# Assessing the Human Resource in Science and Technology for Asian Countries: Application of Fuzzy AHP and Fuzzy TOPSIS

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. HRST Competitiveness

#### 2.2. Indicators of HRST Competitiveness

#### 2.2.1. Infrastructure Indicators

#### 2.2.2. Input Indicators

#### 2.2.3. Output Indicators

## 3. Methods

#### 3.1. Fuzzy AHP

#### 3.1.1. Establishing Fuzzy Numbers

#### 3.1.2. Determining the Linguistic Variables

#### 3.1.3. The Fuzzy AHP Method

**Step 1**:- Conduct pair-wise comparison matrices for all criteria in the dimensions of the hierarchy system. Equation (7) shows that $\tilde{{d}_{ij}^{k}}$ represents the k
^{th}decision makers’ preference of the i^{th}criterion over the j^{th}criterion via TFNs.$${\tilde{A}}^{k}=\left[\begin{array}{cccc}{\tilde{d}}_{11}^{k}& {\tilde{d}}_{12}^{k}& \dots & {\tilde{d}}_{1n}^{k}\\ {\tilde{d}}_{21}^{k}& \dots & \dots & {\tilde{d}}_{2n}^{k}\\ \dots & \dots & \dots & \dots \\ {\tilde{d}}_{n1}^{k}& {\tilde{d}}_{n2}^{k}& \dots & {\tilde{d}}_{nn}^{k}\end{array}\right]$$ **Step 2**:- If more than one decision maker is present, then the preferences for each decision maker are average as shown in the following equation:$$\tilde{{d}_{ij}}=\frac{{{\displaystyle \sum}}_{k=1}^{k}{\tilde{d}}_{ij}^{k}}{K}$$
**Step 3**:- Update the pair-wise comparison matrices for all criteria in the hierarchy system dimensions on the basis of the averaged preferences.$$\tilde{\mathrm{A}}=\left[\begin{array}{ccc}\tilde{{d}_{11}}& \cdots & \tilde{{d}_{1n}}\\ \cdots & \ddots & \dots \\ \tilde{{d}_{n1}}& \cdots & \tilde{{d}_{nn}}\end{array}\right]$$
**Step 4**:- Use the geometrical mean technique to define the fuzzy geometrical mean and fuzzy weights of each criterion.$${\tilde{\mathrm{r}}}_{i}={\left({\displaystyle \prod}_{j=1}^{n}{\tilde{d}}_{ij}\right)}^{1/n},i=1,2,\dots ,n$$
**Step 5**:- Determine the fuzzy weight of the criteria.$${\tilde{\mathrm{w}}}_{i}={\tilde{\mathrm{r}}}_{i}\otimes {\left({\tilde{\mathrm{r}}}_{1}\oplus {\tilde{\mathrm{r}}}_{2}\oplus \dots \oplus {\tilde{\mathrm{r}}}_{n}\right)}^{-1}$$
**Step 6**:- Calculate the average and normalized weight criteria.$${\mathrm{M}}_{i}=\frac{{\tilde{w}}_{1}\oplus {\tilde{w}}_{2}\oplus \dots \oplus {\tilde{w}}_{n}}{n}$$$${\mathrm{N}}_{i}=\frac{{\mathrm{M}}_{i}}{{\mathrm{M}}_{1}\oplus {\mathrm{M}}_{2}\oplus \dots \oplus {\mathrm{M}}_{n}}$$

#### 3.2. Fuzzy TOPSIS

**Step 1**:- Determine the weights of the evaluation criteria.The present study applies fuzzy AHP to determine fuzzy preference weights.
**Step 2**:- Construct the fuzzy decision matrix and choose the appropriate linguistic variables as alternatives for the criteria.$$\tilde{\mathrm{D}}=\begin{array}{c}{A}_{1}\\ \dots \\ {A}_{m}\end{array}\begin{array}{c}{C}_{1}\dots {C}_{n}\\ \left[\begin{array}{ccc}{\tilde{x}}_{11}& \cdots & {\tilde{x}}_{1n}\\ \vdots & \ddots & \vdots \\ {\tilde{x}}_{m1}& \cdots & {\tilde{x}}_{mn}\end{array}\right]\end{array},i=1,2,\dots ,m;j=1,2,\dots ,n$$${\tilde{x}}_{ij}=\frac{1}{K}({\tilde{x}}_{ij}^{1}\oplus \cdots \oplus {\tilde{x}}_{ij}^{k}\oplus \cdots \oplus {\tilde{x}}_{ij}^{K})$,where ${\tilde{x}}_{ij}^{k}$ is the performance rating of the alternative ${A}_{i}$ with respect to criterion ${C}_{j}$ evaluated by the $k$
^{th}expert and ${\tilde{x}}_{ij}^{k}=({l}_{ij}^{k},{m}_{ij}^{k},{u}_{ij}^{k})$. **Step 3**:- Normalize the fuzzy decision matrix.The normalized fuzzy decision matrix denoted by $\tilde{\mathrm{R}}$ is depicted as follows:$$\tilde{\mathit{R}}={\left[{\tilde{r}}_{ij}\right]}_{m\times n},\hspace{0.17em}i=1,2,\cdots ,m;\hspace{0.17em}j=1,2,\cdots ,n.$$Thereafter, the normalization process can be performed as follows:where ${\tilde{r}}_{ij}=\left(\frac{{l}_{ij}}{{u}_{j}^{+}},\frac{{m}_{ij}}{{u}_{j}^{+}},\frac{{u}_{ij}}{{u}_{j}^{+}}\right),$ ${u}_{j}^{+}=\underset{i}{\mathrm{max}}\left\{{u}_{ij}\right|i=1,2,\mathrm{...},n\}$. Alternatively, we can set the best aspired level ${u}_{j}^{+}$ and $j=1,2,\dots ,n$ is equal to 1; otherwise, the worst is 0.The normalized ${\tilde{r}}_{ij}$ continues to be TFNs. For trapezoidal fuzzy numbers, the normalization process can be performed in the same manner. The weighted fuzzy normalized decision matrix is stated as the following matrix $\tilde{\mathrm{V}}$:$$\tilde{\mathit{V}}={[{\tilde{v}}_{ij}]}_{n\times n},i=1,2,\dots ,m;\hspace{0.17em}j=1,2,\dots ,n,$$
**Step 4**:- Determine the fuzzy positive-ideal solution (FPIS) and fuzzy negative-ideal solution (FNIS).The weighted normalized fuzzy decision matrix indicates that the elements ${\tilde{v}}_{ij}$ are normalized positive $TFN$ and their ranges belong to the closed interval [0,1]. Thereafter, we can define the FPIS ${A}^{+}$ (aspiration levels) and FNIS ${A}^{-}$ (the worst levels) as follows:$${A}^{+}=({\tilde{v}}_{1}^{\ast},\mathrm{...},{\tilde{v}}_{j}^{\ast},\mathrm{...},{\tilde{v}}_{n}^{\ast})$$$${A}^{-}=({\tilde{v}}_{1}^{-},\mathrm{...},{\tilde{v}}_{j}^{-},\mathrm{...},{\tilde{v}}_{n}^{-})$$
**Step 5**:- Calculate the distance of each alternative from FPIS and FNIS.The distances (${\tilde{d}}_{i}^{+}$ and ${\tilde{d}}_{i}^{-}$) of each alternative from ${A}^{+}$ and ${A}^{-}$ can be calculated using the area compensation method:$${\tilde{d}}_{i}^{+}={\displaystyle \sum _{j=1}^{n}d({\tilde{v}}_{ij},{\tilde{v}}_{j}^{\ast}}),i=1,2,\dots ,m;\hspace{0.17em}j=1,2,\dots ,n$$$${\tilde{d}}_{i}^{-}={\displaystyle \sum _{j=1}^{n}d({\tilde{v}}_{ij},{\tilde{v}}_{j}^{-}}),i=1,2,\dots ,m;\hspace{0.17em}j=1,2,\dots ,n$$
**Step 6**:- Obtain the closeness coefficients (relative gaps–degree) and improve the alternatives to achieve the aspiration levels in each criterion.

