# A Cooperative Partner Selection Study of Military-Civilian Scientific and Technological Collaborative Innovation Based on Interval-Valued Intuitionistic Fuzzy Set

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Preliminaries

**Definition**

**1**

**([23]).**

**Definition**

**2**

**([24]).**

**Definition**

**3**

**([33]**).

- (1)
- ${\tilde{\alpha}}_{1}\oplus {\tilde{\alpha}}_{2}=\left(\left[{\tilde{u}}^{L}{}_{{\tilde{\alpha}}_{1}}+{\tilde{u}}^{L}{}_{{\tilde{\alpha}}_{2}}-{\tilde{u}}^{L}{}_{{\tilde{\alpha}}_{1}}{\tilde{u}}^{L}{}_{{\tilde{\alpha}}_{2}},{\tilde{u}}^{U}{}_{{\tilde{\alpha}}_{1}}+{\tilde{u}}^{U}{}_{{\tilde{\alpha}}_{2}}-{\tilde{u}}^{U}{}_{{\tilde{\alpha}}_{1}}{\tilde{u}}^{U}{}_{{\tilde{\alpha}}_{2}}\right],\left[{\tilde{\nu}}^{L}{}_{{\tilde{\alpha}}_{1}}{\tilde{\nu}}^{L}{}_{{\tilde{\alpha}}_{2}},{\tilde{\nu}}^{U}{}_{{\tilde{\alpha}}_{1}}{\tilde{\nu}}^{U}{}_{{\tilde{\alpha}}_{2}}\right]\right)$
- (2)
- ${\tilde{\alpha}}_{1}\otimes {\tilde{\alpha}}_{2}=\left(\left[{\tilde{u}}^{L}{}_{{\tilde{\alpha}}_{1}}{\tilde{u}}^{L}{}_{{\tilde{\alpha}}_{2}},{\tilde{u}}^{U}{}_{{\tilde{\alpha}}_{1}}{\tilde{u}}^{U}{}_{{\tilde{\alpha}}_{2}}\right],\left[{\tilde{\nu}}^{L}{}_{{\tilde{\alpha}}_{1}}+{\tilde{\nu}}^{L}{}_{{\tilde{\alpha}}_{2}}-{\tilde{\nu}}^{L}{}_{{\tilde{\alpha}}_{1}}{\tilde{\nu}}^{L}{}_{{\tilde{\alpha}}_{2}},{\tilde{\nu}}^{U}{}_{{\tilde{\alpha}}_{1}}+{\tilde{\nu}}^{U}{}_{{\tilde{\alpha}}_{2}}-{\tilde{\nu}}^{L}{}_{{\tilde{\alpha}}_{1}}{\tilde{\nu}}^{L}{}_{{\tilde{\alpha}}_{2}}\right]\right)$
- (3)
- $\lambda {\tilde{\alpha}}_{1}=\left(\left[1-{\left(1-{\tilde{u}}^{L}{}_{{\tilde{\alpha}}_{1}}\right)}^{\lambda},1-{\left(1-{\tilde{u}}^{U}{}_{{\tilde{\alpha}}_{1}}\right)}^{\lambda}\right],\left[{\left({\tilde{\nu}}^{L}{}_{{\tilde{\alpha}}_{1}}\right)}^{\lambda},{\left({\tilde{\nu}}^{U}{}_{{\tilde{\alpha}}_{1}}\right)}^{\lambda}\right]\right)$
- (4)
- ${\tilde{\alpha}}_{1}{}^{\lambda}=\left(\left[{\left({\tilde{u}}^{L}{}_{{\tilde{\alpha}}_{1}}\right)}^{\lambda},{\left({\tilde{u}}^{U}{}_{{\tilde{\alpha}}_{1}}\right)}^{\lambda}\right],\left[1-{\left(1-{\tilde{\nu}}^{L}{}_{{\tilde{\alpha}}_{1}}\right)}^{\lambda},1-{\left(1-{\tilde{\nu}}^{U}{}_{{\tilde{\alpha}}_{1}}\right)}^{\lambda}\right]\right)$

