2.2.2. Establishing the Functional Technology Matrix of the Rehabilitation Chair
Decompose the overall function of the rehabilitation chair until it is decomposed into functional elements composed of structures or components, establish the functional technology matrix diagram with the decomposed technical elements, comprehensively analyze the technical pathways of each function, and screen the functional solutions with high practical value, sustainable use, superior technology and economy, and aesthetics. The specific steps are as follows.
Step 1: Total function disassembled into technical elements.
Organize the functional elements according to the realization relationship between the functions. Distinguish between basic and non-basic functions according to the importance of the functions and decompose the functions into technical elements according to the purpose of rehabilitation and means of realization, as shown in
Figure 3.
Step 2: Create a Functional Technology Matrix
As shown in
Table 1, a functional matrix is a combination of different forms of assistive technology around a product’s functions, qualitatively or quantitatively analyzing the different forms of achieving each function to find a reliable solution.
Step 3: Functional sequence importance coefficient rating
The functional importance coefficient is also known as the functional coefficient or functional index. The rehabilitation chair functional importance coefficient rating is based on the different roles of each functional element in the whole system, through the mandatory scoring method (0–1 or 0–4 scoring method), multiple proportional scoring method, logical scoring method, ring scoring method, and so on. In this paper, the 0–4 scoring method is adopted, that is, 10 professionals are asked to compare the two functional elements, and the specific scoring is shown in
Table 2, where the very important functional element scores 4 points, and the other very important functional element scores 1 point; the more important functional element scores 3 points, and the other not-so-important functional element scores 1 point; when they are of equal importance or basically of equal importance, each of the two functional elements scores 2 points, the very unimportant scores 1 point, and no points are scored for their own comparisons.
According to the example
Table 1 to establish the functional technology matrix, we get the functional results of the rehabilitation instrument as shown in
Table 3, specifically: the massage function is 0.174, the stretching function is 0.130, the chest expansion function is 0.081, the arm lifting function is 0.174, the flexion and extension function is 0.093, the leg patting function is 0.093, and the foot stirrup function is 0.174.
Step 4: Construct the Functional Technical Matrix
Based on the results of the rating of functional importance factors, the functional technology matrix was constructed. In order to expand the scope of the technology pathway and improve the creativity and effectiveness of the final solution, the latest scientific research results and manufacturing technologies were adopted as the technology pathway for the rehabilitation chair.
Table 4 shows the functional technology path of the rehabilitation chair, in which the massage function mainly utilizes structures such as rollers, worm gear structures, and struts, the extension function mainly utilizes structures such as rollers, socketed telescopic sliders, and telescopic sliders, the chest expansion function mainly utilizes structures such as screws, chucks, mandrels, and telescopic rods, the arm lift function mainly utilizes structures such as supports, rotating sections, and rotating telescopic sections, and the flexion function mainly utilizes folding rod ends, locking rings, and fixing pins, the leg knocking function mainly utilizes wooden knockers, support wheels, and hinged rods, and the pedal function mainly utilizes turntables, connecting plates, and foot pedals.
Step 5: Comprehensive analysis of technical pathways
Comprehensive analysis of the technical pathways refers to the comprehensive consideration of the indicators of the evaluation of the rehabilitation chair program, such as technical, practical, aesthetic, and other indicators. The scoring items are developed according to the requirements, and the scoring method refers to the 0–4 scoring method. For example, when two technical elements, T1 and T2, are compared, if T1 is more important, then T1 receives a score of 3 and T2 receives a score of 1; if T1 is very important, then T1 receives a score of 4 and T2 receives a score of 0; and if the two elements are equally important, then both elements receive a score of 2; refer to the scoring method in
Table 2. Finally, the scores obtained for each technical element are added together and then divided by the total score of technical elements, see formula (1) to obtain the Technical Index Factors.
The evaluation indexes of the functional elements of the rehabilitation chairs in this study include technology, environmental friendliness, and applicability, and the technical elements are scored with each index as an evaluation dimension, where
Table 5,
Table 6 and
Table 7 are obtained.
Z is the technical indicator coefficient. n is the number of technical elements in the function.
Table 5.
Evaluation of the technicality index coefficients of the functional elements of the rehabilitation chair.
Table 5.
