# Selecting Products Considering the Regret Behavior of Consumer: A Decision Support Model Based on Online Ratings

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

#### 2.1. Stochastic Variables

**Definition**

**1.**

**Definition**

**2.**

**Definition**

**3.**

**Definition**

**4.**

#### 2.2. Regret Theory

**Property**

**1.**

**Property**

**2.**

**Property**

**3.**

## 3. Problem Formulation and Resolution Procedure

#### 3.1. Formulation of the Problem

#### 3.2. Framework and Processing for the Problem

## 4. The Proposed Stochastic Decision Model Considering Consumer’s Regret Behavior

#### 4.1. Determining the Stochastic Evaluation Information

#### 4.2. Calculation of the Gain and Loss Degrees

**Property**

**4.**

**Property**

**5.**

**Proof.**

**Property**

**6.**

**Proof.**

**Property**

**7.**

**Proof.**

**Example**

**1.**

#### 4.3. Determining the Stochastic Evaluation Information

**Property**

**8.**

**Property**

**9.**

**Property**

**10.**

#### 4.4. Determination of Evaluation Attributes’ Weights

**Property**

**11.**

**Proof.**

**Property**

**12.**

**Proof.**

#### 4.5. Ranking Alternatives

- Step 1.
- Crawl the online ratings and construct evaluation in format of stochastic variable ${P}_{ij}$.
- Step 2.
- Construct gain matrix ${G}_{j}=[{g}_{ik}^{j}{]}_{m\times m}$ and loss matrix ${L}_{j}=[{l}_{ik}^{j}{]}_{m\times m}$ on attribute ${\mathrm{O}}_{j}$ according to Equations (5) and (6).
- Step 3.
- Obtain perceived utility matrix ${\mathsf{\Phi}}_{j}={[{\phi}_{ik}^{j}]}_{m\times m}$ on attribute ${\mathrm{O}}_{j}$ according to Equations (10)–(12).
- Step 4.
- Determine the prior weight vector ${\mathsf{\Omega}}_{i}={({\omega}_{1}^{i},{\omega}_{2}^{i},\cdots ,{\omega}_{n}^{i})}^{T}$ associated with ${\mathsf{\Theta}}_{i}$ according to Equations (13)–(16).
- Step 5.
- Calculate overall perceived utility value ${\mathrm{Z}}_{i}$ of alternative ${\mathsf{\Theta}}_{i}$ according to Equation (17).
- Step 6.
- Determine the alternatives ranking result.

## 5. A Case Study

- ${\mathsf{\Theta}}_{1}$: Apple iPad mini 2
- ${\mathsf{\Theta}}_{2}$: GALAXY Tab S T800
- ${\mathsf{\Theta}}_{3}$: MI Pad
- ${\mathsf{\Theta}}_{4}$: ASUS ZenPad 3S 10
- ${\mathsf{\Theta}}_{5}$: Apple iPad Air 2

#### 5.1. Methodology and Results

#### 5.2. Analysis on the Effect of the Parameter of Regret Aversion

#### 5.3. Comparison Analysis

**Example.**

## 6. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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${\mathit{B}}_{\mathit{i}}$ | 2 | 4 | 6 | 8 | 10 |
---|---|---|---|---|---|

${p}_{ij}^{q}$ | 0.3 | 0.2 | 0.25 | 0.35 | 0.2 |

${p}_{kj}^{h}$ | 0.3 | 0.2 | 0 | 0.55 | 0.4 |

Alternatives | Evaluations in Format of Stochastic Variables | ||||
---|---|---|---|---|---|

2 | 4 | 6 | 8 | 10 | |

${\mathsf{\Theta}}_{1}$ | 0.204 | 0.184 | 0.263 | 0.118 | 0.23 |

${\mathsf{\Theta}}_{2}$ | 0.259 | 0.259 | 0.241 | 0.107 | 0.098 |

${\mathsf{\Theta}}_{3}$ | 0.455 | 0.210 | 0.210 | 0.042 | 0.084 |

${\mathsf{\Theta}}_{4}$ | 0.179 | 0.277 | 0.295 | 0.116 | 0.134 |

${\mathsf{\Theta}}_{5}$ | 0.184 | 0.170 | 0.220 | 0.135 | 0.291 |

Alternatives | Evaluations in Format of Stochastic Variables | ||||
---|---|---|---|---|---|