**Definition**

**4**

**([33])**.

- (1)
- IF$S({\tilde{\alpha}}_{1})>S({\tilde{\alpha}}_{2})$, then${\tilde{\alpha}}_{1}>{\tilde{\alpha}}_{2}$; IF$S({\tilde{\alpha}}_{1})<S({\tilde{\alpha}}_{2})$, then${\tilde{\alpha}}_{1}<{\tilde{\alpha}}_{2}$.
- (2)
- IF$S({\tilde{\alpha}}_{1})=S({\tilde{\alpha}}_{2})$, then when$H({\tilde{\alpha}}_{1})>H({\tilde{\alpha}}_{2})$, ${\tilde{\alpha}}_{1}>{\tilde{\alpha}}_{2}$; when$H({\tilde{\alpha}}_{1})<H({\tilde{\alpha}}_{2})$, ${\tilde{\alpha}}_{1}<{\tilde{\alpha}}_{2}$; when$H({\tilde{\alpha}}_{1})=H({\tilde{\alpha}}_{2})$, ${\tilde{\alpha}}_{1}={\tilde{\alpha}}_{2}$.

**Definition**

**5**

**([33]**).

**Definition**

**6**

**([34]).**

## 4. Index Selection

#### 4.1. Top-Level Design

#### 4.2. Main Characteristics

#### 4.3. Technical Characteristics

#### 4.4. Interaction between Cooperative Entities

## 5. Model Building

#### 5.1. Determination of Index Weights

#### 5.1.1. Improvement of Scoring Function Based on Accuracy Function and Interval Length

**Definition**

**7.**

**Proposition**

**1.**

- I.
- $\alpha -1\le \widehat{S}\left({r}_{ij}^{k}\right)\le \alpha +1$
- II.
- $\widehat{S}\left({r}_{ij}^{k}\right)=\alpha +1\iff {r}_{ij}^{k}=\left(\left[1,1\right],\left[0,0\right]\right)$
- III
- $\widehat{S}\left({r}_{ij}^{k}\right)=\alpha -1\iff {r}_{ij}^{k}=\left(\left[0,0\right],\left[1,1\right]\right)$

**Proof.**

**Proposition**

**2.**

**Proof**.

**Proposition**

**3.**

**Proof**.

**Definition**

**8.**

- I.
- If$\widehat{S}\left({}^{1}r_{ij}^{k}\right)>\widehat{S}\left({}^{2}r_{ij}^{k}\right)$, then${}^{1}r_{ij}^{k}>{}^{2}r_{ij}^{k}$
- II.
- If$\widehat{S}\left({}^{1}r_{ij}^{k}\right)<\widehat{S}\left({}^{2}r_{ij}^{k}\right)$, then${}^{1}r_{ij}^{k}<{}^{2}r_{ij}^{k}$
- III.
- If$\widehat{S}\left({}^{1}r_{ij}^{k}\right)=\widehat{S}\left({}^{2}r_{ij}^{k}\right)$, then${}^{1}r_{ij}^{k}\sim {}^{2}r_{ij}^{k}$