Evaluation of the technicality index coefficients of the functional elements of the rehabilitation chair.
Functions | Technology Element Score | Technical Index Scores | Technical Index Factors |
---|
F1 | | T1(1) | T1(2) | T1(3) | | |
T1(1) | 0 | 2 | 3 | 5 | 0.42 |
T1(2) | 2 | 0 | 3 | 5 | 0.42 |
T1(3) | 1 | 1 | 0 | 2 | 0.17 |
F2 | | T2(1) | T2(2) | T2(3) | | |
T2(1) | 0 | 1 | 1 | 2 | 0.17 |
T2(2) | 3 | 0 | 2 | 5 | 0.17 |
T2(3) | 3 | 2 | 0 | 5 | 0.42 |
F3 | | T3(1) | T3(2) | T3(3) | | |
T3(1) | 0 | 2 | 3 | 5 | 0.42 |
T3(2) | 2 | 0 | 3 | 5 | 0.42 |
T3(3) | 1 | 1 | 0 | 2 | 0.17 |
F4 | | T4(1) | T4(2) | T4(3) | | |
T4(1) | 0 | 3 | 3 | 6 | 0.46 |
T4(2) | 2 | 0 | 3 | 5 | 0.38 |
T4(3) | 1 | 1 | 0 | 2 | 0.15 |
F5 | | T5(1) | T5(2) | T5(3) | | |
T5(1) | 0 | 2 | 2 | 4 | 0.33 |
T5(2) | 2 | 0 | 3 | 5 | 0.42 |
T5(3) | 2 | 1 | 0 | 3 | 0.25 |
F6 | | T6(1) | T6(2) | T6(3) | | |
T6(1) | 0 | 2 | 1 | 3 | 0.25 |
T6(2) | 2 | 0 | 2 | 4 | 0.33 |
T6(3) | 1 | 2 | 0 | 5 | 0.42 |
F7 | | T7(1) | T7(2) | T7(3) | | |
T7(1) | 0 | 2 | 2 | 4 | 0.25 |
T7(2) | 2 | 0 | 2 | 4 | 0.25 |
T7(3) | 2 | 2 | 0 | 4 | 0.25 |
Table 6.
Evaluation of environmental protection index coefficients of the functional elements of the rehabilitation chair.
Table 6.
Evaluation of environmental protection index coefficients of the functional elements of the rehabilitation chair.
Functions | Technology Element Score | Technical Index Scores | Technical Index Factors |
---|
F1 | | T1(1) | T1(2) | T1(3) | | |
T1(1) | 0 | 2 | 1 | 3 | 0.25 |
T1(2) | 2 | 0 | 1 | 3 | 0.25 |
T1(3) | 3 | 3 | 0 | 6 | 0.50 |
F2 | | T2(1) | T2(2) | T2(3) | | |
T2(1) | 0 | 3 | 1 | 4 | 0.33 |
T2(2) | 1 | 0 | 1 | 2 | 0.17 |
T2(3) | 3 | 3 | 0 | 6 | 0.50 |
F3 | | T3(1) | T3(2) | T3(3) | | |
T3(1) | 0 | 2 | 3 | 5 | 0.42 |
T3(2) | 2 | 0 | 3 | 5 | 0.42 |
T3(3) | 1 | 1 | 0 | 2 | 0.16 |
F4 | | T4(1) | T4(2) | T4(3) | | |
T4(1) | 0 | 2 | 3 | 5 | 0.42 |
T4(2) | 2 | 0 | 3 | 5 | 0.42 |
T4(3) | 1 | 1 | 0 | 2 | 0.16 |
F5 | | T5(1) | T5(2) | T5(3) | | |
T5(1) | 0 | 3 | 1 | 4 | 0.33 |
T5(2) | 1 | 0 | 1 | 2 | 0.17 |
T5(3) | 3 | 3 | 0 | 6 | 0.50 |
F6 | | T6(1) | T6(2) | T6(3) | | |
T6(1) | 0 | 2 | 3 | 5 | 0.42 |
T6(2) | 2 | 0 | 3 | 5 | 0.42 |
T6(3) | 1 | 1 | 0 | 2 | 0.16 |
F7 | | T7(1) | T7(2) | T7(3) | | |
T7(1) | 0 | 3 | 2 | 5 | 0.42 |
T7(2) | 1 | 0 | 1 | 2 | 0.16 |
T7(3) | 2 | 3 | 0 | 5 | 0.42 |
Table 7.