2 | 4 | 6 | 8 | 10 | |

${\mathsf{\Theta}}_{1}$ | 0.204 | 0.184 | 0.263 | 0.118 | 0.23 |

${\mathsf{\Theta}}_{2}$ | 0.259 | 0.259 | 0.241 | 0.107 | 0.098 |

${\mathsf{\Theta}}_{3}$ | 0.455 | 0.210 | 0.210 | 0.042 | 0.084 |

${\mathsf{\Theta}}_{4}$ | 0.179 | 0.277 | 0.295 | 0.116 | 0.134 |

${\mathsf{\Theta}}_{5}$ | 0.184 | 0.170 | 0.220 | 0.135 | 0.291 |

Alternatives | Evaluations in Format of Stochastic Variables | ||||
---|---|---|---|---|---|

2 | 4 | 6 | 8 | 10 | |

${\mathsf{\Theta}}_{1}$ | 0.204 | 0.184 | 0.263 | 0.118 | 0.23 |

${\mathsf{\Theta}}_{2}$ | 0.259 | 0.259 | 0.241 | 0.107 | 0.098 |

${\mathsf{\Theta}}_{3}$ | 0.455 | 0.210 | 0.210 | 0.042 | 0.084 |

${\mathsf{\Theta}}_{4}$ | 0.179 | 0.277 | 0.295 | 0.116 | 0.134 |

${\mathsf{\Theta}}_{5}$ | 0.184 | 0.170 | 0.220 | 0.135 | 0.291 |

Alternatives | Evaluations in Format of Stochastic Variables | ||||
---|---|---|---|---|---|

2 | 4 | 6 | 8 | 10 | |

${\mathsf{\Theta}}_{1}$ | 0.204 | 0.184 | 0.263 | 0.118 | 0.23 |

${\mathsf{\Theta}}_{2}$ | 0.259 | 0.259 | 0.241 | 0.107 | 0.098 |

${\mathsf{\Theta}}_{3}$ | 0.455 | 0.210 | 0.210 | 0.042 | 0.084 |

${\mathsf{\Theta}}_{4}$ | 0.179 | 0.277 | 0.295 | 0.116 | 0.134 |

${\mathsf{\Theta}}_{5}$ | 0.184 | 0.170 | 0.220 | 0.135 | 0.291 |

Alternatives | Evaluations in Format of Stochastic Variables | ||||
---|---|---|---|---|---|

2 | 4 | 6 | 8 | 10 | |

${\mathsf{\Theta}}_{1}$ | 0.204 | 0.184 | 0.263 | 0.118 | 0.23 |

${\mathsf{\Theta}}_{2}$ | 0.259 | 0.259 | 0.241 | 0.107 | 0.098 |

${\mathsf{\Theta}}_{3}$ | 0.455 | 0.210 | 0.210 | 0.042 | 0.084 |

${\mathsf{\Theta}}_{4}$ | 0.179 | 0.277 | 0.295 | 0.116 | 0.134 |

${\mathsf{\Theta}}_{5}$ | 0.184 | 0.170 | 0.220 | 0.135 | 0.291 |

Tablet Computer | $\mathit{\delta}=0.3$ | $\mathit{\delta}=0.5$ | $\mathit{\delta}=0.7$ | $\mathit{\delta}=0.9$ | ||||
---|---|---|---|---|---|---|---|---|

Perceived Utility Values | Ranking | Perceived Utility Values | Ranking | Perceived Utility Values | Ranking | Perceived Utility Values | Ranking | |

${\mathsf{\Theta}}_{1}$ | 0.031 | 3 | −0.554 | 3 | −1.577 | 2 | −2.975 | 2 |

${\mathsf{\Theta}}_{2}$ | 0.114 | 2 | −0.522 | 2 | −1.742 | 3 | −3.511 | 3 |

${\mathsf{\Theta}}_{3}$ | −7.918 | 5 | −21.250 | 5 | −48.828 | 5 | −106.007 | 5 |

${\mathsf{\Theta}}_{4}$ | 0.974 | 1 | 1.142 | 1 | 1.078 | 1 | 0.836 | 1 |

${\mathsf{\Theta}}_{5}$ | −0.114 | 4 | −1.417 | 4 | −2.778 | 4 | −4.286 | 4 |

Alternative SUVs | Rating Scales | Attributes | |||||||
---|---|---|---|---|---|---|---|---|---|

${\mathbf{O}}_{1}$ | ${\mathbf{O}}_{2}$ | ${\mathbf{O}}_{3}$ | ${\mathbf{O}}_{4}$ | ${\mathbf{O}}_{5}$ | ${\mathbf{O}}_{6}$ | ${\mathbf{O}}_{7}$ | ${\mathbf{O}}_{8}$ | ||