#### 5.1.2. Entropy Weighting Theory to Determine Index Weights

#### 5.2. Considering Matrix Assembly and Transformation of Decision Makers’ Risk Attitudes

#### 5.2.1. Assembly of Expert Evaluation Matrix

#### 5.2.2. Matrix Transformation Based on Hesitancy Distribution

#### 5.2.3. Decision-Making Process Based on Grey Correlation Analysis and the TOPSIS Method

## 6. Numerical Examples

**,**${e}_{4}$

**,**${e}_{5}$ to evaluate the cooperation qualifications of the five units. These five experts are the deputy director of the Strategic Planning Bureau of the Office of the Central Civil-Military Integration Development Committee, the professor of the Civil-Military Integration Development Research Center of China People’s Liberation Army National Defense University, the professor of Beijing Institute of Technology, the researcher of the 714th Research Institute of China Shipbuilding Industry Group Co., Ltd., and the engineer of Leike Defense Technology Co., Ltd., representing five types of entities from government departments, military academy, colleges and universities, research institutions, and private enterprises. The indicators of qualification evaluation include the policy and operation mechanism of MCSTCI ${g}_{1}$, the willingness of civil-military integration ${g}_{2}$, the organizational structure (unit nature) ${g}_{3}$, the level of technological innovation ${g}_{4}$, the technology transfer capability ${g}_{5}$, the coordinative configuration of elements ${g}_{6}$ and the benefit distribution model ${g}_{7}$, which are the seven judging criteria. Therefore, $m=5$, $n=7$, $l=5$. The experts’ evaluation of the qualification of selected objects is expressed by the interval intuitionistic fuzzy numbers, where the membership degree interval represents the extent to which experts think the candidate object meets the requirements of the index, and the non-membership interval represents the extent to which experts think the candidate object doesn’t meet the requirements of the index. The original evaluation values given by each expert are shown in Table 2.

## 7. Discussion

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Structural analysis of the military-civilian technological collaborative innovation system.

**Table 1.**Indicators for the selection of military-civilian scientific and technological collaborative innovation partners.

First-Level Indicators | Second-Level Indicators | Authors | Index Description |
---|---|---|---|

Top-level Design | Civil-Military integration policy, technology policy, and operating mechanism | You and Zhao [35], Shen and Zheng [36], Tian, et al. [37] | Standards and rules formulated to meet the Chinese strategic needs and realize civil-military integration. |

Main characteristics | Civil-Military integration willingness | Fang, el al. [3], Tian, et al. [37] | The concept and intention of the innovation entities to participate in civil-military integration. |

Organizational structure (unit nature) | Wang and Chen [16], Jiang, el al. [38] | The division of labor and cooperation system of the innovation entities in terms of management system, department setting, function planning, and normal operation. | |

Technical char-acteristics | Technological innovation level | Kulve and Smit [12], Wang and Chen [16], Tian, el al. [37], Chen and Zhou [39] | The core technology and innovation capabilities of the innovation entities, including the degree of generality and matching that meet the requirements of civil-military integration. |

Technology transfer capability | Zhou, el al. [10], Tian et al. [37], Yin and Tan [40] | The ability of technology to transfer and diffuse among different innovation entities. | |

Interaction between cooperative entities | Collaborative configuration of elements | You and Zhao [35], Shen and Zheng [36] | The interaction of various innovative entities through the coordinative configuration of platforms. |

Benefit distribution model | Fang and Wang [14] | The interest relationship between the entities is manifested in the distribution of revenue and the ownership of technological intellectual property rights. |

${\mathit{g}}_{1}$ | ${\mathit{g}}_{2}$ | ${\mathit{g}}_{3}$ | ${\mathit{g}}_{4}$ | ${\mathit{g}}_{5}$ | ${\mathit{g}}_{6}$ | ${\mathit{g}}_{7}$ | ||
---|---|---|---|---|---|---|---|---|

${r}^{1}$ | ${h}_{1}$ | [0.62, 0.71], [0.13, 0.21] | [0.51, 0.73], [0.16, 0.21] | [0.59, 0.86], [0.06, 0.10] | [0.16, 0.46], [0.41, 0.53] | [0.14, 0.28], [0.47, 0.66] | [0.25, 0.45], [0.46, 0.53] | [0.63, 0.96], [0.02, 0.04] |

${h}_{2}$ | [0.50, 0.83], [0.11, 0.15] | [0.45, 0.66], [0.12, 0.23] | [0.66, 0.72], [0.14, 0.21] | [0.21, 0.36], [0.46, 0.58] | [0.31, 0.51], [0.14, 0.31] | [0.51, 0.57], [0.21, 0.31] | [0.12, 0.46], [0.23, 0.43] | |

${h}_{3}$ | [0.72, 0.82], [0.05, 0.16] | [0.41, 0.81], [0.11, 0.18] | [0.36, 0.51], [0.26, 0.36] | [0.11, 0.38], [0.56, 0.60] | [0.13, 0.56], [0.26, 0.43] | [0.16, 0.56], [0.21, 0.42] | [0.55, 0.90], [0.02, 0.05] | |