## 4. Empirical Data Analysis and Results

**Step 1**: Obtain the weights of the evaluation dimensions.

- (1)
- In accordance with the committee of sixteen representatives, if the relative importance of the dimensions is followed, then the pair-wise comparison matrices of the dimensions will be obtained. We apply the fuzzy numbers provided in Table 1 and transfer the linguistic scales to the corresponding fuzzy numbers.
- (2)
- Buckley [15] suggested computing the elements of synthetic pair-wise comparison matrix by using the geometric mean method.${\tilde{a}}_{ij}=({\tilde{a}}_{ij}^{1}\otimes {\tilde{a}}_{ij}^{2}\otimes \dots \otimes {\tilde{a}}_{ij}^{11})$, for ${\tilde{a}}_{12}$ as the example:$$\begin{array}{l}{\tilde{a}}_{12}=(1,1,1)\otimes (1/6,1/5,1/4)\otimes \cdots \otimes {(5,6,7)}^{1/11}\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\u200a=({(1\times 1/6\times \cdots \times 5)}^{1/11},{(1\times 1/5\times \cdots \times 6)}^{1/11},{(1\times 1/4\cdots \times 7)}^{1/11})\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}=(0.387,0.426,0.474)\end{array}$$The results can be obtained from the other matrix elements via the same computational procedure. Therefore, the synthetic pair-wise comparison matrices of the five representatives will be constructed as follows for matrix $\mathit{A}$:$$\begin{array}{l}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.17em}\hspace{1em}\hspace{0.17em}{D}_{1}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.17em}\hspace{1em}\hspace{0.17em}{D}_{2}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.17em}{D}_{3}\\ A=\begin{array}{c}{D}_{1}\\ {D}_{2}\\ {D}_{3}\end{array}\left[\begin{array}{ccc}(1.000,1.000,1.000)& (0.387,0.426,0.474)& (0.342,0.399,0.476)\\ (2.111,2.349,2.585)& (1.000,1.000,1.000)& (0.802,0.967,1.195)\\ (2.102,2.507,2.921)& (0.837,1.034,1.246)& (1.000,1.000,1.000)\end{array}\right]\end{array}.$$
- (3)
- To calculate the fuzzy weights of dimensions, the computational procedures are displayed as the following components:$$\begin{array}{l}{\tilde{r}}_{{D}_{1}}={({\tilde{a}}_{11}\otimes {\tilde{a}}_{12}\otimes {\tilde{a}}_{13})}^{1/3}\\ \hspace{0.17em}\hspace{0.17em}=({(1.000\times 0.387\times 0.342)}^{1/3},\hspace{0.17em}\hspace{0.17em}{(1.000\times 0.462\times 0.399)}^{1/3},\hspace{0.17em}\hspace{0.17em}{(1.000\times 0.474\times 0.476)}^{1/3})\\ \hspace{0.17em}\hspace{0.17em}=(0.510,0.554,0.609)\end{array}$$$$\begin{array}{l}{\tilde{r}}_{{D}_{2}}=(1.192,1.314,1.456)\\ {\tilde{r}}_{{D}_{3}}=(1.207,1.374,1.538)\end{array}$$$$\begin{array}{l}{\tilde{w}}_{{D}_{1}}={\tilde{r}}_{1}\otimes {({\tilde{r}}_{1}\oplus {\tilde{r}}_{2}\oplus {\tilde{r}}_{3})}^{-1}\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}=(0.510,0.554,0.609)\otimes (1/(0.609+1.456+1.538),1/(0.554+1.314+1.374),\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}1/(0.510+1.192+1.207\left)\right)\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}=(0.141,0.171,0.209)\end{array}$$$$\begin{array}{l}{\tilde{w}}_{{D}_{2}}=(0.331,0.405,0.501)\\ {\tilde{w}}_{{D}_{3}}=(0.335,0.424,0.529)\end{array}$$
- (4)
- The COA method is used to compute the $BNP$ value of the fuzzy weights of each dimension. As an example, the following calculation process is used to obtain the $BNP$ value of the weight of ${D}_{1}$ (Infrastructure):$$\begin{array}{l}BN{P}_{{w}_{{D}_{1}}}=\left[({U}_{{w}_{1}}-{L}_{{w}_{1}})+({M}_{{w}_{1}}-{L}_{{w}_{1}})\right]/3+{L}_{{w}_{1}}\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}=\left[(0.209-0.141)+(0.171-0.141)\right]/3+0.141\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}=0.174\end{array}$$

