# Multi-Attribute Decision Making Method Based on Aggregated Neutrosophic Set

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

#### 2.1. Neutrosophic Sets

**Definition**

**1.**

**Definition**

**2.**

#### 2.2. SVNS

**Definition**

**3.**

**Definition**

**4.**

**Definition**

**5.**

**Definition**

**6.**

#### 2.3. Score Function

**Definition**

**7.**

#### 2.4. Distance between Two Neutrosophic Sets

## 3. An Improved Multi-Criteria Decision Making Method

**Example**

**1.**

## 4. Illustrative Example

**Example**

**2.**

**Example**

**3.**

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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${\mathit{C}}_{1}$ | ${\mathit{C}}_{2}$ | ${\mathit{C}}_{3}$ | ${\mathit{C}}_{4}$ | |
---|---|---|---|---|

${A}_{1}$ | $(0.6,0.3,0.5)$ | $(0.5,0.7,0.6)$ | $(0.7,0.6,0.5)$ | $(0.5,0.5,0.6)$ |

${A}_{2}$ | $(0.6,0.4,0.5)$ | $(0.4,0.5,0.6)$ | $(0.3,0.5,0.6)$ | $(0.4,0.5,0.6)$ |

${A}_{3}$ | $(0.5,0.6,0.7)$ | $(0.7,0.2,0.8)$ | $(0.7,0.6,0.3)$ | $(0.4,0.4,0.5)$ |

${A}_{4}$ | $(0.4,0.3,0.2)$ | $(0.5,0.4,0.3)$ | $(0.6,0.7,0.2)$ | $(0.4,0.3,0.2)$ |

${\mathit{C}}_{1}$ | ${\mathit{C}}_{2}$ | ${\mathit{C}}_{3}$ | ${\mathit{C}}_{4}$ | |
---|---|---|---|---|

${A}_{1}$ | $-\frac{1}{15}$ | $-\frac{4}{15}$ | $-\frac{2}{15}$ | $-\frac{1}{5}$ |

${A}_{2}$ | $-\frac{1}{10}$ | $-\frac{7}{30}$ | $-\frac{4}{15}$ | $-\frac{7}{30}$ |

${A}_{3}$ | $-\frac{4}{15}$ | $-\frac{1}{10}$ | $-\frac{1}{15}$ | $-\frac{1}{6}$ |

${A}_{4}$ | $-\frac{1}{30}$ | $-\frac{1}{15}$ | $-\frac{1}{10}$ | $-\frac{1}{30}$ |

${C}_{1}$ | ${C}_{2}$ | ${C}_{3}$ | |

${A}_{1}$ | $(0.864,0.136,0.081)$ | $(0.853,0.147,0.092)$ | $(0.800,0.200,0.150)$ |

${A}_{2}$ | $(0.667,0.333,0.277)$ | $(0.727,0.273,0.219)$ | $(0.667,0.333,0.277)$ |

${A}_{3}$ | $(0.880,0.120,0.067)$ | $(0.887,0.113,0.064)$ | $(0.834,0.166,0.112)$ |

${A}_{4}$ | $(0.667,0.333,0.277)$ | $(0.735,0.265,0.195)$ | $(0.768,0.232,0.180)$ |

${C}_{4}$ | ${C}_{5}$ | ${C}_{6}$ | |

${A}_{1}$ | $(0.704,0.296,0.241)$ | $(0.823,0.177,0.123)$ | $(0.864,0.136,0.081)$ |

${A}_{2}$ | $(0.744,0.256,0.204)$ | $(0.652,0.348,0.293)$ | $(0.608,0.392,0.336)$ |

${A}_{3}$ | $(0.779,0.256,0.204)$ | $(0.811,0.189,0.109)$ | $(0.850,0.150,0.092)$ |

${A}_{4}$ | $(0.727,0.273,0.221)$ | $(0.791,0.209,0.148)$ | $(0.808,0.192,0.127)$ |

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

${A}_{1}$ | 0.216 | 0.205 | 0.150 | 0.056 | 0.174 | 0.216 |

${A}_{2}$ | 0.019 | 0.078 | 0.019 | 0.095 | 0.004 | -0.040 |

${A}_{3}$ | 0.231 | 0.237 | 0.185 | 0.106 | 0.171 | 0.203 |

${A}_{4}$ | 0.019 | 0.092 | 0.119 | 0.078 | 0.145 | 0.163 |

Methods | Indexes for Decision Making | Rank of Indexes | The Chosen Alternative |
---|---|---|---|

Elhassouny’s [57] | ${T}_{1}=0.8190,{T}_{2}=0,1158,{T}_{3}=0.8605,{T}_{4}=0.4801$ | ${T}_{3}>{T}_{1}>{T}_{4}>{T}_{2}$ | ${A}_{3}$ |

correlation coefficient [44] | ${B}_{1}=0.959,{B}_{2}=0.846,{B}_{3}=0.970,{B}_{4}=0.917$ | ${B}_{3}>{B}_{1}>{B}_{4}>{B}_{2}$ | ${A}_{3}$ |

cross-entropy [45] | ${E}_{1}=0.530,{E}_{2}=0.966,{E}_{3}=0.466,{E}_{4}=0.763$ | ${E}_{3}<{E}_{1}<{E}_{4}<{E}_{2}$ | ${A}_{3}$ |

Presented method | ${T}_{1}=0.870,{T}_{2}=0.038,{T}_{3}=0.976,{T}_{4}=0.473$ | ${T}_{3}>{T}_{1}>{T}_{4}>{T}_{2}$ | ${A}_{3}$ |

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**MDPI and ACS Style**

Jiang, W.; Zhang, Z.; Deng, X.
Multi-Attribute Decision Making Method Based on Aggregated Neutrosophic Set. *Symmetry* **2019**, *11*, 267.
https://doi.org/10.3390/sym11020267

**AMA Style**

Jiang W, Zhang Z, Deng X.
Multi-Attribute Decision Making Method Based on Aggregated Neutrosophic Set. *Symmetry*. 2019; 11(2):267.
https://doi.org/10.3390/sym11020267

**Chicago/Turabian Style**

Jiang, Wen, Zihan Zhang, and Xinyang Deng.
2019. "Multi-Attribute Decision Making Method Based on Aggregated Neutrosophic Set" *Symmetry* 11, no. 2: 267.
https://doi.org/10.3390/sym11020267