Design of One-Leg Cane Handle Using AHP-TOPSIS Comparative Study to Improve The Mobility of The Elderly

. The number of elderly people in Indonesia has increased significantly. Indonesia has an elderly population of 29 million or 11% of the total population, and around 39% of the population or 11.5 million live with disabilities. The elderly who experience disabilities caused by physical and cognitive changes can decrease their quality of life. Disability in the elderly is caused by the weakening of the lower extremity muscles, resulting in decreased balance and walking stability. Appropriate walking aids for the elderly are crucial in improving balance and stability to reduce the risk of falling. The most commonly used mobility aid for the elderly is a cane, but the use by the elderly is mostly not appropriately instructed, where up to 70% use the wrong cane handle and use it incorrectly. As a result of incorrect use of canes and inadequate instructions, 30-50% of the elderly stop using the cane after receiving it. So, to keep the elderly using the cane, this study tries to design a cane handle with a comparative study using the AHP-TOPSIS Method. The purpose of designing a cane handle is to mantain the balance and stability of the elderly for mobility to improve quality of life and keep the elderly using a cane to reduce the risk of falling. The output obtained is a visualization of the concept & prototype of the improved cane handle design. The improved cane handle is simulated using Autodesk Inventor software with a loading of 150 N. The maximum stress analysis result is 25.31 Mpa, the maximum displacement analysis is 0.2273 mm, and the safety factor value is 7.54 ul.


INTRODUCTION
Indonesia is experiencing a significant increase in the number of elderly people.The elderly are people aged ≤60 years at risk of experiencing a decreased quality of life (QOL) and activity of daily living (ADL) due to physical and cognitive changes due to aging.The effects of progressive aging will cause a person to experience chronic morbidity and disability [1].The elderly are more vulnerable to healthproblems and need assistive devices for daily activities [2].Indonesia has 29 million elderly people or 11% of the total population and around 11.5 million elderly people or 39% are people with disabilities [3].A person with a disability has an impairment in body function or structure, which limits participation.The cause of these impairments appears to be an unhealthy lifestyle [4].The increase in disability in the elderly is due to a lack of walking [5].Indonesians only take 3,513 steps daily, which indicates that they are less active in walking [6].Physical activity, especially walking, is very important in predicting quality of life, where dynamic and static balance functions in the elderly have decreased because the muscles of the lower extremities are significantly weakened [7].Weakness in the lower extremity muscles that occur in the elderly can reduce walking speed by 40% [8].Muscle mass and strength positively correlate with walking balance, especially in the elderly [9].Mobility might be affected in elderly people with balance and stability issues.These conditions can raise the risk of falls if they are not handled [10].The incidence of falls among the elderly rises each year, reaching 28-35% in those over 65 and 32-42% in those over 70 [11].In Indonesia, the prevalence of fall injuries in the elderly over 55 years reached 49.4%, and over 65 years Corresponding author: dirgantaraputra14@gmail.com reached 67.1%.The highest number of falls is experienced by the elderly aged 60 years or older [12].Appropriate walking aids for the elderly are crucial in improving balance and stability and reducing the risk of falls [13].Walking aids for the elderly are used to maintain and improve independence for a better quality of life.The most commonly used mobility aid for the elderly is a cane, but the use of canes by the elderly is mostly not correctly instructed, where up to 70% use the wrong cane handle and use it incorrectly [14] [15].Most elderly get a cane by choice or by the suggestion of friends or family [16].Only 20% of the old population got instruction on how to use a cane, and only approximately a third of the elderly population received canes from medical experts [17].The problem identified in cane selection is that more than half of elderly cane users have poor posture due to incorrect gait patterns or holding the handle incorrectly.[17].As a result of incorrect cane use and inadequate instruction, 30-50% of older people stop using the cane after receiving it [18].When the elderly are not using a cane, it will increase the risk of the elderly falling due to loss of support to maintain balance and stability.Based on the data, 75% of the elderly fell when not using a cane [19].To keep the elderly using a cane is necessary to develop a cane handle design to help maintain balance and stability for mobility.Design development generally requires a reference or initial design selected with certain considerations.Several.studies use comparative studies as the basis for developing improvement designs.The design development application of assistive devices for moving wheelchair users using AHP Method by comparing 11 reference designs and 34 criteria.[20].Research [21] also compared 7 wheelchair designs by considering 11 criteria using the AHP method.This study used 8 types of cane handle reference designs generally available in the market.From these 8 types of designs, a comparative study will be conducted by considering the criteria identified from the literature study and expert opinion (medical rehabilitation specialists and elderly cane users).The process of determining criteria was carried out using the Delphi method to obtain consensus from decision makers [22].Then weighting the criteria using Analytical Hierarchy Process (AHP) Method and ranking alternatives using Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) Method.After weighing the criteria and ranking all alternatives, the selected alternative is used as a reference in the development design based on cane handle selection criteria.The weaknesses of the cane handle design reference are slippery surfaces, discomfort to grip, and pain in the palm due to the pounding of the cane handle during use.The reference cane handle design's weaknesses can be developed to get a better cane handle design.The design development results are expected to get a cane handle design that is comfortable to grip, non-slip, and does not cause pain due to pounding when used and able to support the user's body weight.The improved cane handle design aims to maintain the balance and stability of the elderly for mobility to improve the quality of life and keep the elderly using a cane to reduce the risk of falling.