**Step 2**: Construct the fuzzy decision matrix and choose the appropriate linguistic variables for the alternatives with respect to criteria.

**Step 3**: Establish the weighted normalized fuzzy decision matrix.

**Step 4**: Determine the fuzzy positive and fuzzy negative ideal reference points.

**Step 5**: Calculate the distance of each alternative from FPIS and FNIS.

**Step 6**: Estimate the performance and rank the alternatives.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Saaty Scale | Definition | Fuzzy Triangle Scale |
---|---|---|

1 | Equally important | (1,1,1) |

3 | Weakly important | (2,3,4) |

5 | Fairly important | (4,5,6) |

7 | Strongly important | (6,7,8) |

9 | Absolutely important | (9,9,9) |

2 | Intermittent values between two adjacent scales | (1,2,3) |

4 | (3,4,5) | |

6 | (5,6,7) | |

8 | (7,8,9) |

Dimensions | Criteria | Sub-Criteria | Weights | BNP | Rank | |
---|---|---|---|---|---|---|

Infrastructure | (0.141,0.171,0.209) | |||||

Education | (0.144,0.207,0.299) | |||||

Higher education achievement | (0.115,0.169,0.245) | (0.002,0.006,0.015) | 0.008 | 23 | ||

Total public expenditure on education | (0.170,0.249,0.361) | (0.003,0.009,0.023) | 0.012 | 19 | ||

Science degrees | (0.224,0.325,0.475) | (0.005,0.012,0.030) | 0.015 | 18 | ||

Language skills | (0.177,0.257,0.377) | (0.004,0.009,0.024) | 0.012 | 19 | ||

Value | (0.187,0.280,0.418) | |||||

Value of society | (0.166,0.218,0.290) | (0.004,0.010,0.025) | 0.013 | 16 | ||

Youth interest in science | (0.266,0.349,0.461) | (0.007,0.017,0.040) | 0.021 | 13 | ||

Flexibility and adaptability | (0.320,0.433,0.579) | (0.008,0.021,0.051) | 0.027 | 9 | ||

Cooperation | (0.154,0.223,0.325) | |||||

Technological cooperation | (0.369,0.522,0.717) | (0.008,0.020,0.049) | 0.026 | 10 | ||

Knowledge Transfer | (0.166,0.224,0.310) | (0.004,0.009,0.021) | 0.011 | 21 | ||

Development an application of technology | (0.186,0.254,0.360) | (0.004,0.010,0.024) | 0.013 | 16 | ||

Labor Market | (0.192,0.290,0.433) | |||||

Overall productivity | (0.066,0.088,0.121) | (0.002,0.004,0.011) | 0.006 | |||

Compensation levels | (0.225,0.315,0.468) | (0.006,0.016,0.042) | 0.021 | 13 | ||

Working hours | (0.410,0.597,0.838) | (0.011,0.030,0.076) | 0.039 | 8 | ||

Input | (0.331,0.405,0.501) | |||||

R&D Expenses | (0.622,0.748,0.888) | |||||

Total expenditure on R&D per capita | (0.342,0.457,0.604) | (0.070,0.138,0.269) | 0.159 | 3 | ||

Business expenditure on R&D per capita | (0.410,0.543,0.725) | (0.084,0.165,0.322) | 0.191 | 1 | ||

Human Capital | (0.215,0.252,0.307) | |||||

Total R&D personnel nationwide per capita | (0.295,0.389,0.511) | (0.021,0.040,0.079) | 0.046 | 7 | ||

Total R&D personnel in business per capita | (0.323,0.432,0.578) | (0.023,0.044,0.089) | 0.052 | 5 | ||

Qualified engineers | (0.134,0.179,0.241) | (0.010,0.018,0.037) | 0.022 | 12 | ||

Output | (0.335,0.424,0.529) | |||||

Intermediate output | (0.502,0.647,0.816) | |||||

High-tech exports | (0.439,0.567,0.721) | (0.074,0.155,0.311) | 0.180 | 2 | ||

Basic research | (0.343,0.433,0.558) | (0.058,0.119,0.241) | 0.139 | 4 | ||

Immediate output | (0.282,0.353,0.459) | |||||

Scientific articles | (0.437,0.604,0.816) | (0.041,0.090,0.198) | 0.110 | 21 | ||

Patents granted to residents | (0.190,0.253,0.346) | (0.018,0.038,0.084) | 0.047 | 6 | ||

Securing patents abroad | (0.109,0.143,0.195) | (0.010,0.021,0.047) | 0.026 | 10 |