${\mathsf{\Theta}}_{1}$ | 1 | 6 | 1 | 1 | 6 | 2 | 1 | 6 | 4 |

2 | 21 | 14 | 3 | 53 | 25 | 1 | 58 | 12 | |

3 | 256 | 163 | 48 | 282 | 305 | 46 | 392 | 132 | |

4 | 790 | 652 | 382 | 572 | 632 | 208 | 655 | 573 | |

5 | 282 | 525 | 921 | 442 | 391 | 1099 | 244 | 634 | |

${\mathsf{\Theta}}_{2}$ | 1 | 5 | 6 | 6 | 7 | 6 | 6 | 12 | 9 |

2 | 5 | 13 | 2 | 3 | 13 | 2 | 30 | 3 | |

3 | 66 | 157 | 5 | 20 | 283 | 68 | 464 | 53 | |

4 | 981 | 908 | 106 | 198 | 979 | 378 | 975 | 480 | |

5 | 728 | 701 | 1666 | 1557 | 504 | 1331 | 304 | 1240 | |

${\mathsf{\Theta}}_{3}$ | 1 | 0 | 0 | 1 | 3 | 2 | 0 | 10 | 2 |

2 | 2 | 5 | 0 | 15 | 22 | 3 | 82 | 23 | |

3 | 46 | 75 | 12 | 139 | 358 | 122 | 478 | 210 | |

4 | 385 | 651 | 286 | 538 | 714 | 661 | 724 | 695 | |

5 | 1061 | 763 | 1195 | 799 | 389 | 708 | 200 | 564 | |

${\mathsf{\Theta}}_{4}$ | 1 | 0 | 5 | 5 | 1 | 0 | 1 | 17 | 4 |

2 | 0 | 7 | 20 | 27 | 4 | 0 | 98 | 7 | |

3 | 2 | 199 | 228 | 173 | 71 | 50 | 569 | 84 | |

4 | 29 | 770 | 689 | 564 | 493 | 424 | 530 | 521 | |

5 | 1394 | 444 | 483 | 660 | 857 | 950 | 211 | 809 | |

${\mathsf{\Theta}}_{5}$ | 1 | 0 | 4 | 3 | 13 | 1 | 0 | 0 | 0 |

2 | 1 | 19 | 4 | 88 | 8 | 5 | 13 | 4 | |

3 | 6 | 378 | 83 | 456 | 143 | 91 | 226 | 24 | |

4 | 121 | 720 | 560 | 582 | 659 | 581 | 734 | 233 | |

5 | 1135 | 142 | 613 | 124 | 452 | 586 | 290 | 1002 |

Methods | Ranking of Alternatives | |
---|---|---|

The method presented by Kang and Park (2014) | ${\mathsf{\Theta}}_{2}\succ {\mathsf{\Theta}}_{4}\succ {\mathsf{\Theta}}_{1}\succ {\mathsf{\Theta}}_{3}\succ {\mathsf{\Theta}}_{5}$ | |

The method presented by Fan et al. (2017) | ${\mathsf{\Theta}}_{2}\succ {\mathsf{\Theta}}_{3}\succ {\mathsf{\Theta}}_{4}\succ {\mathsf{\Theta}}_{1}\succ {\mathsf{\Theta}}_{5}$ | |

The proposed method in this study | Considering entire rationality | ${\mathsf{\Theta}}_{2}\succ {\mathsf{\Theta}}_{3}\succ {\mathsf{\Theta}}_{4}\succ {\mathsf{\Theta}}_{1}\succ {\mathsf{\Theta}}_{5}$ |

Considering regret behavior ($\delta =0.1,0.3,0.5$) | ${\mathsf{\Theta}}_{2}\succ {\mathsf{\Theta}}_{3}\succ {\mathsf{\Theta}}_{4}\succ {\mathsf{\Theta}}_{1}\succ {\mathsf{\Theta}}_{5}$ | |

Considering regret behavior ($\delta =0.7$) | ||

Considering regret behavior ($\delta =0.9$) | ${\mathsf{\Theta}}_{3}\succ {\mathsf{\Theta}}_{2}\succ {\mathsf{\Theta}}_{4}\succ {\mathsf{\Theta}}_{1}\succ {\mathsf{\Theta}}_{5}$ |

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## Share and Cite

**MDPI and ACS Style**

Liang, X.; Liu, P.; Liu, Z.
Selecting Products Considering the Regret Behavior of Consumer: A Decision Support Model Based on Online Ratings. *Symmetry* **2018**, *10*, 178.
https://doi.org/10.3390/sym10050178

**AMA Style**

Liang X, Liu P, Liu Z.
Selecting Products Considering the Regret Behavior of Consumer: A Decision Support Model Based on Online Ratings. *Symmetry*. 2018; 10(5):178.
https://doi.org/10.3390/sym10050178

**Chicago/Turabian Style**

Liang, Xia, Peide Liu, and Zhengmin Liu.
2018. "Selecting Products Considering the Regret Behavior of Consumer: A Decision Support Model Based on Online Ratings" *Symmetry* 10, no. 5: 178.
https://doi.org/10.3390/sym10050178