Evaluation of applicability index coefficients of the functional elements of the modular rehabilitation chair.
Table 7.
Evaluation of applicability index coefficients of the functional elements of the modular rehabilitation chair.
Functions | Technology Element Score | Technical Index Scores | Technical Index Factors |
---|
F1 | | T1(1) | T1(2) | T1(3) | | |
T1(1) | 0 | 2 | 3 | 5 | 0.42 |
T1(2) | 2 | 0 | 3 | 5 | 0.42 |
T1(3) | 1 | 1 | 0 | 2 | 0.16 |
F2 | | T2(1) | T2(2) | T2(3) | | |
T2(1) | 0 | 1 | 1 | 2 | 0.17 |
T2(2) | 3 | 0 | 3 | 6 | 0.50 |
T2(3) | 3 | 1 | 0 | 4 | 0.33 |
F3 | | T3(1) | T3(2) | T3(3) | | |
T3(1) | 0 | 1 | 3 | 4 | 0.33 |
T3(2) | 3 | 0 | 3 | 6 | 0.50 |
T3(3) | 1 | 1 | 0 | 2 | 0.17 |
F4 | | T4(1) | T4(2) | T4(3) | | |
T4(1) | 0 | 3 | 3 | 6 | 0.50 |
T4(2) | 1 | 0 | 3 | 4 | 0.33 |
T4(3) | 1 | 1 | 0 | 2 | 0.17 |
F5 | | T5(1) | T5(2) | T5(3) | | |
T5(1) | 0 | 3 | 2 | 5 | 0.45 |
T5(2) | 1 | 0 | 1 | 2 | 0.18 |
T5(3) | 2 | 3 | 0 | 4 | 0.36 |
F6 | | T6(1) | T6(2) | T6(3) | | |
T6(1) | 0 | 1 | 2 | 3 | 0.23 |
T6(2) | 3 | 0 | 2 | 5 | 0.38 |
T6(3) | 3 | 2 | 0 | 5 | 0.38 |
F7 | | T7(1) | T7(2) | T7(3) | | |
T7(1) | 0 | 3 | 2 | 5 | 0.42 |
T7(2) | 1 | 0 | 1 | 2 | 0.16 |
T7(3) | 2 | 3 | 0 | 5 | 0.42 |
Step 6: Technology compatibility analysis
Technology compatibility analysis is an important method to determine whether the combination of technology paths of each functional element is compatible with each other and the feasibility of the combination scheme. The N×N order matrix is constructed using the adjacency matrix method to perform the technical pathway compatibility analysis, as shown in
Table 8. If the combination condition is feasible, it is counted as 1, and if the combination condition is not feasible, it is counted as 0. The technical pathway ratings of T1(1), T1(2), T1(3) …, etc., are performed sequentially, and finally a number of combination schemes Q are obtained.
Table 8.
Technical compatibility scoring matrix.
Table 8.
Technical compatibility scoring matrix.
| Compatibility |
---|
T1(1) | T1(2) | … | Tn(m) |
---|
T1(1) | 0/1 2 | 0/1 | … | 0/1 |
T1(2) | 0/1 | 0/1 | … | 0/1 |
… | … | … | … | … |
Tn(m) 1 | 0/1 | 0/1 | … | 0/1 |
Here, qn is the nth feasible solution and m is the number of feasible solutions.
Step 7: Determine a feasible functional solution for the rehabilitation chair.
As shown in
Table 8, the pathways with higher technical excellence index coefficient scores in
Table 5,
Table 6 and
Table 7 were subjected to technical compatibility matrix analysis, with compatibility as 1 and incompatibility as 0. The feasible options for the rehabilitation chair function were obtained as follows:
- (1)
Massage Function: roller, worm gear worm gear, strut.
- (2)
Stretching Function: sleeve type expansion slider, telescopic slider.
- (3)
Chest Expansion Function: screw, mandrel.
- (4)
Arm Lift Function: support piece, rotating section.
- (5)
Flexion Function: folded movable rod end, retaining pin.
- (6)
Leg Lift Function: wooden knockout head, hinge rod.