Linguistic Variable | Corresponding Triangular Fuzzy Number |
---|---|

Very poor (VP) | (0, 1, 3) |

Poor (P) | (1, 3, 5) |

Fair (F) | (3, 5, 7) |

Good (G) | (5, 7, 9) |

Very good (VG) | (7, 9,10) |

**Table 4.**Subjective cognition results of evaluators towards the five levels of linguistic variables.

${\mathit{A}}_{1}$ | ${\mathit{A}}_{2}$ | ${\mathit{A}}_{3}$ | ${\mathit{A}}_{4}$ | ${\mathit{A}}_{5}$ | ${\mathit{A}}_{6}$ | ${\mathit{A}}_{7}$ | ${\mathit{A}}_{8}$ | ${\mathit{A}}_{9}$ | ||
---|---|---|---|---|---|---|---|---|---|---|

Higher education achievement | ${C}_{1}$ | (6.09,8.09,9.45) | (5.18,7.18,8.91) | (5.36,7.36,8.91) | (5.00,7.00,8.73) | (3.00,5.00,6.91) | (2.82,4.64,6.64) | (1.55,3.18,5.18) | (1.45,3.18,5.18) | (2.45,4.27,6.27) |

Total public expenditure on education | ${C}_{2}$ | (5.36,7.36,9.00) | (4.82,6.82,8.64) | (3.91,5.91,7.82) | (4.27,6.27,8.27) | (2.45,4.45,6.45) | (2.91,4.64,6.55) | (1.45,3.00,4.91) | (1.18,2.82,4.82) | (2.09,3.73,5.73) |

Science degrees | ${C}_{3}$ | (4.27,6.27,8.09) | (4.64,6.64,8.45) | (4.64,6.64,8.36) | (4.27,6.27,8.00) | (2.82,4.82,6.82) | (3.18,5.18,7.09) | (1.45,3.00,4.91) | (0.82,2.27,4.27) | (3.00,4.82,6.82) |

Language skills | ${C}_{4}$ | (6.27,8.27,9.64) | (2.64,4.64,6.64) | (3.18,5.18,7.09) | (5.36,7.36,9.00) | (3.73,5.73,7.55) | (2.45,4.45,6.45) | (0.91,2.45,4.45) | (2.45,4.27,6.27) | (3.91,5.91,7.82) |

Value of society | ${C}_{5}$ | (4.82,6.82,8.64) | (3.09,5.00,6.91) | (3.18,5.18,7.09) | (4.64,6.64,8.55) | (3.00,5.00,7.00) | (2.18,4.09,6.00) | (2.82,4.64,6.64) | (1.91,3.73,5.73) | (2.55,4.45,6.45) |

Youth interest in science | ${C}_{6}$ | (3.73,5.73,7.64) | (3.91,5.91,7.73) | (4.27,6.27,8.18) | (3.00,5.00,7.00) | (2.45,4.45,6.45) | (3.55,5.55,7.45) | (1.82,3.73,5.73) | (1.64,3.55,5.55) | (3.91,5.91,7.91) |

Flexibility and adaptability | ${C}_{7}$ | (4.45,6.45,8.27) | (3.55,5.55,7.45) | (5.00,7.00,8.73) | (5.36,7.36,9.09) | (2.64,4.64,6.64) | (2.90,4.80,6.70) | (2.82,4.64,6.64) | (2.55,4.45,6.45) | (3.18,5.18,7.09) |

Technological cooperation | ${C}_{8}$ | (4.82,6.82,8.55) | (4.82,6.82,8.73) | (4.27,6.27,8.09) | (4.82,6.82,8.55) | (2.45,4.45,6.45) | (2.36,4.27,6.27) | (1.36,3.18,5.18) | (1.36,3.36,5.36) | (3.00,5.00,7.00) |

Knowledge transfer | ${C}_{9}$ | (5.18,7.18,8.82) | (4.82,6.82,8.64) | (4.60,6.60,8.40) | (4.45,6.45,8.18) | (2.45,4.45,6.45) | (2.55,4.45,6.45) | (1.20,3.00,5.00) | (1.36,3.36,5.36) | (3.00,5.00,7.00) |

Development an application of technology | ${C}_{10}$ | (5.18,7.18,8.91) | (4.82,6.82,8.55) | (4.64,6.64,8.55) | (4.45,6.45,8.27) | (2.36,4.27,6.18) | (2.55,4.45,6.45) | (1.09,2.82,4.82) | (0.82,2.64,4.64) | (2.82,4.82,6.82) |

Overall productivity | ${C}_{11}$ | (5.73,7.73,9.36) | (5.55,7.55,9.27) | (5.73,7.73,9.27) | (5.73,7.73,9.27) | (3.18,5.18,7.18) | (3.55,5.55,7.27) | (1.82,3.73,5.73) | (1.64,3.55,5.55) | (3.36,5.36,7.27) |

Compensation levels | ${C}_{12}$ | (5.73,7.73,9.27) | (4.27,6.27,8.18) | (4.09,6.09,8.09) | (5.18,7.18,8.82) | (2.82,4.82,6.82) | (2.09,4.09,6.09) | (1.73,3.55,5.55 | (1.18,3.00,5.00) | (1.91,3.73,5.73) |

Working hours | ${C}_{13}$ | (5.18,7.18,9.00) | (4.27,6.27,8.09) | (3.73,5.55,7.27) | (4.45,6.45,8.18) | (3.55,5.55,7.36) | (3.09,5.00,6.82) | (2.91,4.82,6.73) | (2.82,4.82,6.73) | (3.09,5.00,6.91) |

Total expenditure on R&D per capita | ${C}_{14}$ | (4.45,6.45,8.36) | (5.55,7.55,9.18) | (4.09,6.09,8.00) | (4.09,6.09,8.09) | (2.27,4.27,6.27) | (4.09,6.09,7.91) | (2.00,3.91,5.91) | (1.45,3.36,5.36) | (2.45,4.27,6.27) |

Business expenditure on R&D per capita | ${C}_{15}$ | (4.82,6.82,8.64) | (5.00,7.00,8.73) | (3.91,5.91,7.91) | (3.73,5.73,7.64) | (2.45,4.45,6.45) | (3.36,5.36,7.18) | (1.91,3.73,5.73) | (1.64,3.55,5.55) | (2.27,4.09,6.09) |