RESEARCH METHOD 2.1 Analytical Hierarchy Process (AHP)
The Analytic Hierarchy Process (AHP) is one of the Multi Criteria Decision Making (MCDM) methods developed by Thomas L. Saaty in 1972 [23].AHP helps make decisions to deal with complex problems with several conflicting and subjective criteria.AHP organizes problems hierarchically, from objectives to criteria, subcriteria, sub-sub criteria and alternatives [24].AHP method is widely applied in various sectors, such as planning, selecting the best alternative, resource allocation, conflict resolution, optimization and other problems [23].The first step of the AHP method is to define the problem and determine the decision making objectives by creating a hierarchy shown in Fig 1 .In the second step, a pairwise comparison matrix can be compiled based on the decision makers (DM) scores.The pairwise comparison matrix is created based on the fundamental scale developed by Saaty [25].The fundamental scale is shown in TABLE I.The pairwise comparison matrix is a comparison of a criterion with other criteria.The value  represents the scale of preference of criterion against criterion , where ⁄ =  = 1 ⁄ ,  = 1 when  = , and  = 1 with ,  = 1, 2, …,  and states the number of criteria to be compared,  states the weight for the -th criterion and  states the weight for the -th criterion.Then  is the comparison of the weights of the -th and -th criteria.Calculate the pairwise comparison matrix using (1).
(1) After making a pairwise comparison matrix, a decision matrix will be made where a decision-making problem consists of n criteria, namely 1, 2, … ,  , where a comparison of criteria 1 with 2 has been carried out, which will make the comparison value 12.The results of pairwise comparisons between criteria will produce an  ×  matrix A, where states the number of criteria to be compared, as shown in ( 2). (

2)
The weight values in all columns are summed up to determine the normalization score.The sum of the weights in each column is represented by .The calculation of the sum of the weights of each column is shown in (3).
(3) After the weights in each column have been summed, in the next step, the values in each column are divided by the sum of the weights for that column, represented by  .The calculation of  is shown in (4).
(4) After knowing the  value, the next step is to calculate the priority vector.The priority vector is the average of the values of each criterion row , the priority vector value is obtained by adding up the total  values in row which are represented by  divided by the number of criterion values in row (n), the priority vector of the criteria is represented by , as shown in ( 5). (5) The next step is calculating the CR value by dividing the CI (consistency index) value against the RI (random index).The calculation of the consistency of a matrix is based on the maximum eigen value.The calculation of the maximum eigenvalue (λ max) is shown in (6).
A .x = λmax .x (6) After calculating the λ max value, then calculate the CI value.The calculation of the CI value is shown in (7).After the CI value is obtained, continue to calculate the CR value by comparing the CI value with the RI value.The RI value is shown in TABLE II.After the CI and RI values are obtained, calculate CR, as shown in (8).( 8) A matrix close to consistency is important to increase the validity of decision prioritization [26].A matrix is considered to be consistent if the Consistency Ratio (CR) value is 0 or the inconsistency threshold is less than 0.1 or 10% [27]