${h}_{4}$ | [0.59, 0.85], [0.07, 0.12] | [0.62, 0.78], [0.14, 0.20] | [0.41, 0.76], [0.11, 0.18] | [0.21, 0.33], [0.44, 0.57] | [0.21, 0.54], [0.07, 0.36] | [0.26, 0.46], [0.14, 0.21] | [0.40, 0.75], [0.10, 0.15] | |

${h}_{5}$ | [0.73, 0.89], [0.06, 0.09] | [0.43, 0.55], [0.27, 0.38] | [0.36, 0.61], [0.03, 0.11] | [0.08, 0.21], [0.31, 0.56] | [0.20, 0.42], [0.36, 0.56] | [0.51, 0.81], [0.12, 0.18] | [0.34, 0.55], [0.22, 0.45] | |

${r}^{2}$ | ${h}_{1}$ | [0.40, 0.72], [0.10, 0.15] | [0.10, 0.42], [0.33, 0.58] | [0.13, 0.25], [0.54, 0.70] | [0.12, 0.34], [0.40, 0.60] | [0.74, 0.85], [0.10, 0.15] | [0.13, 0.58], [0.27, 0.42] | [0.46, 0.67], [0.15, 0.25] |

${h}_{2}$ | [0.55, 0.65], [0.07, 0.15] | [0.37, 0.39], [0.51, 0.61] | [0.57, 0.90], [0.02, 0.05] | [0.05, 0.36], [0.17, 0.42] | [0.35, 0.60], [0.10, 0.25] | [0.16, 0.32], [0.27, 0.47] | [0.26, 0.31], [0.12, 0.16] | |

${h}_{3}$ | [0.43, 0.88], [0.06, 0.12] | [0.41, 0.75], [0.08, 0.15] | [0.35, 0.47], [0.12, 0.48] | [0.12, 0.45], [0.26, 0.50] | [0.20, 0.52], [0.15, 0.25] | [0.41, 0.66], [0.13, 0.22] | [0.35, 0.45], [0.16, 0.25] | |

${h}_{4}$ | [0.70, 0.88], [0.05, 0.12] | [0.10, 0.42], [0.43, 0.65] | [0.25, 0.46], [0.13, 0.15] | [0.20, 0.34], [0.10, 0.15] | [0.09, 0.14], [0.36, 0.42] | [0.44, 0.71], [0.15, 0.27] | [0.10, 0.35], [0.55, 0.61] | |

${h}_{5}$ | [0.30, 0.54], [0.10, 0.15] | [0.34, 0.54], [0.22, 0.42] | [0.60, 0.81], [0.02, 0.10] | [0.40, 0.81], [0.06, 0.16] | [0.74, 0.92], [0.01, 0.06] | [0.13, 0.25], [0.35, 0.50] | [0.26, 0.34], [0.51, 0.52] | |

${r}^{3}$ | ${h}_{1}$ | [0.41, 0.66], [0.21, 0.31] | [0.45, 0.72], [0.06, 0.14] | [0.74, 0.83], [0.01, 0.02] | [0.11, 0.46], [0.25, 0.29] | [0.21, 0.36], [0.05, 0.27] | [0.21, 0.25], [0.41, 0.43] | [0.72, 0.82], [0.03, 0.12] |

${h}_{2}$ | [0.16, 0.56], [0.30, 0.37] | [0.28, 0.45], [0.12, 0.33] | [0.35, 0.42], [0.12, 0.21] | [0.36, 0.55], [0.24, 0.35] | [0.11, 0.23], [0.35, 0.42] | [0.33, 0.46], [0.12, 0.19] | [0.21, 0.44], [0.05, 0.26] | |

${h}_{3}$ | [0.66, 0.71], [0.20, 0.26] | [0.46, 0.81], [0.15, 0.19] | [0.22, 0.48], [0.41, 0.45] | [0.50, 0.61], [0.11, 0.14] | [0.41, 0.65], [0.11, 0.16] | [0.21, 0.56], [0.05, 0.25] | [0.16, 0.22], [0.47, 0.65] | |