Total R&D personnel nationwide per capita | ${C}_{16}$ | (4.45,6.45,8.36) | (4.45,6.45,8.36) | (4.82,6.82,8.55) | (3.18,5.18,7.09) | (2.36,4.27,6.27) | (2.27,4.09,6.00) | (1.73,3.55,5.55) | (1.45,3.36,5.36) | (2.27,3.91,5.91) |

Total R&D personnel in business per capita | ${C}_{17}$ | (5.18,7.18,8.82) | (4.64,6.64,8.36) | (4.09,6.09,7.91) | (4.09,6.09,7.91) | (2.36,4.27,6.27) | (2.45,4.27,6.27) | (1.91,3.73,5.73) | (1.64,3.55,5.55) | (2.36,4.09,6.00) |

Qualified engineers | ${C}_{18}$ | (6.27,8.27,9.45) | (5.73,7.73,9.00) | (5.36,7.36,8.73) | (6.27,8.27,9.45) | (3.91,5.91,7.55) | (3.18,5.18,7.00) | (1.64,3.36,5.36) | (1.18,3.00,5.00) | (4.45,6.45,8.00) |

High-tech exports | ${C}_{19}$ | (5.00,7.00,8.45) | (5.73,7.73,9.00) | (4.27,6.27,7.91) | (4.18,6.09,7.64) | (2.82,4.82,6.64) | (3.55,5.55,7.27) | (0.82,2.45,4.45) | (0.73,2.45,4.45) | (3.00,4.82,6.55) |

Basic research | ${C}_{20}$ | (5.18,7.18,8.64) | (5.36,7.36,8.73) | (5.36,7.36,8.73) | (5.00,7.00,8.45) | (2.82,4.82,6.73) | (4.82,6.82,8.27) | (1.00,2.64,4.64) | (0.64,2.27,4.27) | (3.00,4.82,6.55) |

Scientific articles | ${C}_{21}$ | (5.73,7.73,9.09) | (5.36,7.36,8.73) | (5.55,7.55,8.91) | (5.36,7.36,8.73) | (2.09,3.91,5.82) | (4.09,6.09,7.73) | (0.73,2.27,4.27) | (0.36,1.73,3.73) | (3.55,5.36,7.00) |

Patents granted to residents | ${C}_{22}$ | (4.45,6.45,8.00) | (6.09,8.09,9.27) | (5.55,7.55,8.91) | (4.00,5.91,7.45) | (2.09,3.91,5.82) | (3.55,5.55,7.27) | (1.00,2.64,4.64) | (0.55,2.09,4.09) | (3.18,5.00,6.73) |

Securing patents abroad | ${C}_{23}$ | (4.73,6.64,8.09) | (6.09,8.09,9.27) | (5.55,7.55,8.91) | (3.91,5.91,7.55) | (2.27,4.09,5.91) | (3.00,5.00,6.82) | (0.73,2.27,4.27) | (0.55,2.09,4.09) | (2.30,4.00,5.90) |

${\mathit{A}}_{1}$ | ${\mathit{A}}_{2}$ | ${\mathit{A}}_{3}$ | ${\mathit{A}}_{4}$ | ${\mathit{A}}_{5}$ | ${\mathit{A}}_{6}$ | ${\mathit{A}}_{7}$ | ${\mathit{A}}_{8}$ | ${\mathit{A}}_{9}$ | ||
---|---|---|---|---|---|---|---|---|---|---|

Higher education achievement | ${C}_{1}$ | (0.63,0.84,0.98) | (0.56,0.77,0.96) | (0.58,0.79,0.96) | (0.53,0.74,0.92) | (0.40,0.66,0.92) | (0.34,0.56,0.80) | (0.23,0.47,0.77) | (0.22,0.47,0.77) | (0.31,0.53,0.78) |

Total public expenditure on education | ${C}_{2}$ | (0.56,0.76,0.93) | (0.52,0.74,0.93) | (0.42,0.64,0.84) | (0.45,0.66,0.88) | (0.33,0.59,0.86) | (0.35,0.56,0.79) | (0.22,0.45,0.73) | (0.18,0.42,0.72) | (0.26,0.47,0.72) |

Science degrees | ${C}_{3}$ | (0.44,0.65,0.84) | (0.50,0.72,0.91) | (0.50,0.72,0.90) | (0.45,0.66,0.85) | (0.37,0.64,0.90) | (0.38,0.63,0.86) | (0.22,0.45,0.73) | (0.12,0.34,0.64) | (0.38,0.60,0.85) |

Language skills | ${C}_{4}$ | (0.65,0.86,1.00) | (0.28,0.50,0.72) | (0.34,0.56,0.76) | (0.57,0.78,0.95) | (0.49,0.76,1.00) | (0.30,0.54,0.78) | (0.14,0.36,0.66) | (0.36,0.64,0.93) | (0.49,0.74,0.98) |

Value of society | ${C}_{5}$ | (0.50,0.71,0.90) | (0.33,0.54,0.75) | (0.34,0.56,0.76) | (0.49,0.70,0.90) | (0.40,0.66,0.93) | (0.26,0.49,0.73) | (0.42,0.69,0.99) | (0.28,0.55,0.85) | (0.32,0.56,0.81) |

Youth interest in science | ${C}_{6}$ | (0.39,0.59,0.79) | (0.42,0.64,0.83) | (0.46,0.68,0.88) | (0.32,0.53,0.74) | (0.33,0.59,0.86) | (0.43,0.67,0.90) | (0.27,0.55,0.85) | (0.24,0.53,0.82) | (0.49,0.74,0.99) |

