Risk Level Calculation for Body Physical Exercise with Different Fuzzy Based Methods

Risk Level Calculation for Body Physical Exercise with Different Fuzzy Based Methods

Edit Tóth-Laufer^*,^**, Márta Takács^***

* Donát Bánki Faculty of Mechanical and Safety Engineering, Óbuda University, Budapest, Hungary

** Óbuda University, Doctoral School, Budapest, Hungary

*** John von Neumann Faculty of Informatics, Óbuda University, Budapest, Hungary laufer.edit@bgk.uni-obuda.hu, takacs.marta@nik.uni-obuda.hu

Abstract—In this paper two types of hierarchical multilevel models will be introduced for the calculation of risk of physical exercise in fuzzy environment. One of them is the Analytic Hierarchy Process with Fuzzy Comprehensive Evaluation based model and the other was made in Simulink-Fuzzy Toolbox environment with Mamdani-type fuzzy evaluation. The two methods were tested on several input data and the result of them has been compared and analyzed.

I. INTRODUCTION

Sport and physical exercises play a very important role in human life, it can make one healthier and the lack of sport can lead to our health deteriorating. It is however important to be aware that improper movement can be harmful, if it is not the right movements for our capability or not the proper duration, frequency, intensity that was chosen. The basic physical information, actual physical status, age and so many other sub factors-should be considered, in order for the sport to be safe and healthy rather than making the situation worse.

The two methods below Analytic Hierarchy Process with Fuzzy Comprehensive Evaluation (AHP-FCE) and the authors’ model constructed in Matlab Fuzzy Toolbox environment, try to find the best way to calculate the risk of physical exercise. Both models use fuzzy logic-based decision making, because in risk management it is very beneficial, that the uncertainty, imprecision and subjectivity in data and in evaluation process can be handled. In this way the result is more realistic. Fuzzy based techniques work best in situations where not enough reliable data has been given for statistical model, the cause and effect connection is imprecise or the observations and conditions in linguistic form can be given [1].

The models below use a hierarchical structure with a multilevel decision tree. The input parameters are the measured risk factors and the multi-criteria rules. The alignment based on the event is analyzed and a fuzzy set is associated to each group such as very dangerous, moderately dangerous, medium, moderately safe and very safe. If it is necessary the parameters or the result in each level can be weighted [2],[3].

II. AHP-FCE METHOD

This method adopted for body physical exercise risk calculation is attached to the names of Yizhi Wu, Yongsheng Ding and Hongang Xu [4], which is a combination of Analytic Hierarchy Process (AHP) and

Fuzzy Comprehensive Evaluation (FCE) to have the advantages of both. Using fuzzy mathematic in hierarchical environment and it combines quantitative and qualitative analysis. It allows a complex risk analysis thereby FCE is used in each level of AHP through the priorities and fuzzy parameters. This method comes in useful in complex uncertain systems.

The first step of AHP-FCE is a hierarchical structure of the factors generate. The highest level is the problem that risk will be analyzed. At the intermediate levels are the groups to affect the problem and at the lowest level are the sub-factors of the groups.

After the hierarchical structure was determined the relative weights of the element should be given (AHP method). The factors of the same group are compared in couples and a comparison matrix is generated. The relative weights are the relative importance and interaction of the factors between 1 and 9, where the larger the number, the more important the first factor [5]. They relate the group upper level, represented by A={a1,a2,…,am} (0≤ ai≤1) where A is computed from the components of the normalized eigenvector associated with the highest eigenvalue.

The next step is using the FCE in each level of the structure so the uncertainty of the risk factors is handled better. Let U={u1,u2,…,um} be the set of evaluation factors of FCE and V={v1,v2,…,vn} be the set of evaluation remarks. The relative weights the elements of factors set U at the previous level was given for AHP. Let B={b1,b2,…,bn} (0≤ bj≤1) be a fuzzy subset on V and the membership degree of the remark vj. A fuzzy transformation is used

R A

B= D ^{. (1)}

R is a fuzzy relation on U×V. µR(ui,vj)=rij (i=1,2,…,m;

j=1,2,…,n); rij=[0,1] is the membership degree of the (vj) for the factor ui. The fuzzy evaluation matrix R= (rij)m×n

The membership degree of the different factors definition depend on the factor’s characteristic. If the weight vector A and evaluation matrix R is given, the FCE can be computed by (1). Based on this we defined:

( ) ( )

⎟⎟

⎟⎟

⎟

⎠

⎞

⎜⎜

⎜⎜

⎜

⎝

⎛

=

mn 2

m 1 m

n 2 22 21

n 1 12 11

m 2 1 n 2 1

r ...

r r

r r

r

r ...

r r a ,..., a , a b ,..., b ,

b D (2)

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Where

b

= min ( 1 , ^∑

( ) a

⋅ r

)

The final step is the calculation of the total risk for the problem. The evaluation is executed through the hierarchy from the bottom level to the highest with multiplying the weights vector by the fuzzy relation matrix each segment of the path. The result is a normalized vector of the overall weights of the risk remarks and the normalized evaluation value is calculated by

∑

∑

=

n 1

i

v

b

b

O

III. THE VISUALISED MODEL

This model was generated in Matlab environment with Simulink and Fuzzy Toolbox based on the AHP-FCE model structure with its own membership functions and rules, but without AHP type weighted factors and with hierarchical structure of the decision tree.

The frame of the Simulink model is seen in Fig. 1. The structure follows the logic of the evaluation process. On the left side there is the lowest level with the sub factors, in the middle of the figure are the groups of the elements and on the right side is the highest level with the problem which one the risk level will be calculated. The evaluation is executed from the left side to the right. The risk level for each group with a Fuzzy Logic Controller (FLC) is calculated and the next highest level the total risk is determined by the group results with an FLC again. The total risk level in the Display component will be shown.

The rules were set up with contribution of a trainer.

The membership functions of input data are simple trapeze shaped in each group, but the output functions are different, these are given by (4)-(8). The groups of risk

factors are Medical condition, Activity load and Environmental condition as the figure of the model shows.

The Medical condition is a basic risk group, because it fundamentally determines the loadability. The sub-factors of this group are Disease condition (dis_con), Current physical status (phy_sta) and Basic physical information (bas_inf). Disease condition is maybe the most important among the sub factors. This group includes such persistent diseases as hypertension, diabetes or cardiac diseases. In all cases the personalized medical recommendations of these sub factors should be considered. Possible values are very bad, bad, medium, healthy and very healthy. Current physical status is used to assess the actual physical condition. Parameters such as pulse or blood pressure are measured. Monitoring these values in real time in the future allows not only for the initial level of risk to be calculated, but the person ought to be controlled continuously. Possible values of this sub-factor are very bad, bad, medium, good and very good. Basic physical information is about age, sex and the living conditions such as occupation (stress and activity). Possible values of this sub-factor are inactive, moderately inactive, medium, active and very active. Inputs are for each sub-factor in this group between 0 and 1.

The Activity load refers to the current activity with sub- factors Intensity (int), Duration (dur) and Frequency (freq). Intensity is given in percentage between 0 and 100 and the membership function called very light, light, medium, intensive and very intensive. Duration is between 0 and 120 minutes per occasion and the possible values are very short, short, medium, long, very long. Finally Frequency means, how many times per week does the person do this physical activity, it can be between 1 and 7 times.

Figure 1. The model structure in Simulink

E. Tóth-Laufer and M. Takács • Risk Level Calculation for Body Physical Exercise with Different Fuzzy Based Methods

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The third main group is Environmental condition first of all at outdoor sports is important, but humidity and temperature together can influence the risk level indoor too. The first sub-factors are air temperature and humidity (TH), because their effect shows up together, because of their combination influence of thermal sensation. Possible values are low, moderately low, medium, high and very high. The other sub-factor is air temperature and wind (TW) important together too also because of their effect on thermal sensation. Values are weak, moderately weak, medium, strong and very strong. Both sub-factors has values between 0 and 1.

The output membership functions’ all levels of the hierarchy are scaled in the same form. Risk level calculation for the actual group of risk factors is given by the following equations with results between 0 and 1. The possible values of risk level are very safe, moderately safe, medium, moderately dangerous and very dangerous [4].

