, Maryland: ORC Macro, 1999.

31. L. F. C. Nascimento, P. M. S. R. Rizol, and L. B. Abiuzi, “Establishing the risk of neonatal mortality using a fuzzy predictive model”, Cad. Saúde Pública,

Rio de Janeiro, vol. 25, no. 9, pp. 2043-2052, 2009.

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Fuzzy Linguistic Model for Estimating the Risk of Child ...ijarcsms.com/docs/paper/volume5/issue7/V5I7-0016.pdf · Child mortality, a core indicator for child health and well-being