Flexibility and adaptability | ${C}_{7}$ | (0.46,0.67,0.86) | (0.38,0.60,0.80) | (0.54,0.75,0.94) | (0.57,0.78,0.96) | (0.35,0.61,0.88) | (0.35,0.58,0.81) | (0.42,0.69,0.99) | (0.38,0.66,0.96) | (0.40,0.65,0.89) |

Technological cooperation | ${C}_{8}$ | (0.50,0.71,0.89) | (0.52,0.74,0.94) | (0.46,0.68,0.87) | (0.51,0.72,0.90) | (0.33,0.59,0.86) | (0.29,0.52,0.76) | (0.20,0.47,0.77) | (0.20,0.50,0.80) | (0.38,0.63,0.88) |

Knowledge transfer | ${C}_{9}$ | (0.54,0.75,0.92) | (0.52,0.74,0.93) | (0.50,0.71,0.91) | (0.47,0.68,0.87) | (0.33,0.59,0.86) | (0.31,0.54,0.78) | (0.18,0.45,0.74) | (0.20,0.50,0.80) | (0.38,0.63,0.88) |

Development an application of technology | ${C}_{10}$ | (0.54,0.75,0.92) | (0.52,0.74,0.92) | (0.50,0.72,0.92) | (0.47,0.68,0.88) | (0.31,0.57,0.82) | (0.31,0.54,0.78) | (0.16,0.42,0.72) | (0.12,0.39,0.69) | (0.35,0.60,0.85) |

Overall productivity | ${C}_{11}$ | (0.59,0.80,0.97) | (0.60,0.81,1.00) | (0.62,0.83,1.00) | (0.61,0.82,0.98) | (0.42,0.69,0.95) | (0.43,0.67,0.88) | (0.27,0.55,0.85) | (0.24,0.53,0.82) | (0.42,0.67,0.91) |

Compensation levels | ${C}_{12}$ | (0.59,0.80,0.96) | (0.46,0.68,0.88) | (0.44,0.66,0.87) | (0.55,0.76,0.93) | (0.37,0.64,0.90) | (0.25,0.49,0.74) | (0.26,0.53,0.82) | (0.18,0.45,0.74) | (0.24,0.47,0.72) |

Working hours | ${C}_{13}$ | (0.54,0.75,0.93) | (0.46,0.68,0.87) | (0.40,0.60,0.78) | (0.47,0.68,0.87) | (0.47,0.73,0.98) | (0.37,0.60,0.82) | (0.43,0.72,1.00) | (0.42,0.72,1.00) | (0.39,0.63,0.86) |

Total expenditure on R&D per capita | ${C}_{14}$ | (0.46,0.67,0.87) | (0.60,0.81,0.99) | (0.44,0.66,0.86) | (0.43,0.64,0.86) | (0.30,0.57,0.83) | (0.49,0.74,0.96) | (0.30,0.58,0.88) | (0.22,0.50,0.80) | (0.31,0.53,0.78) |

Business expenditure on R&D per capita | ${C}_{15}$ | (0.50,0.71,0.90) | (0.54,0.75,0.94) | (0.42,0.64,0.85) | (0.39,0.61,0.81) | (0.33,0.59,0.86) | (0.41,0.65,0.87) | (0.28,0.55,0.85) | (0.24,0.53,0.82) | (0.28,0.51,0.76) |

Total R&D personnel nationwide per capita | ${C}_{16}$ | (0.46,0.67,0.87) | (0.48,0.70,0.90) | (0.52,0.74,0.92) | (0.34,0.55,0.75) | (0.31,0.57,0.83) | (0.27,0.49,0.73) | (0.26,0.53,0.82) | (0.22,0.50,0.80) | (0.28,0.49,0.74) |

Total R&D personnel in business per capita | ${C}_{17}$ | (0.54,0.75,0.92) | (0.50,0.72,0.90) | (0.44,0.66,0.85) | (0.43,0.64,0.84) | (0.31,0.57,0.83) | (0.30,0.52,0.76) | (0.28,0.55,0.85) | (0.24,0.53,0.82) | (0.30,0.51,0.75) |

Qualified engineers | ${C}_{18}$ | (0.65,0.86,0.98) | (0.62,0.83,0.97) | (0.58,0.79,0.94) | (0.66,0.88,1.00) | (0.52,0.78,1.00) | (0.38,0.63,0.85) | (0.24,0.50,0.80) | (0.18,0.45,0.74) | (0.56,0.81,1.00) |

High-tech exports | ${C}_{19}$ | (0.52,0.73,0.88) | (0.62,0.83,0.97) | (0.46,0.68,0.85) | (0.44,0.64,0.81) | (0.37,0.64,0.88) | (0.43,0.67,0.88) | (0.12,0.36,0.66) | (0.11,0.36,0.66) | (0.38,0.60,0.82) |

Basic research | ${C}_{20}$ | (0.54,0.75,0.90) | (0.58,0.79,0.94) | (0.58,0.79,0.94) | (0.53,0.74,0.89) | (0.37,0.64,0.89) | (0.58,0.82,1.00) | (0.15,0.39,0.69) | (0.09,0.34,0.64) | (0.38,0.60,0.82) |

Scientific articles | ${C}_{21}$ | (0.59,0.80,0.94) | (0.58,0.79,0.94) | (0.60,0.81,0.96) | (0.57,0.78,0.92) | (0.28,0.52,0.77) | (0.49,0.74,0.93) | (0.11,0.34,0.64) | (0.05,0.26,0.55) | (0.44,0.67,0.88) |

Patents granted to residents | ${C}_{22}$ | (0.46,0.67,0.83) | (0.66,0.87,1.00) | (0.60,0.81,0.96) | (0.42,0.63,0.79) | (0.28,0.52,0.77) | (0.43,0.67,0.88) | (0.15,0.39,0.69) | (0.08,0.31,0.61) | (0.40,0.63,0.84) |