Technique for Order of Preference by Similarity to Ideal (TOPSIS)
TOPSIS is one of the MADM methods introduced in 1981 by Hwang and Yoon.TOPSIS is a method for solving multicriteria decision making (MCDM) problems by ranking or selecting some alternatives determined by measuring distances [28].The TOPSIS method has the principle that the selected alternative must have the shortest distance from the ideal solution and the longest from the negative ideal solution.
Here is how to apply the TOPSIS method.
The first stage begins with making a decision matrix containing a performance rating from the decision maker (DM) assessment results.The performance rating matrix is shown in (9).(9) In the second stage, it is continued by normalizing the decision matrix.Calculation of the normalized decision matrix as shown in (10).(10)  is a performance rating that has been normalized to be denoted as the normalized decision matrix .The normalized matrix is shown in (11).(11) In the next step, the normalized performance rating  on the normalized matrix multiplied by the criteria weight (), where () is the criteria weight of which will get a weighted normalized performance rating denoted by ().The normalized weighted performance rating calculation is shown in (12).
=  ×  (12) The weighted normalized performance rating value  is arranged into a normalized weighted decision matrix denoted by .The normalized matrix is shown in (13).( 13) The next step is to determine the calculation of the positive ideal solution  * and negative  − shown in ( 14) and ( 15).16) and ( 17). ( 16) (17) The alternative ranking is carried out by calculating the relative closeness value to the ideal solution.The calculation of relative closeness is shown in (18).(18).

METHODOLOGY
This research focuses on the design of a single-leg cane handle using an AHP-TOPSIS comparison study to assist the elderly in improving balance and stability during mobility.AHP Method is used to determine the criteria weights and the TOPSIS Method is used to rank the alternatives.Fig. 2 shows the research methodology of designing a single-leg cane handle using an AHP-TOPSIS comparison study.

Identification of selection criteria
Identify criteria for selecting cane handles from literature sources and expert experience through questionnaire 1. Questionnaire 1 aims to validate the cane handle selection criteria to experts consisting of 4 medical rehabilitation specialists.Irrelevant cane handle selection criteria will be removed.

Constructing of selection hierarchy
Constructing a hierarchy of cane handle selection and calculation of criteria weights using AHP was assessed by 14  (19) where : GM = Geometric mean = Weight value 1,2,3...n = Amount of rating After the weight value is obtained, calculate the consistency ratio to check the consistency of the respondents assessment.

Alternative ranking
Ranking cane handle alternatives with the TOPSIS Method.The assessment of cane handle alternatives is based on input from questionnaire 3 by considering the weights calculated by the AHP Method.The results of the assessment are used to determine the ranking of each cane handle alternatives.

Design development for the selected cane handle alternative
Cane handle design development based on the selected cane handles alternative with the highest weight value in the AHP-TOPSIS calculation.Developing selected cane handle alternative using cane handle selection criteria as a reference in making design improvements.

RESULT AND DISUCCISON
This study identified 5 criteria, 14 sub criteria, and 6 sub-sub criteria through literature and expert experience assessed using questionnaire 1.There are 8 alternative cane handles used in this study consisting of fritz handle, derby handle, fischer handle, crook handle, escort handle, capstick handle, offset handle, and pyramid handle.Respondents filled out questionnaire 1 to ensure that the criteria were relevant to selecting cane handles.

Criteria weighting
In questionnaire 2, respondents assessed the weight of each criterion.Criteria weighting is carried out at all levels, both on criteria, sub-criteria, and sub-sub-criteria.All criteria weights at each level are combined into a global priority vector.Questionnaire 2 was prepared based on the satty fundamental scale and the weighting was processed using Microsoft Excel software.The usability criterion has the highest priority vector value at the first level with a score of 0.442, followed by safety with a score of 0.220, material accuracy with a score of 0.096, and sustainability with a score of 0.053, as shown in TABLE III.In the global priority vector value, the non-slip criterion has the highest value with a score of 0.135, followed by the pressure distribution criterion with a score of 0.114.In contrast, the ease of access criterion has the lowest value with a score of 0.024, as shown in Figure 4.