- (7)
Pedal Function: turntable, foot pedal.
Step 8: Functional structure design of the rehabilitation chair
According to the above technical elements, combined with the functions obtained from user research, including back massage, leg flexion and extension, chest expansion movement, arm lifting, leg bending, leg lifting, and footrest movement, the rehabilitation chair functional program is designed. This is shown in
Figure 4,
Figure 5 and
Figure 6.
2.2.3. Multi-Level Comprehensive Evaluation
Using the gray correlation method to get the correlation degree of each functional scheme and then using the AHP-Entropy weight method to calculate the comprehensive weight, it is possible to finally calculate the gray weighting weight of each scheme to obtain the optimal scheme. This process is shown in
Figure 1.
Step 1: Establish the comparison matrix and determine the reference number.
Establish the decision-making evaluation system of the rehabilitation chair program, as shown in
Figure 7, the evaluated program is C (C = 1, 2, 3, n), the set of evaluation level 1 indicators is E′ = (
), and the set of level 2 indicators is E′ =
,
,
, …,
)}.
Determine the optimal value of each indicator as the reference data column, and set the reference data column as = , , , …, ).
Step 2: Data normalization.
To improve the validity of the data, the different indicators are normalized. The comparison matrix E =
=
= (J = [1,m]; k = [1,n]) was obtained. The normalized data for each of the three types of scenarios are shown in
Figure 8.
Step 3: Determine the extreme values.
Two levels of absolute difference:
represents the difference between two extreme values in the matrix,
represents the smallest number in the matrix, and
represents the largest number in the matrix.
Step 4: Calculation of correlation coefficients
The correlation coefficient represents the correlation between the comparison series and the reference series at a certain value. The correlation coefficient is calculated according to Equation (6), in which the smaller ρ is, the stronger the difference between the correlation coefficients [
19].
Here,
is the resolution factor and takes the value of 0.5.
Step 5: Calculate the correlation.
Calculate the average value of the correlation coefficient between each index and the reference series at a certain value [
20].
Here,
is the correlation between the comparison series and the reference series; m is the number of evaluation indicator.
Step 6: Use the AHP method to calculate subjective weights.
(1) Establishment of the judgement matrix.
The AHP method can decompose the complex problem into a number of basic units, and group them according to their mutual dominance, forming an orderly progressive hierarchical structure [
18], using a 9-point system for the evaluation of the indexes of the two-two comparative scoring. The scoring standards are shown in
Table 9, the establishment of the judgement matrix being A′ = {
,
,
, …,
}.
(2) Calculation of relative weights.
The scalar product of each row is calculated according to Equations (9) and (10), and then its geometric mean is determined.
(3) Calculate the maximum characteristic value of each evaluation index [
19].
Here,
is the nth component of the vector
and n is the number of steps.
(4) Consistency test.
Calculating the consistency ratio:
Here, RI is the average random consistency index; CR is the consistency ratio. CR ≤ 0.1 indicates that the consistency test is passed, and vice versa, it is failed.
Step 7: Entropy weighting method to calculate objective weights.
(1) Convert the scoring matrix into a normalized matrix
The assessment indicators in the matrix are normalized according to Equation (14):
Here,
is the normalized decision matrix, is the original matrix value,
J = 1, 2, …, m,
k = 1, 2, …, m,
k = 1, 2, …, n.
(2) Determine the entropy of each evaluation index.
Calculate the entropy value of the kth indicator according to Equation (15):
Here,
is the information entropy of each indicator, and the smaller
is, the higher dispersion of the data under
k indicators and the greater the amount of information provided.
(3) Calculate entropy weights.
After defining the entropy of the
k indicators, the entropy weights can be obtained as follows:
Step 8: Gray weighted composite weight calculation.
Calculate the average of the correlation coefficients between each indicator and the reference series at a certain value according to Equation (17):
Here,
is the correlation between the comparison series and the reference series;
m is the number of evaluation indicators.
The gray weighted correlation is calculated and ranked according to Equation (18), and the top-ranked scheme is the preferred scheme. The indicators with a high weight and low score in the design scheme need to be optimized to a high degree [
19].
Here,
is the weight value of the kth assessment index;
is the correlation between the kth assessment index of the Jth product and the reference series.