Securing patents abroad | ${C}_{23}$ | (0.49,0.69,0.84) | (0.66,0.87,1.00) | (0.60,0.81,0.96) | (0.41,0.63,0.80) | (0.30,0.54,0.78) | (0.36,0.60,0.82) | (0.11,0.34,0.64) | (0.08,0.31,0.61) | (0.29,0.50,0.74) |

${\mathit{A}}_{1}$ | ${\mathit{A}}_{2}$ | ${\mathit{A}}_{3}$ | ${\mathit{A}}_{4}$ | ${\mathit{A}}_{5}$ | ${\mathit{A}}_{6}$ | ${\mathit{A}}_{7}$ | ${\mathit{A}}_{8}$ | ${\mathit{A}}_{9}$ | ||
---|---|---|---|---|---|---|---|---|---|---|

Higher education achievement | ${C}_{1}$ | (0.001,0.005,0.015) | (0.001,0.005,0.015 | (0.001,0.005,0.015) | (0.001,0.004,0.014) | (0.001,0.004,0.014) | (0.001,0.003,0.012) | (0.001,0.003,0.012) | (0.001,0.003,0.012) | (0.001,0.003,0.012) |

Total public expenditure on education | ${C}_{2}$ | (0.002,0.007,0.021) | (0.002,0.006,0.021) | (0.001,0.006,0.019) | (0.002,0.006,0.020) | (0.001,0.005,0.019) | (0.001,0.005,0.018) | (0.001,0.004,0.016) | (0.001,0.004,0.016) | (0.001,0.004,0.016) |

Science degrees | ${C}_{3}$ | (0.002,0.008,0.025) | (0.002,0.008,0.027) | (0.002,0.008,0.027) | (0.002,0.008,0.025) | (0.002,0.007,0.027) | (0.002,0.007,0.025) | (0.001,0.005,0.022) | (0.001,0.004,0.019) | (0.002,0.007,0.025) |

Language skills | ${C}_{4}$ | (0.002,0.008,0.024) | (0.001,0.005,0.017) | (0.001,0.005,0.018) | (0.002,0.007,0.022) | (0.002,0.007,0.024) | (0.001,0.005,0.018) | (0.000,0.003,0.016) | (0.001,0.006,0.022) | (0.002,0.007,0.023) |

Value of society | ${C}_{5}$ | (0.002,0.007,0.023) | (0.001,0.006,0.019) | (0.002,0.006,0.019) | (0.002,0.007,0.023) | (0.002,0.007,0.024) | (0.001,0.005,0.018) | (0.002,0.007,0.025) | (0.001,0.006,0.022) | (0.001,0.006,0.020) |

Youth interest in science | ${C}_{6}$ | (0.003,0.010,0.032) | (0.003,0.011,0.034) | (0.003,0.011,0.036) | (0.002,0.009,0.030) | (0.002,0.010,0.035) | (0.003,0.011,0.036) | (0.002,0.009,0.034) | (0.002,0.009,0.033) | (0.003,0.012,0.040) |

Flexibility and adaptability | ${C}_{7}$ | (0.004,0.014,0.044) | (0.003,0.012,0.041) | (0.005,0.016,0.048) | (0.005,0.016,0.049) | (0.003,0.013,0.045) | (0.003,0.012,0.041) | (0.004,0.014,0.050) | (0.003,0.014,0.049) | (0.003,0.013,0.045) |

Technological cooperation | ${C}_{8}$ | (0.004,0.014,0.043) | (0.004,0.015,0.046) | (0.004,0.013,0.042) | (0.004,0.014,0.044) | (0.003,0.012,0.042) | (0.002,0.010,0.037) | (0.002,0.009,0.038) | (0.002,0.010,0.039) | (0.003,0.012,0.043) |

Knowledge transfer | ${C}_{9}$ | (0.002,0.006,0.019) | (0.002,0.006,0.020) | (0.002,0.006,0.019) | (0.002,0.006,0.018) | (0.001,0.005,0.018) | (0.001,0.005,0.016) | (0.001,0.004,0.016) | (0.001,0.004,0.017) | (0.001,0.005,0.018) |

Development an application of technology | ${C}_{10}$ | (0.002,0.007,0.023) | (0.002,0.007,0.023) | (0.002,0.007,0.023) | (0.002,0.007,0.021) | (0.001,0.005,0.020) | (0.001,0.005,0.019) | (0.001,0.004,0.017) | (0.000,0.004,0.017) | (0.001,0.006,0.021) |

Overall productivity | ${C}_{11}$ | (0.001,0.003,0.011) | (0.001,0.004,0.011) | (0.001,0.004,0.011) | (0.001,0.004,0.011) | (0.001,0.003,0.010) | (0.001,0.003,0.010) | (0.000,0.002,0.009) | (0.000,0.002,0.009) | (0.001,0.003,0.010) |

Compensation levels | ${C}_{12}$ | (0.004,0.012,0.041) | (0.003,0.011,0.037) | (0.003,0.010,0.037) | (0.003,0.012,0.040) | (0.002,0.010,0.038) | (0.002,0.008,0.031) | (0.002,0.008,0.035) | (0.001,0.007,0.031) | (0.001,0.007,0.030) |

Working hours | ${C}_{13}$ | (0.006,0.022,0.071) | (0.005,0.020,0.066) | (0.004,0.018,0.060) | (0.005,0.020,0.066) | (0.005,0.022,0.074) | (0.004,0.018,0.063) | (0.005,0.021,0.076) | (0.005,0.021,0.076) | (0.004,0.018,0.066) |

Total expenditure on R&D per capita | ${C}_{14}$ | (0.033,0.093,0.233) | (0.042,0.113,0.266) | (0.031,0.091,0.232) | (0.030,0.089,0.230) | (0.021,0.078,0.223) | (0.035,0.102,0.257) | (0.021,0.080,0.236) | (0.015,0.069,0.214) | (0.022,0.074,0.211) |