${h}_{4}$ | [0.51, 0.62], [0.11, 0.13] | [0.52, 0.63], [0.03, 0.13] | [0.66, 0.71], [0.03, 0.05] | [0.11, 0.32], [0.35, 0.46] | [0.35, 0.50], [0.13, 0.30] | [0.13, 0.42], [0.38, 0.49] | [0.55, 0.65], [0.23, 0.31] | |

${h}_{5}$ | [0.30, 0.42], [0.04, 0.09] | [0.26, 0.46], [0.12, 0.15] | [0.42, 0.57], [0.23, 0.31] | [0.51, 0.73], [0.02, 0.20] | [0.52, 0.61], [0.22, 0.30] | [0.35, 0.50], [0.25, 0.32] | [0.20, 0.58], [0.10, 0.32] | |

${r}^{4}$ | ${h}_{1}$ | [0.42, 0.61], [0.12, 0.15] | [0.51, 0.76], [0.03, 0.20] | [0.42, 0.60], [0.12, 0.33] | [0.15, 0.22], [0.20, 0.38] | [0.31, 0.52], [0.11, 0.25] | [0.70, 0.72], [0.12, 0.18] | [0.42, 0.61], [0.25, 0.33] |

${h}_{2}$ | [0.38, 0.55], [0.11, 0.23] | [0.26, 0.51], [0.11, 0.14] | [0.52, 0.70], [0.01, 0.23] | [0.20, 0.45], [0.40, 0.41] | [0.45, 0.50], [0.22, 0.23] | [0.24, 0.30], [0.40, 0.61] | [0.15, 0.21], [0.43, 0.51] | |

${h}_{3}$ | [0.61, 0.72], [0.02, 0.05] | [0.72, 0.92], [0.01, 0.06] | [0.56, 0.70], [0.21, 0.26] | [0.13, 0.30], [0.26, 0.42] | [0.43, 0.52], [0.21, 0.27] | [0.52, 0.60], [0.08, 0.12] | [0.09, 0.12], [0.45, 0.66] | |

${h}_{4}$ | [0.12, 0.31], [0.36, 0.40] | [0.40, 0.61], [0.12, 0.28] | [0.21, 0.54], [0.37, 0.39] | [0.50, 0.71], [0.26, 0.38] | [0.20, 0.30], [0.24, 0.27] | [0.44, 0.49], [0.21, 0.24] | [0.42, 0.53], [0.33, 0.35] | |

${h}_{5}$ | [0.22, 0.57], [0.02, 0.25] | [0.57, 0.66], [0.13, 0.15] | [0.50, 0.57], [0.31, 0.40] | [0.15, 0.24], [0.55, 0.62] | [0.34, 0.51], [0.21, 0.26] | [0.26, 0.35], [0.15, 0.20] | [0.16, 0.23], [0.34, 0.39] | |

${r}^{5}$ | ${h}_{1}$ | [0.42, 0.78], [0.12, 0.20] | [0.39, 0.53], [0.25, 0.30] | [0.42, 0.55], [0.05, 0.21] | [0.13, 0.32], [0.34, 0.38] | [0.32, 0.36], [0.30, 0.39] | [0.22, 0.35], [0.31, 0.39] | [0.45, 0.48], [0.21, 0.25] |

${h}_{2}$ | [0.30, 0.36], [0.02, 0.11] | [0.50, 0.57], [0.20, 0.31] | [0.35, 0.42], [0.22, 0.30] | [0.42, 0.46], [0.31, 0.35] | [0.52, 0.69], [0.21, 0.30] | [0.52, 0.67], [0.21, 0.30] | [0.38, 0.58], [0.10, 0.24] | |

${h}_{3}$ | [0.42, 0.55], [0.35, 0.37] | [0.36, 0.38], [0.15, 0.20] | [0.17, 0.28], [0.32, 0.40] | [0.22, 0.32], [0.38, 0.45] | [0.41, 0.46], [0.20, 0.25] | [0.41, 0.48], [0.20, 0.25] | [0.60, 0.78], [0.15, 0.18] | |