( )

( )

⎪⎩

⎪⎨

⎧

>

≤

≤

−

<

=

9 . 0 x 1

9 . 0 x 7 . 0 2

. 0 7 . 0 x

7 . 0 x 0

) x (

F₁ ^1.2 (4)

( )

( )

( )

( )

⎪⎪

⎪

⎩

⎪⎪

⎪

⎨

⎧

≥

≤

≤

−

≤

≤

≤

≤

−

<

=

9 . 0 x 0

9 . 0 x 725 . 0 175

. 0 x 9 . 0

725 . 0 x 675 . 0 1

675 . 0 x 5 . 0 175

. 0 5 . 0 x

5 . 0 x 0

) x ( F

2 . 1 2 . 1

2

(5)

( )

( )

( )

( )

⎪⎪

⎪

⎩

⎪⎪

⎪

⎨

⎧

≥

≤

≤

−

≤

≤

≤

≤

−

<

=

7 . 0 x 0

7 . 0 x 525 . 0 175

. 0 x 7 . 0

525 . 0 x 475 . 0 1

475 . 0 x 3 . 0 175

. 0 3 . 0 x

3 . 0 x 0

) x ( F

2 . 1

2 . 1

3

(6)

( )

( )

( )

( )

⎪⎪

⎪

⎩

⎪⎪

⎪

⎨

⎧

≥

≤

≤

−

≤

≤

≤

≤

−

<

=

5 . 0 x 0

5 . 0 x 325 . 0 175

. 0 x 5 . 0

325 . 0 x 275 . 0 1

275 . 0 x 1 . 0 175

. 0 1 . 0 x

1 . 0 x 0

) x ( F

2 . 1 2 . 1

4

(7)

( )

( )

⎪⎩

⎪⎨

⎧

>

≤

≤

−

<

=

3 . 0 x 0

3 . 0 x 1 . 0 2

. 0 x 3 . 0

1 . 0 x 1

) x (

F₅ ^1.2 (8)

IV. COMPARISION OF THE METHODS A. Test environment and input data selection

The AHP-FCE was tested in Matlab by the appropriate functions programming and the other model were simulated with Simulink model Fig. 1 use Fuzzy Toolbox.

Test groups were selected based on several typical parameters of people such as average healthy adult, middle-aged person with light cardiac disease, healthy adult who would like to lose weight, healthy senior over 65 and person between 50 and 65 years old in bad condition. The parameters for Medical condition that have been specified for the test groups are shown in Table I.

The values are not measured, but theoretical. Optimal values were established by the American Heart Association (AHA) Guidelines [6],[7],[8],[9],[10]. Every group was tested based on several input parameters in both models to examine the extreme and normal values too.

B. The result of the comparision

It has been found that the calculated risk level for two groups, middle-aged person with light cardiac disease and person between 50 and 65 years old in bad condition is almost the same with both methods. These results are shown in Table II. and Table III. The average difference between them amounts to only 4-5%, but the range for each risk level is 20%. This small difference between the results of the two calculations means that it is completely acceptable. Two other groups, the average healthy adult and healthy senior over 65 showed a somewhat greater difference, but most of the results here are similar, too. If the difference is higher, every time our model is more careful than the AHP-FCE model. The only group where a greater difference was found than what had been expected was the healthy adult who would like to lose weight. In this case the optimal range of AHA is higher than for the other groups and our model focus on the health promotion and did not allow extreme limits, so our model is more careful again than the AHP-FCE. It is important to mention that AHP-FCE is a weighted fuzzy model, but our novel model does not use weights. In the future works the interpreted method will be extended with the weights, to represent the priority and the importance of the risk factors and groups of the risk factors.

TABLE I.

MEDICAL CONDITION PARAMETERS

Group Dis_con Phy_sta Bas_inf Average healthy adult 0,5 0,5 0,5

Middle-aged with light

cardiac disease 0,4 0,4 0,7 Healthy adult to lose

weight 0,64 0,64 0,6

Healthy senior 0,64 0,5 0,3 50-65 years old in bad

condition 0,25 0,3 0,5

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C. Possibilities for Improvement

− To use weights in our model at factors and sub- factors to point out the major elements in the risk calculation and to find the best way to determine these weights

− To increase the model with a lower level by the sub-factors division more sub-factors, for example the group Medical condition

− The Current physical status monitoring in real time to give a continuous control

− To use more parameters to handle if the goal is not just health promotion, but for example losing weight

V. CONCLUSION

The hierarchical fuzzy-based models are useful for body physical exercise risk management. These models are based on complex, multi-criteria and multilevel systems with full of uncertainty. The Fuzzy environment is able to handle vague input factors and use a hierarchical structure with a multilevel decision tree and approximate reasoning methods.