Alternative ranking
The ranking of alternatives is based on the TOPSIS approach.The global weight of the criteria from AHP is used as the weight of each criterion in the assessment using TOPSIS.The ranking of alternatives is processed using Microsoft Excel software.TABLE IV and TABLE V determine the positive and negative ideal solutions of the alternatives.The last stage of the alternative ranking process is to calculate the relative closeness of alternatives and the euclidean distance value shown in TABLE VI.The alternative with the highest relative closeness value will be a reference in developing cane handle design.TABLE VI shows that the fritz handle has a relative closeness value that is closest to 1, which is 0.875 so it is the first ranked alternative.The 2nd ranked alternative is the pyramid handle type with a value of 0.753 followed by the escort handle which is ranked 3rd with a value of 0.725, the offset handle is ranked 4th with a value of 0.602, the derby handle is ranked 5th with a value of 0.516, the fischer handle is ranked 6th with a value of 0.504, the crook handle is ranked 7th with a value of 0.254, and the capstick handle is ranked 8th with a value of 0.177.

Development of selected cane handle alternative based On selected criteria
The fritz handle alternative was chosen as a reference in the development of the cane handle because it has the highest relative closeness value.The design development of the fritz handle is implemented based on the criteria that have the potential for improvement shown in TABLE VII.The design concept development derived from the potential criteria were used as the basis for improving the cane handle design.After the design concept is determined, the cane handle design uses Autodesk Inventor software to visualize the design development concept.Fig. 5 and Fig. 6 shows the visualization of the developed cane handle design.The 50th percentile was chosen in the cane handle development to ensure that the average elderly population can use the developed cane handle.The size of the cane handle after adjusting to the anthropometric dimensions of the elderly is shown in Figure .7.
In addition, improvements to the cane handle are also adding shock absorbers on the cane handle used to absorb shocks, the addition of a frame on the cane handle aims to increase the strength of the handle to bear the load, the end of the cane handle is designed to widen so that it is not easily released from the grip and an additional strap is added to help the elderly improve the grip, and the groove or texture on the surface of the cane handle to increase grip when grasping.Testing was conducted to determine the level of strength of the cane handle design using Finite Element Analysis.The cane shaft is made of stainless steel and the handle is made of PBT plastic.For finite element analysis testing, it is assumed that the body weight of the elderly is 60 kg.The elderly cane user distributes 25% of his body weight to the cane handle [29].So, the test uses a load of 15 Kg or 150N.The following are the results of testing with Finite Element Analysis.
The safety factor of the cane with stainless steel on the shaft and PBT plastic on the handle is a minimum of 7.54 ul and a maximum of 15 ul, a maximum stress analysis of 25,31 Mpa, and a maximum displacement analysis of 0.2273 mm.

CONCLUSION
Based on the data, there are 5 criteria, 14 sub criteria, and 6 sub-sub criteria for cane handle selection.There are 8 alternative cane handle references and the fritz handle is the highest ranked alternative.The fritz handle is used as a reference in improving the cane handle design.The simulation was carried out on the developed cane handle by performing a load of 150 N using the Autodesk Inventor software.The minimum safety level value on the developed cane handle is 7.54 ul and the maximum is 15 ul, the maximum stress analysis of the cane handle is 25.31 Mpa, and the maximum displacement analysis is 0.2273 mm.The design of the one-legged cane handle development can improve the balance and stability of the elderly during mobility

( 14 )
− = [1 − , 2 − , … ,  − ] (15) Calculation of alternative distances with positive and negative ideal solutions by calculating the Euclidean distance.Calculation of the alternative ideal positive and negative ( − ) ideal solution distances can be shown in (

Fig. 5 .
Fig. 5. Cane handle design development concept One of the cane handle design developments is to adjust the size of the cane handle to the anthropometry of the elderly palm.The anthropometric dimensions of the elderly palm used in the development of the cane handle design are shown inTABLE VII.

Table I .
SATTY

Table 2 .
RANDOM RI 0 0 0.58 0.90 1.12 1.24 1.32 1.41 1.451.49 Can be developed by widening the cross section of the handle at the end so that it is not easily separated from the grip & Adding a rope to the cane handle.
Surface texture Can be developed by giving texture to the cane handle