${h}_{4}$ | [0.12, 0.46], [0.30, 0.32] | [0.22, 0.48], [0.31, 0.44] | [0.71, 0.85], [0.03, 0.07] | [0.26, 0.37], [0.05, 0.10] | [0.57, 0.60], [0.06, 0.14] | [0.57, 0.60], [0.06, 0.15] | [0.51, 0.71], [0.10, 0.21] | |

${h}_{5}$ | [0.11, 0.14], [0.37, 0.40] | [0.42, 0.63], [0.20, 0.21] | [0.55, 0.62], [0.07, 0.14] | [0.43, 0.56], [0.09, 0.12] | [0.80, 0.91], [0.02, 0.06] | [0.80, 0.91], [0.02, 0.06] | [0.22, 0.35], [0.40, 0.43] |

**Table 3.**Weighting table of indicators for the selection of military-civilian scientific and technological collaborative innovation partners.

Indicators Weight | ${\mathit{g}}_{1}$ | ${\mathit{g}}_{2}$ | ${\mathit{g}}_{3}$ | ${\mathit{g}}_{4}$ | ${\mathit{g}}_{5}$ | ${\mathit{g}}_{6}$ | ${\mathit{g}}_{7}$ |
---|---|---|---|---|---|---|---|

${\tilde{\omega}}^{1}$ | 0.126 | 0.129 | 0.133 | 0.149 | 0.158 | 0.148 | 0.157 |

${\tilde{\omega}}^{2}$ | 0.107 | 0.144 | 0.161 | 0.144 | 0.160 | 0.145 | 0.139 |

${\tilde{\omega}}^{3}$ | 0.127 | 0.124 | 0.140 | 0.152 | 0.148 | 0.134 | 0.175 |

${\tilde{\omega}}^{4}$ | 0.132 | 0.115 | 0.113 | 0.166 | 0.112 | 0.135 | 0.226 |

${\tilde{\omega}}^{5}$ | 0.146 | 0.111 | 0.136 | 0.234 | 0.124 | 0.127 | 0.122 |

Decision Maker’s Risk Attitude | $\mathit{\theta}$ | Degree of Comprehensive Closeness | Ranking of Candidate Partners |
---|---|---|---|

risk-seeking attitude | 0.8 | $\left(0.4550.3950.4440.4580.558\right)$ | ${h}_{5}\succ {h}_{4}\succ {h}_{1}\succ {h}_{3}\succ {h}_{2}$ |

risk-neutral attitude | 0.5 | $\left(0.5300.4290.5110.5280.588\right)$ | ${h}_{5}\succ {h}_{1}\succ {h}_{4}\succ {h}_{3}\succ {h}_{2}$ |

risk-averse attitude | 0.2 | $\left(0.5160.4020.5020.5080.538\right)$ | ${h}_{5}\succ {h}_{1}\succ {h}_{4}\succ {h}_{3}\succ {h}_{2}$ |

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**MDPI and ACS Style**

Li, B.; Zhang, J.
A Cooperative Partner Selection Study of Military-Civilian Scientific and Technological Collaborative Innovation Based on Interval-Valued Intuitionistic Fuzzy Set. *Symmetry* **2021**, *13*, 553.
https://doi.org/10.3390/sym13040553

**AMA Style**

Li B, Zhang J.
A Cooperative Partner Selection Study of Military-Civilian Scientific and Technological Collaborative Innovation Based on Interval-Valued Intuitionistic Fuzzy Set. *Symmetry*. 2021; 13(4):553.
https://doi.org/10.3390/sym13040553

**Chicago/Turabian Style**

Li, Bing, and Jihai Zhang.
2021. "A Cooperative Partner Selection Study of Military-Civilian Scientific and Technological Collaborative Innovation Based on Interval-Valued Intuitionistic Fuzzy Set" *Symmetry* 13, no. 4: 553.
https://doi.org/10.3390/sym13040553