Business expenditure on R&D per capita | ${C}_{15}$ | (0.042,0.117,0.289) | (0.046,0.124,0.303) | (0.036,0.105,0.275) | (0.033,0.100,0.260) | (0.027,0.097,0.276) | (0.034,0.107,0.280) | (0.024,0.091,0.275) | (0.021,0.087,0.266) | (0.024,0.084,0.245) |

Total R&D personnel nationwide per capita | ${C}_{16}$ | (0.010,0.027,0.068) | (0.010,0.028,0.071) | (0.011,0.029,0.072) | (0.007,0.022,0.059) | (0.007,0.023,.065) | (0.006,0.020,0.057) | (0.005,0.021,0.065) | (0.005,0.020,0.063) | (0.006,0.019,0.058) |

Total R&D personnel in business per capita | ${C}_{17}$ | (0.012,0.033,0.081) | (0.011,0.032,0.080) | (0.010,0.029,0.076) | (0.010,0.028,0.074) | (0.007,0.025,0.074) | (0.007,0.023,0.067) | (0.007,0.024,0.076) | (0.006,0.023,0.073) | (0.007,0.023,0.067) |

Qualified engineers | ${C}_{18}$ | (0.006,0.016,0.036) | (0.006,0.015,0.036) | (0.006,0.015,0.035) | (0.006,0.016,0.037) | (0.005,0.014,0.037) | (0.004,0.011,0.031) | (0.002,0.009,0.029) | (0.002,0.008,0.027) | (0.005,0.015,0.037) |

High-tech exports | ${C}_{19}$ | (0.038,0.113,0.273) | (0.046,0.130,0.302) | (0.034,0.105,0.265) | (0.033,0.100,0.251) | (0.028,0.099,0.274) | (0.032,0.104,0.273) | (0.009,0.057,0.206) | (0.008,0.057,0.206) | (0.028,0.094,0.254) |

Basic research | ${C}_{20}$ | (0.031,0.088,0.216) | (0.033,0.094,0.227) | (0.033,0.094,0.227 | (0.030,0.088,0.215) | (0.022,0.076,0.215) | (0.034,0.098,0.241) | (0.009,0.047,0.166) | (0.005,0.040,0.153) | (0.022,0.071,0.197) |

Scientific articles | ${C}_{21}$ | (0.025,0.072,0.187) | (0.024,0.072,0.187 | (0.025,0.074,0.190) | (0.023,0.070,0.183) | (0.011,0.047,0.153) | (0.020,0.067,0.185) | (0.004,0.031,0.126) | (0.002,0.023,0.110) | (0.018,0.061,0.173) |

Patents granted to residents | ${C}_{22}$ | (0.008,0.025,0.070) | (0.012,0.033,0.084) | (0.011,0.031,0.081) | (0.008,0.024,0.066) | (0.005,0.020,0.065) | (0.008,0.025,0.074) | (0.003,0.015,0.058) | (0.001,0.012,0.051) | (0.007,0.024,0.071) |

Securing patents abroad | ${C}_{23}$ | (0.005,0.015,0.040) | (0.007,0.019,0.047) | (0.006,0.017,0.046) | (0.004,0.013,0.038) | (0.003,0.012,0.037) | (0.004,0.013,0.039) | (0.001,0.007,0.030) | (0.001,0.007,0.029) | (0.003,0.011,0.035) |

Countries | ${\mathit{d}}_{\mathit{i}}^{+}$ | ${\mathit{d}}_{\mathit{i}}^{-}$ | Gap degree of $\mathit{C}{\mathit{C}}_{\mathit{i}}^{+}$ | Satisfaction degree of $\mathit{C}{\mathit{C}}_{\mathit{i}}^{-}$ | |
---|---|---|---|---|---|

Singapore | ${A}_{1}$ | 22.074 | 1.174 | 0.950 | 0.0505 |

South Korea | ${A}_{2}$ | 22.021 | 1.237 | 0.947 | 0.0532 |

Taiwan | ${A}_{3}$ | 22.088 | 1.163 | 0.950 | 0.0500 |

Hong Kong | ${A}_{4}$ | 22.127 | 1.115 | 0.952 | 0.0480 |

Malaysia | ${A}_{5}$ | 22.168 | 1.104 | 0.953 | 0.0474 |

China | ${A}_{6}$ | 22.118 | 1.143 | 0.951 | 0.0491 |

Thailand | ${A}_{7}$ | 22.283 | 0.984 | 0.958 | 0.0423 |

Philippines | ${A}_{8}$ | 22.328 | 0.934 | 0.960 | 0.0401 |

India | ${A}_{9}$ | 22.200 | 1.052 | 0.955 | 0.0452 |

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## Share and Cite

**MDPI and ACS Style**

Chou, Y.-C.; Yen, H.-Y.; Dang, V.T.; Sun, C.-C.
Assessing the Human Resource in Science and Technology for Asian Countries: Application of Fuzzy AHP and Fuzzy TOPSIS. *Symmetry* **2019**, *11*, 251.
https://doi.org/10.3390/sym11020251

**AMA Style**

Chou Y-C, Yen H-Y, Dang VT, Sun C-C.
Assessing the Human Resource in Science and Technology for Asian Countries: Application of Fuzzy AHP and Fuzzy TOPSIS. *Symmetry*. 2019; 11(2):251.
https://doi.org/10.3390/sym11020251

**Chicago/Turabian Style**

Chou, Ying-Chyi, Hsin-Yi Yen, Van Thac Dang, and Chia-Chi Sun.
2019. "Assessing the Human Resource in Science and Technology for Asian Countries: Application of Fuzzy AHP and Fuzzy TOPSIS" *Symmetry* 11, no. 2: 251.
https://doi.org/10.3390/sym11020251