The novel introduced fuzzy based model is safe for health promotion for every group that was tested, but if relative weights will be applied, the results could become better. At special goals with higher reference range our model is more careful than the AHP-FCE, but a new parameter for goals should be included.

ACKNOWLEDGMENT

The research was supported by the Research Grant of Óbuda University (ÓE-RH 1186/2-2011) and Vojvodina Secretary of the Science and Technological development (title of the project: Mathematical Models for Decision Making under Uncertain Conditions and Their Applications).

REFERENCES

[1] Y. Kleiner, B. Rajani, R. Sadiq, Failure risk management of buried infrastructure using fuzzy-based techniques, Journal of Water Supply Research and Technology: Aqua, Vol. 55, no. 2, pp.81-94, March (2006)

[2] M. Takács, Multilevel Fuzzy Approach to the Risk and Disaster Management, Acta Polytechnika Hungarica, Vol. 7, Issue No.4., (2010).

[3] M. Takács, Extended Fuzzy Methods in Risk Management, Proc., of 14^th WSEAS International Conference on Applied Mathematics, ISBN 978-960-474-138-0, pp-300-304.

[4] Y. Wu, Y. Ding, H. Xu, Comprehensive Fuzzy Evaluation Model for Body Physical Excercise, Risk Life System Modeling and Simulation Lecture Notes in Computer Science, 2007, Volume 4689/2007, pp.227–235, DOI: 10.1007/978-3-540-74771-0_26.

[5] T.L. Saaty, L.G Vargas, Models, Methods, Concepts and Applications of the Analytic Hierarchy Process, Kluwer Academic press (2001)

[6] J American Heart Association Exercise Guidelines, doi: 10.1161/

01.CIR.96.1.345.

[7] Physical activity and Public health Guideline, http://circ.ahajournals.org/content/116/9/1094.full.pdf.

[8] American Heart Association Recommended Exercise http://www.livestrong.com/article/124077-american-heart - association-recommended-exercise/.

[9] American Heart Association & Exercise.

http://circ.ahajournals.org/content/116/9/1081.full.pdf [10] AHA Guidelines on Exercise for Seniors.

http://www.livestrong.com/article/529168-aha-guidelines-on- exercise-for-seniors/

TABLE III.

PERSON BETWEEN 50 AND 65 YEARS OLD IN BAD CONDITION

Int Dur Freq TH TW FTB AHP-

FCE Diff 20 20 5 0,5 0,5 0,5616 0,5352 0,0264 20 80 3 0,5 0,5 0,5828 0,5512 0,0316 50 25 5 0,5 0,5 0,5576 0,5715 0,0139 50 60 3 0,5 0,5 0,5828 0,5769 0,0059 20 120 7 0,5 0,5 0,5828 0,5898 0,007 50 120 7 0,5 0,5 0,5828 0,6232 0,0404 80 25 5 0,5 0,5 0,6076 0,652 0,0444 80 25 7 0,5 0,5 0,6076 0,6612 0,0536 100 50 3 0,5 0,5 0,6076 0,6865 0,0789 100 120 1 0,5 0,5 0,7923 0,7069 0,0854 100 120 3 0,5 0,5 0,7923 0,715 0,0773 100 120 7 0,5 0,5 0,7923 0,7401 0,0522

TABLE II.

MIDDLE-AGED PERSON WITH LIGHT CARDIAC DISEASE

Int Dur Freq TH TW FTB AHP-

FCE Diff 20 20 5 0,6 0,2 0,4519 0,4763 0,0244 20 80 3 0,6 0,2 0,5 0,4913 0,0087 50 25 5 0,6 0,2 0,5 0,5173 0,0173 50 60 3 0,6 0,2 0,5 0,523 0,023 20 120 7 0,6 0,2 0,5 0,5298 0,0298 50 120 7 0,6 0,2 0,5 0,5682 0,0682 80 25 5 0,6 0,2 0,5 0,5953 0,0953 80 25 7 0,6 0,2 0,5 0,6043 0,1043 100 50 3 0,6 0,2 0,5 0,6263 0,1263 100 120 1 0,6 0,2 0,7 0,6461 0,0539 100 120 3 0,6 0,2 0,7 0,6543 0,0457 100 120 7 0,6 0,2 0,7 0,6794 0,0206

E. Tóth-Laufer and M. Takács • Risk Level Calculation for Body Physical Exercise with Different Fuzzy Based Methods

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